Antoine De Rengervé
email: antoine.rolland-de-rengerve@ensea.fr

Julien Hirel
email: julien.hirel@ensea.fr

Mathias Quoy
email: quoy@ensea.fr

Pierre Andry
email: andry@ensea.fr

Philippe Gaussier
email: gaussier@ensea.fr

A simple neural network controller merging different behaviors for collector robots

Introduction

Robots are expected to become reliable partners for working in human environments. One of the tasks that they could have to perform is collecting objects and gathering/sorting them for any purposes. In such a task the robot would have to explore its environment to discover objects of interest, navigate toward them, grasp them and navigate again to a storage area to drop the object. In this paper we show how the basic principles behind these complex behaviors can be obtained from fairly simple neural network controllers.

In accordance to behavior based approaches [START_REF] Brooks | A robust layered control system for a mobile robot[END_REF], the developped architecture gathers several simple behaviors that affect the dynamic of the robot [START_REF] Schöner | Dynamics of behavior: Theory and applications for autonomous robot architectures[END_REF] to let a meaningful behavior emerge. We will first explain the different principles that enable a robot to display behaviors of exploration, tracking of a specific object and trying to catch that object. Then we present an implementation of the neural network on a mobile robot with a mounted arm. A preferred object recognized by its color is visually detected. The position of the object is projected in a head centered space. In fact, the head and the body of the robot are not dissociable. The head centered space is also a body centered space. A comparison between the current orientation of the gaze and the object position provides the corrective control on the orientation of the camera. The position of the object in the head/body centered space also provides a command for the control of the orientation of the robot. Three different commands are merged on the same body centered frame to control the orientation of the robot:

A neural network generating force signals for motor control

1. A random orientation which enables the robot to perform an exploration of the environment.

2. The attempt to align the orientation of the robot with the orientation of the object in the body-centered space. If the direction of the gaze is associated with the direction of the head, then this control corresponds to moving the body in order to decrease the torsion on the neck and align the body with the head.

3. A direct control by joystick which enables a human to influence directly the trajectory of the robot. It corresponds to the possibility to drive the robot in one direction or another like by pushing or dragging it.

Each movement strategy is weighted differently to introduce priorities in the behaviors. If no particular stimulus is perceived, the default behavior is the random exploration of the environment with a constant speed. If the preferred object is detected, navigation toward it will take precedence over the random exploration behavior. The speed of the robot is proportionnal to the distance to the object (i.e. perceived size of the object calculated as a number of pixels of the preferred color). If the object is close enough, the robot stops. Finally, physical command from an external person through the use of the joystick has the highest priority. The selected direction is always filtered by the activation of the mobile base ultrasound sensors in order to avoid obstacles. The movements of the arm are controlled by the motor controller described in [START_REF] De Rengervé | Emergent Imitative Behavior on a Robotic Arm Based on Visuo-Motor Associative Memories[END_REF] (Figure 2). In a first phase, the robot learns the association of visual positions with their corresponding motor positions. The visual position of the object then activates some attractors in the motor space to generate a movement allowing the gripper to reach the object.

Y

Robotic implementation

The neural network architecture is implemented on a Robulab mobile platform from Robosoft. A Katana electrical 6DOF arm is mounted on the robot. Visual information is provided by a monocular camera mounted on a pan-tilt servo motor setup. In this experiment, the visual information simply corresponds to a pink color detection. Visual processing enables the robot to recognize a favorite object: a pink ball. Ultrasound sensors located around the mobile base of the robot provide range measures about obstacles. In a first phase the robot learns associations between the motor position of the arm and the visual position of its end effector (the robot is holding the pink ball to localize its gripper).

The two main behaviors are the exploration of the environment and the convergence toward the favorite object (Figure 3). In both behaviors, the robot is able to avoid obstacles for its own security. The different mechanisms that are running in parallel provide the robot with an interesting global behavior. In Figure 3, the robot that orientates itself toward the object is also trying to align the end effector of the arm with the visual position of the ball in order to catch it. Due to optical properties, a close object is perceived at a lower position in the visual field than a far object. The arm of the robot is naturally going down as the robot gets closer to the object. It is interesting to note that the system can be used by the robot to reach static objects but can also be used by the experimenter to guide the robot, since any human holding the object will be followed by the robot.

Discussion -Perspectives

The presented architecture proposes simple principles that allow the emergence of an object-seeking behavior. The robot is able to look for a specific object in the environment in order to reach and catch it. This behavior is based on simple mechanisms that can be subsumed by higher level strategies or behaviors. This kind of robotic setup could be used in future studies of multi agent cooperation on real robots [START_REF] Gaussier | Avoiding the world model trap: An acting robot does not need to be so smart![END_REF]. Another perspective is the learning, through interaction and with reinforcement learning, of sequences of actions for both the mobile platform and the arm. After having caught the object, the robot could perform a homing navigation to a specific location to store the object. Such a sequence would require to merge spatial navigation and arm control with a planning architecture. We are working on using a multi-modal state sequence learning architecture inspired from the hippocampus [START_REF] Hirel | Model of the hippocampal learning of spatio-temporal sequences[END_REF], coupled with a cognitive map planning system, to learn and plan sequences of actions for both mobile platform and arm.

1 Figure 1 :

 11 Figure 1: Architecture determining the orientation of the robot.

Figure 2 :

 2 Figure 2: Model of visuo-motor association learner.

Figure 3 :

 3 Figure 3: Robot navigating to and reaching for a pink ball on a box.

Figure 4 :

 4 Figure 4: Obstacle avoidance while reaching for a pink ball held by a human interacting with the robot.


Antoine De Rengervé
email: antoine.rolland-de-rengerve@ensea.fr

Pierre Andry
email: andry@ensea.fr

Philippe Gaussier
email: gaussier@ensea.fr

A Neural Network Generating Force Command for Motor Control of a Robotic Arm

Introduction

Brain can be considered as a system that generates motor commands for a given perception. Understanding how movement is generated and controlled still represents unanswered questions [START_REF] Daniel | Perspectives and problems in motor learning[END_REF]. In [START_REF] De Rengervé | Emergent Imitative Behavior on a Robotic Arm Based on Visuo-Motor Associative Memories[END_REF], an arm controller that learns visuo-motor associations can let emerge immediate and deferred imitation. Visual input activates some attractors in the motor space that are used to generate a speed command to control the arm. In this architecture, visual information gives the motor position to be reached. In [START_REF] Sylvain Calinon | Handling of multiple constraints and motion alternatives in a robot programming by demonstration framework[END_REF], a Gaussian Mixture based arm controller can enable a robot to reproduce a sequence of gestures that was demonstrated during a first phase. In [START_REF] De Rengervé | A study of two complementary encoding strategies based on learning by demonstration for autonomous navigation task[END_REF], a similar Gaussian Mixture model is compared with a neural network based sequence learner that uses fast learned state/action couples [START_REF] Giovannangeli | Robust Mapless Outdoor Vision-based Navigation[END_REF]. The comparison is done on a simple navigation task for which the neural network is designed. The Gaussian Mixture model was adapted for navigation. A left over issue is whether and how such a neural network architecture could be adapted for arm control in the motor space. These considerations about arm controlling lead to looking for a model that could work with both visuo-motor associations and motor state/action paradigms. Several issues are raised as how the attractors can be encoded, what the parameters of the motor controller are and how they should be controlled by the system. Some tests on how the attractors can be constructed have led to a model that defines independent attractors for each articulation of the robot. Biological data give us hints about answers to some of the raised questions. The basic biological motor action is to contract muscles and thus to perform force control of the position of the limbs. As we aim at studying how high level and low level aspects of motor control can be interconnected, we developed a neural network architecture that generates force commands. In this architecture, the higher level structures converge on an internal representation of the motor position that is provided to a homeostatic low level force controller. Some part of the architecture is tested on a real robot in a simple experiment as the reproduction of a temporal sequence of gestures demonstrated during passive manipulation. The influence of some of the parameters that determines the robot behavior reinforces the idea that higher level structures should have specific accesses to the low level control. The force command generator model follows some of the hypothesis developed in the VITE-FLETE model [START_REF] Bullock | Vite and Flete: Neural Modules for Trajectory Formation and Postural Control[END_REF] as they are biologically relevant and enables to realize a minimal motor controller. However, the current model is biologically less accurate as it does not focus exclusively on the modelization of the biological data but it also aims at being easily adaptable for motor control in real robots. The gobal architecture of the system (Figure 1) has been designed as a primary loop that provides an homeostatic control of an internal representation of the proprioception. Perturbation on the internal representation can generate the movements of the arm. As shown in Figure 1, the different channels + and -correspond to the channels of agonist and antagonist muscle proprioception. The force activation signal that is generated for each channel depends on the desired internal proprioception P +/d , the current proprioception p +/-and a non-specific energy gain G. This energy gain is part of the Pattern-Energy Factorization used in VITE model [START_REF] Bullock | Vite and Flete: Neural Modules for Trajectory Formation and Postural Control[END_REF]. It relies on biological data that displays the non-specific influence of the Globus Pallidus from the Basal Ganglia on the strength of the movements. We introduce a fluid friction force as a mechanical constraint from the muscle. The forces are thus the voluntary agonist/antagonist forces

A neural network architecture generating force signals for motor control

F + = G • [P + d -p + ] + and F -= -G • [P - d -p -]
+ and the friction force f v = -α • v with [x] + = 0 when x < 0, x when 0 ≤ x ≤ 1 and 1 when x > 1. The relation p = p + = 1p -links p + and p -. According to the equation of classical dynamic m • ˙ṗ = F , the continuous dynamical equation of the system can be simplified in [START_REF] Sylvain Calinon | Handling of multiple constraints and motion alternatives in a robot programming by demonstration framework[END_REF]. This neural network force generator is equivalent to a second order "mass damping" dynamical system for the control of one articulation. This kind of dynamic motor control has been used with success in robotics in the reproduction of demonstrated tasks [START_REF] Auke | Learning attractor landscapes for learning motor primitives[END_REF], [START_REF] Sylvain Calinon | Handling of multiple constraints and motion alternatives in a robot programming by demonstration framework[END_REF].

F = G • [P d -p] + -G • [p -P d ] + -α • ṗ (1) p = G m • (P d -p) - α m • ṗ (2)
3 Implementation on a robot and reproduction of a demonstrated gesture This architecture has been implemented in a robotic setup (Figure 2(a)) that is made of a Katana robotic arm from Neuronics AG with 6 degrees of freedom and a monocular camera mounted on a pan-tilt servo motor setup. The industrial Katana arm is designed for position control possibly using spline trajectories. An acceleration control is not possible on this arm. A speed control can be realized by modulating the maximum speed of variation of the joint angle while moving to extremum positions. There is no direct access to the real joint speed of the arm. The neural network architecture has been modified to provide speed commands that are generated from the integration of the force signal and an estimation of the speed. The estimation is based on the time derivative of the position of the joints. In the framework of the french project INTERACT, a hydraulic robot is going to be built so that the models can be tested without these limitations.

The capabilities of the motor controller of the robot were tested in the reproduction of a passive demonstration. In a first phase, the robot is set in passive mode ie. a human can manipulate the arm. The movement of two loops is shown to the robot. The recorded data are then provided to the motor control as the desired position P d . Figure 3 plots together the demonstrated trajectory and the reproducted trajectory in the 3D Cartesian space. According to the parameters of the system, the reproduction can be close to the original trajectory. If the energy gain G increases, the arm tries to follows each variation of the demonstrated trajectory. The joint position makes some overshoots and oscillates around the desired position. If the gain decreases, the trajectory becomes smoother, the system does not try to follow each variation of the demonstrated trajectory (Figure 2). The trajectory is also smaller than the demonstrated trajectory even if it respects the topology of the demonstration: two slightly shifted loops. There is no perfect value for the gain G as having a small and smooth trajectory can be as interesting as having an accurate reproduction of the demonstration. The evaluation of the movements can only depend on other factors like a reinforcement signal.

Perspectives

This work raises the question of the control of the parameters of the low level controller. Self-evaluation of the action or social interaction may provide a feedback to determine the adequate values of the parameters, but it is also possible that they should be learned as well with the movement trajectory.

In the presented experiment, the robot is reproducing a trajectory that was entirely recorded. This is one possible way of using this architecture. This system will also be tested with the visuo-motor associative architecture to check the property of emergence of imitation is still present. The state/action paradigm will also be implemented with this system to study the analogy between arm movement planning and navigation planning. Future work will continue to take inspiration from biological data to study the structures that can be used and also how they can be merged all together to increase the ability of real robots.

Figure 1 :

 1 Figure 1: Left: Global architecture. The internal representation of proprioception can be built from various structures: visuo-motor conditioning, temporal sequences, spatial sequences etc. Right: Force control part of the architecture.

Figure 2 :

 2 Figure 2: a: The robot is composed of a Katana electrical arm from Neuronics AG and a monocular camera mounted on a pan-tilt servo motor setup. In this experiment, only the arm was used. b: The value of the desired position from the recorded trajectory (black) and the position in reproduction (grey) are compared for one joint of the arm. With a high energy gain, there are overshoots and oscillation. Here, G = 20 and α = 1. c: A smaller gain enables to have a smoother trajectory. It also induces a phase shifting and a decrease of amplitude in the variation of position. Here, G = 3 and α = 10.

Figure 3 :

 3 Figure 3: Trajectory of the end effector of the arm in the 3D Cartesian space. The black line is the demonstrated trajectory that corresponds to two successive loops. The grey trajectory is the reproduction done by the robot. The reproduction has been done with different values for the energy gain G and the fluid friction coefficient α. Left: G = 20,α = 10. Center: G = 20, α = 1. Right: G = 3, α = 10.

Acknowledgement

This work was supported by the INTERACT french project referenced ANR-09-CORD-014 and the Sesame project TINO funded by the French Region Ile de France.


Antoine De Rengervé
email: antoine.rolland-de-rengerve@ensea.fr

Julien Hirel
email: hirel@ensea.fr

Pierre Andry
email: andry@ensea.fr

Mathias Quoy
email: quoy@ensea.fr

Philippe Gaussier
email: gaussier@ensea.fr

Continuous On-Line Learning and Planning in a Pick-and-Place Task Demonstrated Through Body Manipulation

When a robot is brought into a new environment, it has a very limited knowledge of what surrounds it and what it can do. One way to build up that knowledge is through exploration but it is a slow process. Programming by demonstration is an efficient way to learn new things from interaction. A robot can imitate gestures it was shown through passive manipulation. Depending on the representation of the task, the robot may also be able to plan its actions and even adapt its representation when further interactions change its knowledge about the task to be done. In this paper we present a bio-inspired neural network used in a robot to learn arm gestures demonstrated through passive manipulation. It also allows the robot to plan arm movements according to activated goals. The model is applied to learning a pick-and-place task. The robot learns how to pick up objects at a specific location and drop them in two different boxes depending on their color. As our system is continuously learning, the behavior of the robot can always be adapted by the human interacting with it. This ability is demonstrated by teaching the robot to switch the goals for both types of objects.

I. INTRODUCTION

Autonomous robots that start with no knowledge about the world and have to learn everything should not only depend on the unguided exploration of their possibilities for their development. They also should be able to learn from human caregivers or other robots by imitating them [START_REF] Bakker | Robot See, Robot Do : An Overview of Robot Imitation[END_REF] or interacting with them. A simple visuo-motor associative learning and a motor controller can provide the basis for letting low level immediate imitation emerge as a result of simple mechanisms [START_REF] Andry | Learning Invariant Sensorimotor Behaviors: A Developmental Approach to Imitation Mechanisms[END_REF]. In a first phase, the system learns the body configuration as visuo-motor associations. Due to an ambiguity of perception caused by limited visual capabilities, the robot can confuse the hand of the human teacher with its own. The controller, following the homeostatic principle, tries to maintain an equilibrium between the visual and motor information according to the body learning. To do so, it moves the robot hand at the motor position that corresponds to the believed visual position of the robot hand. The robot consequently reproduces the observed gestures of the human. With almost the same mechanisms and the same controller, the robot can also learn by observation how to reproduce a demonstrated task encoded as a sequence of visual positions [START_REF] De Rengerve | Emergent imitative behavior on a robotic arm based on visuo-motor associative memories[END_REF]. Visual demonstration cannot always be enough to teach what is expected from the learner. During their first years, infants are also taught by "embodying" them i.e. by using passive manipulation. This process enables caregivers to guide the infant's perception and attention so that the infant quickly learns what is taught [START_REF] Zukowgoldring | Affordances, effectivities, and assisted imitation: Caregivers and the directing of attention[END_REF].

Programming by demonstration [START_REF] Billard | Survey: Robot Programming by Demonstration[END_REF] provides robots with the ability to learn how to perform a task as a result of a demonstration provided by a human teacher. This demonstration can be done through passive manipulation. Dynamic Motion Primitives (DMP) [START_REF] Ijspeert | Learning attractor landscapes for learning motor primitives[END_REF] is a framework for learning to perform demonstrated tasks. With little demonstration data from a human demonstrator, the system can determine through regression the adequate parameters for mixing the DMP to generate the correct movement. In [START_REF] Calinon | On Learning, Representing and Generalizing a Task in a Humanoid Robot[END_REF], the learning system uses a statistical model based on Gaussian Mixture that is adapted to fit the data from training demonstrations using passive manipulation. Gaussian Mixture Regression can then provide a probabilistic estimation of the current state of the robot and of the adequate motor command. These systems have proved to be efficient for performing different tasks. They also enable generalization to different initial conditions and different goal positions.

One of the main issues is how to encode and represent the knowledge acquired through demonstration. The chosen model should enable the robot to continuously learn and integrate new knowledge into the representation of the task. Besides, this model should provide the basis for future action planning. Models with both learning by demonstration and planning have been developed in different works [8] [9] as programming by demonstration can speed up the learning of the knowledge needed for planning. In [START_REF] Schneider | Combining Gaussian Processes and Conventional Path Planning in a Learning from Demonstration Framework[END_REF], path planning and Gaussian processes have been combined to use planning capabilities and obstacle avoidance while the robot is reproducing a demonstrated grasp-and-pour task.

In sec. II, an existing bio-inspired model for planning in mobile robot navigation task is used to learn the movements of a robotic arm. The neural network is adapted to work with proprioceptive states. A visual categorization system for goals corresponding to different types of object is implemented. Associations between object goals and proprioceptive state transitions are learned and adapted thanks to reinforcement learning. This system was implemented on a real robot to carry out an experiment of pick-and-place with objects, sorting them depending on their colors (sec. III). Initially, the robot learns the actions to be done after one demonstration for each type of object. As it is continuously learning, new demonstrations are integrated in the model and can be used to adapt the behavior of the robot to match new conditions in the task i.e. a switch of the target boxes for each type of object (sec. IV).

II. ADAPTATION OF A BIO-INSPIRED COGNITIVE MAP MODEL TO ARM CONTROL

We previously developed a bio-inspired model of the hippocampus and prefrontal cortex [START_REF] Banquet | Space-time, order and hierarchy in fronto-hippocamal system: A neural basis of personality[END_REF]. In our model, spatial states would be encoded in the entorhinal cortex and the hippocampus would learn to associate successive states, thus creating transitions cells. The prefrontal cortex would use information about these transitions to create a cognitive map and use it to plan actions toward the fulfillment of specific goals. This model was later used on a real robot navigating in an indoor environment [START_REF] Cuperlier | Neurobiologically inspired mobile robot navigation and planning[END_REF]. The aim of this paper is to reuse the principles of the model, result of a long series of experiments with mobile robots, and adapt them for planning in the proprioceptive space of a robotic arm. In addition, we take full advantage of the possible interactions between human and robot to speed up the learning process and allow for easy adaptation of the conditions of a pick-and-place task. As there are no separate phases of learning and reproduction, the system can adapt at any time. The model is shown in Fig. 1.

According to our model, some brain structures could be involved in both navigation and arm control. The categorization of states would involve different areas in navigation (the entorhinal cortex with place cells) and in arm control (motor cortex for proprioceptive states). However, in both cases the hippocampus would be used to detect new events as changes in the encoded states. The prefrontal cortex would also play a role in planning strategies. The cerebellum, more involved in ballistic control of the movement and prediction of motor consequences, is not considered here.

The hippocampal part of the model focuses on generating attractors that correspond to transitions between learned proprioceptive states. When the robotic arm moves, its proprioception (joint angles, gripper IR and force sensor values) is categorized into distinct states. Each state is associated to a prototypical joint/gripper configuration. The categorization of the states is based on a recruitment of new states depending on a vigilance threshold. This algorithm takes inspiration from the Adaptive Resonance Theory [START_REF] Carpenter | Adaptive Resonance Theory[END_REF]. The states are encoded on the weights of the input links of recruited neurons. The computation of the activity (1) and learning (2) for those neurons is given by the following equations:

A i = 1 - 1 N j | w ij -e j | (1)
∆w kj = e j • H( j H(λ-| Θ i -θ i |)) ( 2
)
where N is the dimension of the input layer, Ai is the activity of the i th neuron of the output layer and w kj is the weight of the connection between an output neuron k that has not been recruited yet and the j th neuron of the input layer. H is the Heavyside function.

The activity of a neuron is similar to a measure of similarity with the encoded proprioceptive configuration. The most activated neuron is considered as the current state of the system. The recruitment of a new neuron depends on the difference between each current joint value θ i and the corresponding joint value Θ i of the best recognized configuration. If this difference is below a given vigilance threshold λ, it triggers the recruitment of a new neuron i.e. the encoding of a new state. The choice of the vigilance threshold λ determines the granularity of the states in the proprioceptive space. The possible transitions between states are learned when the arm moves from one state to the next. This is done in an associative memory that receives information about the newly entered state and the last state. The transition activity is then transmitted to the cognitive map where a graph of the different transitions is created. The cognitive map encodes information about all possible paths by linking subsequent transitions.

In the original navigation architecture [START_REF] Cuperlier | Neurobiologically inspired mobile robot navigation and planning[END_REF], the robot could find resources in its environment. To each type of resource corresponds a drive that represents the motivation of the robot to look for that kind of reward. From an animal's perspective the reward could be food and the drive hunger, for instance. Upon detection of a resource the current transition in the cognitive map is associated to the relevant drive. Here the robot possesses two different contextual goals associated to two types of objects (red or green). The focal vision of the robotic system categorizes the scene using color detection. It can differentiate between two types of objects: a red can and a green can. When a red object is presented to the visual system, the corresponding goal will be activated and stay active until another object is presented. If the new object is green, the first goal will be inhibited and the second goal will stay active. The visual system can also recognize when a large amount of white is present in the visual field. This is a way to use visual interaction to give rewards to the system and use reinforcement learning to associate goals with transitions. When experimenters present a white object, they reward the current behavior of the robot and associate it with the active contextual goal. The learning of the association between goals and transitions is given by the following equation:

dWij dt = r(t).x drive j (t).(α.(1 -Wij(t)).x trans j (t) -γ) (3)
where α is a learning rate, γ a decay rate and r(t) is the reward signal (0 or 1).

In this experiment we use a simple visual categorization system. We assume that the categorization of objects into goals and reward has already been learned. However, more natural and plausible approaches could be taken in the future. The reward signal can be linked to social cues. Zukowgoldring and Arbib [START_REF] Zukowgoldring | Affordances, effectivities, and assisted imitation: Caregivers and the directing of attention[END_REF] stress the importance of some key words like "look" or "now, you do it" combined with gestures that are used by caregivers to raise the attention of their infants. Also, a robot head that can display and recognize facial expressions could be added to the robotic setup of this experiment to make the interaction between human and robots easier. With system, the human could directly give reinforcing or punishing signals through interaction, by displaying positive or negative emotions. This kind of interaction has already successfully been used for the social referencing of objects with good performances [START_REF] Boucenna | Autonomous development of social referencing skills[END_REF]. The facial expression and direction of gaze of the teacher can also provide the necessary cues for guiding the attention of the visual system to interesting objects [START_REF] Boucenna | Development of joint attention and social referencing[END_REF] and help categorize them. The robot would then be able to learn from interaction with a human partner which objects are interesting and which different types of object should be categorized into different goals.

When a goal is active, its activity will be propagated in the map with weights w < 1. As a result, transition neurons in the cognitive map have an activity proportional to their distance (in terms of number of transitions) to the goal. Since a max operator on the input is used in the computation of the activity of each neuron, the map gives the shortest path to the strongest or closest goal. In any given state, the hippocampal system predicts all possible transitions from the current position. The activity in the cognitive map is used to bias the selection of a particular transition. The transition that has the highest potential, ie. that corresponds to the shortest path to get the reward, is selected. During the learning process, the system creates proprioceptive states and memorizes the joint/gripper configuration associated to each state. When a transition between states is performed and learned, the position associated to the second state is associated to the transition. As a result, when the competition between transition occurs and a particular transition is selected, the motor configuration of the target state is given as the target position to the motor control system.

The motor control architecture (Fig. 2) receives the action from the cognitive map. If the arm is being manipulated by the human (by holding the wrist) this action is inhibited. Otherwise the action is transmitted to a force controller which computes the motor command of the robot by comparing the current and target configurations. When the arm is not being manipulated and the cognitive map transmits no action, a memory stores the value of the last action (or proprioceptive configuration if the arm was manipulated) to maintain the arm at that position. While the motor system receives no commands, a stress level increases until it finally reaches a sufficient value to inhibit the memory. A low-priority reactive behavior will then generate an attractor to a given rest position.

III. INTERACTIVE LEARNING OF A PICK-AND-PLACE TASK

The presented model was implemented with a 6DOF Katana robotic arm. At first, the robot has no knowledge about its environment. The task to is a pick-and-place task (see Fig. 3 for the robotic setup and Fig. 4 for the different learning and reproduction phases). An object (a colored can) is present in the reaching space of the robot at a given location (i.e. the pick-up place). The robot must grasp the can and drop it into one of two boxes, also at static positions in reaching space.

A monocular camera is used as the visual system of the robot and is focused on the pick-up place. We assume that the visual attention of the robot is always directed toward that place. At the beginning, the reactive behavior maintains the arm in rest position. The human teacher demonstrates how to grasp an object through passive manipulation of the arm. The first object is a red can. During the movement, proprioceptive states are recruited to encode the trajectory according to the process described in sec. II. The succession of states leads to transitions and the cognitive map being learned. After the arm has been manipulated by the human and brought to the object, the infrared sensors on the gripper detect the presence of an object in its range, triggering a grasping reflex. Force sensors on the gripper detect when an object is hold and determine the state of the gripper as opened or closed on an object. The arm is then manipulated again and brought above one of the drop boxes, learning the trajectory between the pick-up place and the drop box as shown by the human. A button located on the gripper commands the opening of the gripper. The button is used to simulate the interacting human forcing the opening of the gripper of the robot (which cannot be done due to mechanical limitations).

Once the object has been dropped into the box, a positive reinforcement is given by simply presenting a white sheet of paper in front of the camera. So when the robot releases the can, the goal associated to the dropped can (red or green) is linked to the current transition (i.e. changing the state of the gripper from closed to open when above this box). The robot then waits until the teacher demonstrates how to move from the box to its initial position or until the stress level activates the movement to the rest position. Once the loop is connected, the robot can plan the sequence of transitions to move to the position where it previously grasped the object. The robot starts reproducing the task without the help of a human. Since one of the goals (depending on the color of the last seen object) is always active, the robot will constantly try to reach that goal and thereof to drop objects at the learned places (i.e. into on of the boxes).

From its starting position, the cognitive map gives the shortest path in terms of states in order to reach the motivated transition (dropping the object into the correct box). The first step is to go to the pick-up place. If an object is detected, it is grasped and the arm proceeds to the next phase, otherwise the robot waits for an object to be presented. Here we present the red can again and let the robot reproduce what it has just been taught. The arm reaches the position above the box where it opens its gripper and goes back to the pick-up location where a new can has been placed. The action is rewarded by the human for another two reproductions, reinforcing this behavior. When the behavior has been sufficiently reinforced for the red can, the same learning process is used for the green can. The human first demonstrates how to drop the object in the second box and then lets the robot do the task, reinforcing this behavior for the next 2 reproductions. The robot is then given a series of red and green cans to verify that it correctly learned to place them in different boxes.

IV. CONTINUOUS LEARNING AND ADAPTATION TO NEW

CONDITIONS

The robot successfully learned to reproduce the task. The system is still learning and can be adapted thanks to new interactions. For that we place a red can which the robot picks, but when it moves to drop it in the first box, the human teacher grabs the arm and moves it to the second box. When the object has been dropped into the new box, the behavior is rewarded. Due to the learning equation ( 3) the action of dropping the object in the new box is associated to the goal for red objects and the association between this goal and the old box is decaying a little. The stability of a behavior depends on the number of given rewards. The initial behavior was reinforced three times. After the rewarding of the first demonstration of the new behavior, the transitions leading to the new box are still less activated in the cognitive map than the transitions associated to the initial box. With another demonstration and reward, the goal/transition association begins to take precedence with a short lead. The robot is able to autonomously reproduce the correct behavior. A last reward when it has managed to correctly perform the task increases the lead of the new behavior (Fig. 5). After this learning the robotic arm places both types of objects in the second box. Finally, the procedure is repeated for the green objects and the robot is taught to place them in the first box. As a consequence, the 6 for the 3D positions of these states). The graph represents the activity of the two transitions AB and AC in the cognitive map. With each reward for dropping in a box, the potentials of the transitions leading to this box increase while others tends to decrease. When the red and green goals are first presented, there is no activity in the cognitive map because no transition has been associated to these goals yet. In the second half of the experiment, the destination boxes are switched for both goals.

sorting of the objects in the two boxes is reversed compared to what was initially learned. The system benefits from the generalization properties of the planning architecture. During the adaptation to changing conditions in the task, only the part of the movement to the box was shown. After dropping the can, the robot was able to recognize its configuration and determine the path back to the pick-up place using what was previously learned for other conditions. Figure 6 shows the position of the learned states in the workspace and the transitions learned between states at the end of the task. Interestingly, more states were recruited near the pick-up place than for the movement between the boxes. The 3D Cartesian space representation is not the space in which the states are encoded. Close positions in the Cartesian space can be distant in the multi-dimensional joint space of the arm. Besides, during the demonstration of the grasping, the different proximo-distal articulations were manipulated to reach the object with accuracy and with the correct orientation for the gripper. During the demonstration of the simplified left/right and up/down movements to the boxes, only the proximal joints were manipulated as there were no particular movements to be shown for the other joints. As a result, the recruitment process depending on each joint variation from the recognized prototypical joint/gripper configuration (sec. II) explains the different densities of states.

Figure 7 shows the most active state of the system when the end effector is at a given 3D position during reproduction. The color of the point on the trajectory corresponds to the color of the most active learned state. A state can be recognized before the arm end effector is at the learned position for the states. The system consequently anticipates the next move without finishing the current command to reach the center of the states, which leads to small shortcuts being taken in the reproduced trajectories as opposed to what was learned. The effect is more important when there are few states like in the middle of the trajectory from the pick-up place to the boxes. Figure 6 gives an example of the propagation of the activity for the different transitions in the cognitive map when one of the goals is active.

V. CONCLUSION

In this paper, we presented a bio-inspired model that enables a robot to build a representation of a task demonstrated through passive manipulation. This representation is based on proprioceptive states that are recruited and constitute the motor primitives of the system. It can be used by the system to plan its actions depending on visually categorized goals. Our system can continuously develop its model of the task through several interactions with humans. It was tested with a real robot on a changing pick-and-place task.

In this work, we described only one cognitive map built through interaction rather than exploration of the state space. Planning with large DOF systems can quickly lead to dimensionality problems that can be addressed by the use of hierarchical maps [START_REF] Liu | Hierarchical roadmap based rapid path planning for high-dof mobile manipulators in complex environments[END_REF]. We consider the integration of different layers in our cognitive map model. One cognitive map would still be mostly acquired by interacting with humans, whereas another could be completed by exploring the environment (by babbling). This level of representation would be more extensive and only called upon in cases when the robot cannot infer what to do from what it was interactively taught. Future work will also be dedicated to the integration of different control systems for the imitation of observed actions and the imitation of actions experimented through "embodying". This raises a major action selection issue as the different systems might give different motor commands in parallel.

Finally, an interesting addition to the system would be for the robot to indicate to the human that it does not know what to do. Several works [START_REF] Nagai | How a robot's attention shapes the way people teach[END_REF] [START_REF] Thomaz | Teachable robots: Understanding human teaching behavior to build more effective robot learners[END_REF] have stressed the importance of the behavior of the robot in the way the interacting human will teach it. The stress value of the motor control system only increases when the planning system cannot propose any action, it is thus a way to detect that the current knowledge is too limited to perform the task. The signal is used to trigger a return to the rest position but could also activate a visual cue indicating to the human the need for assistance. Signaling to the human that the robot needs help, e.g. by directing its gaze toward the caregiver, would lead to another interaction with the aim of addressing the current situation. If the human accepts to help the robot and demonstrates a solution, new information can be integrated in the representation of the task.

Fig. 2 .

 2 Fig. 2. Detailed architecture for motor control.

Fig. 3 .

 3 Fig. 3. Pick-and-place task learned and adapted through passive manipulation. Example of demonstration for the red-can-in-box-2 condition and reproduction by the robot. The camera looks at the pick-up place to recognize the type of object by color detection (red or green).

Fig. 4 .

 4 Fig.4. Trajectory of the arm end effector in the 3D Cartesian space. The experiment can be explained as different phases, each one corresponding to a row. The first phase is the learning of the pick-and-place task for the red can and the green can. The black thick line corresponds to the trajectory during passive manipulation of the arm. The second phase is the validation of the reproduction of the task after learning. The third phase is the adaptation of the learning to new conditions: the reversal of the boxes for red and green can. The movement of the arm is corrected using passive manipulation to show the expected gestures. The learning of the new conditions needs several reinforced corrections to be learned. The last row shows the adapted reproduction after relearning.

Fig. 5 .

 5 Fig.5. The states A, B and C display the bifurcation of the paths leading to the two different boxes (See Fig.6for the 3D positions of these states). The graph represents the activity of the two transitions AB and AC in the cognitive map. With each reward for dropping in a box, the potentials of the transitions leading to this box increase while others tends to decrease. When the red and green goals are first presented, there is no activity in the cognitive map because no transition has been associated to these goals yet. In the second half of the experiment, the destination boxes are switched for both goals.

Fig. 6 .Fig. 7 .

 67 Fig.6. Propagation of goal activity in the cognitive map for the red can goal at the end of the experiment. The learned states (squares) and the possible transitions (lines) are represented by the positions of the arm end effector in the 3D Cartesian space. The transitions are not symmetrical. The plain part of the line shows the starting state and the dashed part shows the final state of the transition. The darker and thicker lines corresponds to the transitions that have higher potentials in the cognitive map and thus are preferentially chosen.

ACKNOWLEDGMENT

This work was supported by the INTERACT (referenced ANR-09-CORD-014) and NEUROBOT french ANR projects, the CNRS and DGA.


Christophe Parisse Modyco

The unfolding of the verbal temporal system in French children's speech between 18 and 36 months

Keywords: verbal constructions, French language acquisition, time, tense, form/function mapping

In this paper, our aim is to analyze the relationship between the development of verbal forms and verbal functions. We examine all verbal forms produced longitudinally by two French children in terms of their morphosyntactic marking of tense, aspect, mood and situation type, and compare them to their contextually interpreted meanings. We introduce the main issues relevant to the unfolding of the verbal temporal system in children's data.

Our data consists in two longitudinal corpora of French speaking children aged 1;06 to 3;01. The paper focuses on: 1) the relationship between form and function within the verbal system in the earlier stage of development; 2) the children's ability to mark a displacement between speech time and event time.

INTRODUCTION

The development of verbal temporal morphology is a domain in which children's cognitive, communicative and language abilities are clearly intertwined. A number of cognitive prerequisites, particularly the need to remember or anticipate remote events, are essential. The specific semantic and morphosyntactic properties of the language being learned must also be taken into account. French is a language with relatively rich verbal morphology. However, in oral French a large number of forms are homophonous; two of the most frequent phonological forms -past participle and infinitive of the first group as in fermé (closed) / fermer (to close) are overwhelmingly represented. In our previous work, we have observed two main stages of development [START_REF] Morgenstern | A la source du futur : premières formes verbales dans les productions spontanées de deux enfants français de 18 mois à 3 ans[END_REF]:

1) Only a small subset of the large variety of forms available in French is initially used. Children produce forms that are frequent and salient in the input, using them even more frequently and systematically than the adults.

2) Later, a variety of forms appear, including forms that are infrequent in the input. Children start producing several inflections for the same verb.

In this paper, our aim is to analyze the relationship between the development of verbal forms and verbal functions. Can children express various aspects and temporal relations before they have learned to use the conventional grammatical verbal forms? To address this question, we will examine all utterances containing lexical verbal forms as they are produced longitudinally by two French children, focusing on their morphosyntactic marking of tense, mood and situation type, and compare these utterances with their contextually interpreted meanings. 1Section 1 introduces the main issues relevant to the unfolding of the verbal temporal system in children's longitudinal data. In Section 2, we present our French data, our coding system and our quantitative results.

Finally, Section 3 focuses on two issues: 1) the relationship between form and function within the verbal system during the earlier stage of development; and 2) children's ability to mark a displacement between speech time and event time.

MAIN ISSUES

The French tense system

French morphology is traditionally considered to mark tense more than aspect. In English, the past tense refers to completed past events, and the present perfect refers to events with relevance to the present [START_REF] Klein | The present perfect puzzle[END_REF].

In contrast, the French 'passé simple' (corresponding to the English past tense) has almost disappeared from spoken French, except for retellings and reformulations of a written narrative; thus the 'passé composé' corresponds to both past tense and present perfect in English. As a result, the verbal form gives no clues as to whether an utterance refers to a present result or to a past event or activity.

(1) Il a couru [he has run -(which explains why he is tired)].

Il a couru [he ran -(there was a marathon last week)].

We need the context (presented between brackets next to the translation above) -the situation, the previous utterances, the shared knowledge between the interlocutors -to know whether the 'passé composé' used in each example refers to a past event with an impact on the present situation or a past event disconnected from the present situation. This difference which could be called aspectual and described as 'perfective' in the first case, and 'aoristic' in the second case, is not formally marked on the verbal form since the same grammatical tense is used. This lack of an explicitly marked distinction poses an obvious challenge for acquisition.

Other grammatical tenses, such as the 'imparfait', the inflectional future and the conditional (present or past), seem to be more clearly marked as corresponding to more specific functions, and thus may represent less of a challenge during the course of language acquisition.

Acquiring the tense system

Children's ability to include temporal reference in their productions is often reported as developing gradually and slowly [START_REF] Bronckart | Time, tense and aspect[END_REF][START_REF] Ferreiro | Les relations temporelles dans le langage de l'enfant[END_REF][START_REF] Smith | The acquisition of Time Talk: relation between child and adult grammar[END_REF]. Temporal markers can be considered as the expression of the relation between 'speech time' -the moment when the speech occurs -, 'event time' -the moment when the event referred to occurs -and 'reference time' -a moment that provides an anchoring point so that events can be located relative to one another- [START_REF] Reichenbach | Elements of symbolic logic[END_REF].

As shown by [START_REF] Weist | A cross-linguistic perspective on the development of temporal system[END_REF], building on the work introduced by Smith (1980), children are first linguistically, semantically and cognitively limited to the immediate situation -the here and now. Speech time is identical for them to reference time and they don't refer to event times disconnected from the present time. Then they become capable of disconnecting from the present time and refer to event time (past and future), and finally they develop the capacity to change their reference point, from speech time to another time and locate events relative to a reference time.

The pace of acquisition is considered to be governed by a combination of factors, including syntactic, semantic and cognitive complexity, as well as the frequency of the forms in the input.

Cognitive factors

In order to speak about the past, children must have stable mental representations of events in memory. In order to speak about future events or activities, they need to be able to anticipate them.

According to followers of Piaget's developmental theory (Bronckart and Sinclair, 1973:108) The importance of cognitive factors has been demonstrated by naturalistic [START_REF] Cromer | The development of temporal reference during the acquisition of language[END_REF] and experimental studies [START_REF] Ferreiro | Les relations temporelles dans le langage de l'enfant[END_REF]. [START_REF] Bronckart | Time, tense and aspect[END_REF] observed that up to age six, children tend to use the 'passé composé' for events with endpoints and the 'présent simple' for events without clear endpoints. They interpret the different tenses as expressing aspectual rather than temporal distinctions. According to the authors, only later do children begin to use these to mark different temporal relations.

However, a number of scientists have analyzed spontaneous data and introduced facts to reconsider children's cognitive 'limitations' in their use of the temporal system. [START_REF] Halliday | Learning how to mean: Explorations in the development of language[END_REF] showed that his son tried to narrate events in the past at 1;08. For Halliday, the child has a notion of pastness, however rudimentary. [START_REF] Gerhardt | From discourse to semantics: The development of verb morphology and forms of self-reference in the speech or a two year old[END_REF], many children do refer to past occasions with no perceptual anchoring in the present situation. There have been numerous works that show how children can refer to past or future events around age two (see [START_REF] Behrens | Cognitive-conceptual development and the acquisition of grammatical morphemes: the development of time concepts and verb tense[END_REF], for a review). There can be a considerable time lag between the first non-linguistic evidence that certain time concepts are available to the children (such as memory of past events) and their first production with linguistic means. Therefore, cognitive abilities might be more precocious than previously claimed, even before they are explicitly marked in language.

Language-specific factors

Time is a complex, abstract notion that is difficult to define in terms of objective experience or direct perception. Language seems to have a great impact on the children's capacity to comprehend and encode the unfurling of time. As Nelson (1996: 288) explains: 'the child alone cannot discover time, because (unlike concrete objects) it is not an entity that exists to be discovered. Rather, conceptions of process and change have led different societies to conceptualize time in different ways, and those ways are conveyed to children through language forms'.

But the kinds of temporal expressions available to children vary across languages. Language-specific learning of time concepts, just as for spatial concepts (Choi and Bowerman, 1985) has been demonstrated in a variety of studies for languages including Turkish [START_REF] Aksu-Koç | The acquisition of aspect and modality: the case of past reference in Turkish[END_REF], German [START_REF] Behrens | Cognitive-conceptual development and the acquisition of grammatical morphemes: the development of time concepts and verb tense[END_REF], Polish [START_REF] Smoczynska | The acquisition of Polish verb morphology[END_REF], and Inuktitut [START_REF] Swift | Time in child Inuktitut: a developmental study of an Eskimo-Aleut language[END_REF].

These results are consistent with [START_REF] Slobin | Learning to think for speaking: native language, cognition and rhetorical style[END_REF] work suggesting that the particular structures available in the languages children acquire may influence their perception of the world and their cognitive abilities.

Impact of the input

The linguistic systems acquired by children have been increasingly seen as being linked to the input, but many questions remain about the nature of the connection. To what extent can children's grammars be viewed as successive transitory systems with their own coherence [START_REF] Cohen | Sur les langages successifs de l'enfant, in Mélanges linguistiques offerts à M. J. Vendryes par ses amis et ses élèves, Paris, E. Champion[END_REF]?

How exactly are they influenced by the frequency and saliency of the forms in the input [START_REF] Tomasello | Constructing a language, a usage-based theory of language acquisition[END_REF]? Do children replicate the most frequent and salient forms they hear in the adult language addressed to them?

A number of studies of children's early productions have shown that early tense marking is closely linked to the Aktionsart of the verb2 . One of the stronger claims was made by Wagner (1998: 86): 'children initially use present tense and/or imperfective morphology to mark atelicity and use past tense and/or perfective morphology to mark telicity'. However, [START_REF] Shirai | The acquisition of tense-aspect morphology: a prototype account[END_REF] show that this preference might be due to the patterns children hear most in the language surrounding them and that they make prototypical associations between forms and functions that are linked to frequency in the input: telicity, for example, is associated with past events.

Children then broaden the telic, punctual and resultative features to less prototypical aspectual uses that are not produced as frequently in the input.

Children's acquisition of the tense system in French

According to previous studies on the acquisition of the tense system in French:

1) Around age two, children produce past participles with an adjectival value, such as cassé (broken) or pati (gone) [START_REF] Sabeau-Jouannet | L'expression de l'organisation spatiale et temporelle, son évolution chez l'enfant de 2 à 5 ans[END_REF]. The situation is therefore present (speech time) and describes the result of an action.

2) Around 2;06 (i.e. two years and 6 months), they start marking aspectual differences between completed actions and ongoing activities.

With the use of the 'passé composé', as in Jeannot a pris ma voiture (Jeannot took my car) or a fait poum (fell) (Grégoire, 1937), children still anchor their speech in the present situation [START_REF] Meisel | Les phases initiales du développement de notions temporelles, aspectuelles et de modes d'action. Etude basée sur le langage d'enfants bilingues français-allemand[END_REF]: past events are expressed through their impact on the present.

3) Around 3;00, children clearly mark anteriority and posteriority with the use of future tenses and past tenses. They introduce another reference point, for example with adverbs [START_REF] Decroly | Observations relatives au développement de la notion du temps chez une petite fille[END_REF]. They localize events in the past. New uses of the 'passé composé' and the introduction of the 'imparfait' and the inflectional future [START_REF] Morgenstern | A la source du futur : premières formes verbales dans les productions spontanées de deux enfants français de 18 mois à 3 ans[END_REF] mark a real dissociation between speech time and event time. 4) Around age four or five, children can position anteriority and posteriority relative to reference time and not only speech time. However, according to [START_REF] Labelle | L'utilisation de la valeur des temps du passé par les enfants francophones[END_REF], the use of the 'plus-que-parfait' at around age four is not sufficient proof that children rely on reference time that would be displaced from speech time. These first productions of the 'plus-que-parfait' do not express a different reference time but are anchored as perfective in the event time. The value of anteriority arrives later. For [START_REF] Sabeau-Jouannet | L'expression de l'organisation spatiale et temporelle, son évolution chez l'enfant de 2 à 5 ans[END_REF], the 'plus-que-parfait does not situate an event as anterior to the reference time already located in the past' 3 . In fact, [START_REF] Fayol | Le plus que parfait. Etude génétique en compréhension et production chez l'enfant de quatre à dix ans[END_REF] and [START_REF] Vandenplas-Holper | La compréhension d'expressions verbales de la succession temporelle par des enfants de 6 à 11 ans[END_REF] even claim that some speakers can only achieve correct use of reference time (when different from speech time) at 19 years old.

One of the aims of our study is to work on recent spontaneous data that include phonetic transcriptions and are linked to the video, and to test whether, after coding the semantic values of the children's utterances as interpreted in context by their interlocutors, we find evidence for the successive stages described in the literature on the acquisition of French verbal morphology. We examine whether the order in which the children in our data produce the relevant forms is consistent across children, and whether the semantic values of their productions are correlated with their productive use of the conventional verbal forms.

3 Our translation 2. DATA, METHOD AND QUANTITATIVE RESULTS

Data and Method

We used two of the datasets in the Paris corpus, Anaé and Madeleine, from 1;06 to 3;03. We coded only lexical verbs and did not code the verbs être (be) and avoir (have) even in their lexical uses, because these verbs, massively used as auxiliaries or as light verbs with low semantic value, would require a separate study and would bias the quantitative results. We created a coding system in an Excel file linked to the video with 1) the speaker, 2) the utterance produced, 3) situation type, 4) grammatical verbal form. 5) chronological time referred to (past, present and future, 6) marking of a displacement between speech time and event time (referred to as 'DISP' in the rest of the text). Since aspect is rarely marked as such in the oral French system and is difficult to grasp, we used this last category in order to distinguish between past events (coded as 'past') that have a connection with the present situation (impact, result, or clear association), and past events that are usually more remote and clearly disconnected from the present situation (they could for example have taken place in a different location), which were then coded as 'DISP'. Some of these six features required (inter)subjective evaluation of the child's communicative intent, especially since we could not rely on form. However, we do not attribute any knowledge to the children. Our work is based on the coders' interpretation of how they would react with the child at the moment the video was recorded. In other words, coders examined the ongoing discourse context, empathetically taking the perspective of the child's adult interlocutor, but producing their own interpretation. We used the adult's behavior as a coding clue. We limited our coding to focus on a few broad salient semantic distinctions that allowed good inter-coder reliability.

'Situation type' (which includes imperfective and perfective aspects) was coded using four main mutual exclusive dimensions: completed, ongoing, directive and potential. In rare cases that occurred only in the last recording, the code 'hypothetical' also had to be used. Situation type was coded in a very simplified way based on properties derived from the lexical aspect (verbal telicity, for example) and/or from the grammatical form. This approach was taken because it provided us with a complementary view to chronological time. 'Completed' corresponds to completed actions, while 'ongoing' is used for actions performed at the time of speaking, as well as for generic aspect since many cases were ambiguous. 'Directive' corresponds to demands or orders made by the children, 'potential' to any non-realized and not yet performed action. The distinction between directive and potential could be tricky to draw at times, where identifying directive situation type is especially subjective. Once again, this includes the lexical aspect of the verb (je veux -I want -led most often to 'directive' coding).

'Grammatical verbal form' corresponds to a description of the actual verbal morphological forms produced by the children, including any auxiliary or modal verb and even non-finite verb-forms. This allowed for coding of the following forms: present, imperative, past participle, 'passé composé', infinitive, preposition plus infinitive, modal plus infinitive, periphrastic future, imperfect and plus-que-parfait, conditional, inflectional future, gerund, subjunctive. It should be noted that coding of some of the grammatical verbal forms is heavily dependent on the adult interlocutor's interpretation and thus not independent of the other codes. For example, past participle and infinitive are often homophones in French; thus each production must be interpreted in context. The numerous cases of fillers (incomplete or imprecise production of the morphological markings) give rise to the same problems linked to contextual interpretations. Unclear situations (for example situations likely to call for a request for clarification from the adult) were coded as ambiguous.

'Time' was coded according to three dimensions: past, present, and future, although this represents a clear simplification of the linguistic system to refer to time. Talking about processes that are not directly located in the here and now is not impossible for children, but it is difficult to interpret this as such when children do not produce the complete grammatical forms. In 'j'ai tombé' (past: I fell), 'je fais tomber' (present and causative: I make -it -fall), and 'je vais tomber' (future: I'm gonna fall), 'tombé/tomber' is pronounced in exactly the same way (/tɔbɛ/). So if auxiliaries are omitted, and 'tombé/tomber' (past participle of the verb to fall, versus infinitive form) is the sole element produced by the child, coding the intended temporal relation, and its interpretation by the adult-interlocutor, can be problematic. To cope with this difficulty, it was necessary to rely on the extra-linguistic context and the most salient referent (concrete or abstract) of an utterance in deciding how to code the intended temporal meaning. For example, if the child said /tɔbɛ/ in the immediate aftermath of an event in which some object had fallen, we coded 'past'. If the child was pushing some object simultaneously with the utterance, we coded 'present'. If the child (or somebody else) made something fall down a few seconds (or more) later, we coded 'future'. In those cases, the events would be coded as past and future without the 'DISP' component. Verbal forms were thus all coded as either past, present, future, or as non-interpretable. Following Smith (2004), reference to events that occurred prior to the time of utterance were coded as 'past', reference to events that had not yet occurred at the time of utterance was coded as 'future', reference to events or states in progress at the time of utterance was coded as 'present'. We also used the code 'present' for illocutionary language acts grounded in speech time. For example, je veux (I want) (commonly used alone in young French-speaking children) and je veux jouer (I want to play) were both coded as present even though in both cases the action referred to is hypothetical, because we considered the child's expressed intention to be present in chronological time.

We used the coding 'DISP' in order to study early markings of displacements between Speech Time and Event Time, that is, situations in which the action described is dissociated from the immediate context, typically because it occurs in a different location, takes place in the distant past or future, or is clearly hypothetical, as when Anaé, at the age of 3;01, recalls her last summer vacations and says to the observer 'Et moi j'ai allé sur le bateau' (And I went on the boat). Table 1 gives an example of our coding.

Table 1

The data were coded by the two authors of the article. One session was fully coded separately by the two authors so as to allow measurement of inter-coder reliability. We used Cohen's kappa coefficient of reliability for the four codings: grammatical form, k=0.77, chronological tense, k=0.45, situation type, k=0.78, and 'DISP', k=0.60 (Cohen's kappa was measured using the 'irr' package of the R software). We looked at the reasons for disagreement and tried to achieve full agreement between the two coders.

This resulted in a higher value of Cohen's kappa for chronological time, 0.71. To ensure reliability for the purpose of the current work, each child was first fully checked by the same coder, so that comparisons between sessions for the same child could be trusted, and a single coder finally controlled both children.

Overall Results

We counted the codings in the two children's and the two mothers' productions of different forms according to the children's age. The results are summarized in the following tables.

All results are presented for the two children for two major periods (period 1 and period 2), each containing an equal number of sessions:

Anaé's earlier period runs from 1;06 to 2;00 and her later period from 2;01 to 3;01, while Madeleine's go from 1;06 to 2;01 and from 2;02-3;01, respectively (see Tables 2 to 4). This division of the data provides a clear image of the production of the children in early development (when children are usually not considered to be able to express time) and in later development (when children are usually considered to start to express time correctly).

The results for the adults were computed on two sessions of Anaé's data and two sessions of Madeleine's data (one at the beginning and one at the end of the longitudinal data). There was no major difference between the two sessions used for each corpus. However, the productions of the two mothers were different one from the other (see below).

Grammatical forms and tenses

Table 2 As shown in Table 2, no less than 12 different morphological finite and non finite forms are available in the data. Composed forms ('passé composé', periphrastic future, modal + infinitive forms) are coded only once. We coded separately 'Preposition plus infinitive' forms, which correspond to a correct and frequent use of non-finite infinitive forms in French, and 'bare infinitive' forms (for example when Anaé at 2;00 says 'asseoir là' meaning 'I want to sit here'), which are not often found in the adult target language.

The most frequent forms are the present and imperative forms, which are the simplest verbal forms possible in French and are used more often by the adults than the children in our data.

The second most frequent forms are past participles and infinitives. For these two forms, a developmental trend was observed. Children produced more (usually ungrammatical) bare participles and bare infinitives during period 1. During period 2, the trend was opposite, with most participles and infinitives used in complex verbal forms. However, even the relatively low production rate of bare participles and infinitives by the adults is not yet matched by the children during the second period. The other grammatical modes and tenses (such as conditional, subjunctive, and even imperfect and inflectional future) are not productive before period 2. They are not frequent either in the adult data.

Situation type

Table 3 The results presented in Table 3 show that the two children's productions are once again very similar. The small differences between them (especially concerning potential situations) may reflect specific child or family style.

However, for both children, the difference between period 1 and 2 is very small. It should be noted that, whatever the children's preferences, all situation types are used frequently. Ongoing situations are the most frequent for the two children. The two mothers display a slightly different global use, with no preference for ongoing situations but more forms referring to potential situations than the children, especially Madeleine's mother. Anaé's mother had few forms expressing completion, which was parallel to the low percentage of use of past references. Madeleine's mother's use of completion forms was similar to her daughter's. Differences in style were found in directive forms: Anaé's mother had more forms than her daughter, whereas the opposite was true for Madeleine.

Temporal grounding

Table 4 As shown in Table 4, the majority of uses across both children and adults refer to the present. The two children's references to time are very similar.

In particular, there was no difference between the earlier and later periods for any temporal category for either child.

For both children, references to past or future events (as interpreted by the child's interlocutors and the coders and without making the distinction between 'DISP' past and future and 'non DISP' past and future) were relatively sparse but appeared very early. At age 1;06, Anaé produced 14 verbs, one of which was interpreted as referring to the past and one to the future. At the same age, Madeleine produced 27 verbs, two of which referred to past and four to future. From the very first session, the possibility of referring to past and to future was therefore present in both children, in similar percentages as a general trend. Anaé's mother produced few references to the past, much less than her daughter, whereas Madeleine's mother produced more references to the past than her daughter. However, reference to the future was similar between the two mothers, with more references than their daughters. Finally, references to the present were similar across all participants.

Displacement

Table 5 Table 5 presents the percentages of occurrences of displacement ('DISP') between Speech time and Event time against the total number of verbs produced. 'DISP' was rare in the first age range: 6 occurrences for Madeleine for 396 verbs produced and 2 for Anaé for 330 verbs produced. However, they were 10 times more frequent in the second age range for both children. For Anaé's mother, the frequency of 'DISP' values was similar to Anaé's, but in Madeleine's case, her mother used three times more forms with 'DISP' values. Madeleine's more frequent use may thus be explained by her input or the situation induced in the mother-child dialogue.

ANALYSES AND DISCUSSION

Global trends

The specificity of this study lies in the fact that our coding system enabled us to consider and relate four properties of Anaé and Madeleine's verbal systems between ages 1;06 and 3;00. Three of these properties (situation type, chronological time and 'DISP') are language functions produced by the children, as interpreted by the coders who took the perspective of the adult interlocutors. The fourth property is morphological, and categorizes the productions according to oral French grammar (grammatical verbal forms).

The results show a clear developmental trend in the forms used in the verbal system, which are consistent with our previous results on future tenses [START_REF] Morgenstern | A la source du futur : premières formes verbales dans les productions spontanées de deux enfants français de 18 mois à 3 ans[END_REF]. At the beginning of the data and until around 2;00, the two children mostly produce forms corresponding to the most frequent forms in the input. These forms are often used quite 'bare', without their usual accompanying grammatical markers, such as auxiliaries and clitics. After 2;00, the children start to produce a much larger and more complete variety of forms, including imperfect, future, and conditional.

They also produce a greater range of grammatical markers, which result in different codings of the grammatical categories of some of their verbal productions: from past participle to 'passé composé' (from tombé /fallen to il est tombé / he has fallen), from infinitive to preposition plus infinitive (from sauter / jump, to c'est pour sauter / it's to jump), or modal plus infinitive (je veux sauter / I want to jump) and periphrastic future (je vais sauter / I'm going to jump). By 2;01 and 2;02, the children are already producing long utterances, with both Anaé and Madeleine having an MLU of at least 2.8 by age 2;00. It is interesting to note that the children's verbal forms can be categorized into three classes on the basis of child production frequency: a highly frequent category (between 50 and 80%) which contains present and imperative forms, a moderately frequent category (between 10 and 25%) which contains all verbal constructions built around the infinitive and past participle forms (which are often homophones in French), and an infrequent category (less than 5%) which contains future, imperfect, conditional, and subjunctive.

Despite those salient developmental differences in the verbal forms, two of the properties describing the functions of language (situation type and time) did not seem to change much over age. The children produced language that was distributed over all possible functions. All the categories of situation types in our coding system could be found from the first session on. Although the number of verbs produced increased tenfold between age 1;06 and about age 2;04, the percentages of the various situation types were very similar.

References to the chronological present were the most frequent (see Table 4), which is in keeping with traditional results about the deictic quality of children's speech, but the children nonetheless often referred to past and future events, at least from the interlocutor's point of view. This was true for the recordings in period 1 as well as for the recordings in period 2.

The final property studied, 'DISP', appeared infrequently and only in the recordings after age 2;00. This means that the children clearly spoke about elements that were not connected to the here and now only when they also started to produce a lot of complex grammatical forms.

Our overall results could be interpreted in favor of a kind of dissociation between the use and mastery of functions and forms by children. Through their first verbal productions, the two little girls displayed what was interpreted by their interlocutors as a wide range of language functions. In other words, their interaction with the adults provided ample pragmatic support for them to develop and deploy those various communicative functions. So why did they take so long to produce the whole range of conventionalized forms (imperfect, conditional, subjunctive, inflectional future, etc.) corresponding to these functions in the French grammatical system? One possible explanation is simply that the children had not yet in fact mastered these functions -that their adult interlocutors might simply understand or interpret early productions as having these functions even if they are not intended by the children. However, this hypothesis seems to be in contradiction with the children's obvious ease in their interaction with their mothers and the rare cases of apparent misunderstanding.

One of the problems we encounter analyzing interpreting language functions is that they are internalized constructs that cannot be directly transmitted between interlocutors. Usually, speakers have to rely on some external element, such as a word, gesture, body language, deictically indicated objects, or on shared knowledge, to convey function and meaning.

Moreover, even with an external element, there is no guarantee that the function assigned by one interlocutor will be similar or even close to the function assigned by another interlocutor. Our results show that children do not pair form and function as well as adults at the beginning of the developmental process. Shared functions might be attained only after a certain amount of experience, perhaps only once the internal representation of the function has stabilized and evolved based on the successful or unsuccessful interactions of the child with her environment and her interlocutors.

Another explanation for the late production of linguistic forms would be that real mastery of the functions marked linguistically by tense and aspect morphology does not take place before the forms actually appear.

Without forms through which to share knowledge, it is difficult for the adult and the child to build and develop common language functions. This was clear in the problems we encountered with our semantic coding, and during the coding process we needed redefine a common basis to code the functions consistently. In a similar way, adults and children have to build meaning together. On the basis of language forms (the visible parts), they must co-construct the language functions (the hidden parts) that might correspond to them. This is clear in the 'DISP' situations for which specific language forms occur in the children's speech, especially adverbs, prepositional noun phrases, or reference to specific elements in the interaction scene. To illustrate this point, in the sections below, we present analyses of the uses of 'DISP' by the two children.

Analyses of verbal productions coded as 'DISP'

The first five 'DISP' examples in Madeleine's productions are instructive because they increase nicely in complexity and in distance to Speech Time.

(2) Madeleine, 1;09

CHI: [ə] parti [a] bus. [/ə/ gone /a/ bus] (3) Madeleine, 1;09 CHI: dormir. [sleep]
Both examples are from storytelling contexts in which Madeleine, who probably knows the story very well, describes the pictures in the book. It was difficult to determine whether she was talking about a result or a past event, and in fact the coders disagreed about whether the 'DISP' criteria were met (i.e. they are ambiguous examples). What made those examples possible 'DISP' occurrences was that in the first case the page where the 'bus action' was depicted was being turned. In the second case, Madeleine was pointing at a picture of a puppet waking up, although there was also an image of the same puppet sleeping, on the left page. So in both cases, however tentative this interpretation might be, Madeleine could be viewed as referring to some past event disconnected from the present within the process of storytelling. (5) Madeleine, 2;01: Madeleine is using a toy telephone, 'talks to her sister' who is in school and hangs up. In this example, Madeleine is in a situation of pretend play with a fake telephone. Her use of the present tense when she says elle rentre ce soir to her mother echoes her mother's utterance elle rentre and encodes the fact that her sister comes home every day from school in the evening, but she is indeed referring to the chronological future. In this final example, Madeleine is clearly telling a story about herself. She is still mixing things a little bit, since she is talking about the stairs and the bed in a slightly a-grammatical construction (the two terms of the 'et' construction are not parallel), and she is using the wrong personal pronoun (the reduced /l/ production is used by adults to refer to the third person but she should have used the first person to talk about herself). Nonetheless, this is a very complex and quite thoughtful speech for a child aged 2;01.

What is remarkable is that in the first four 'DISP' productions analyzed above -examples (2) to (5) -, the context is storytelling: first by the mother, then by Madeleine herself. It is also interesting to note that in the clear-cut 'DISP' examples (the two final ones), Madeleine uses a temporal expression outside the verb ('ce soir' and 'un jour'). Finally, in these last two examples, Madeleine uses two plurifunctional markers, the present tense (example 5) refers to the future and not the present and the 'passé composé' (example 6) refers to the distant past. So it seems that Madeleine's learning of 'DISP' is grounded in storytelling, which is an ideal situational context for learning about dissociation from Speech Time. At first (examples 2 and 3), the temporal distance is very short, so the elements Madeleine speaks about are probably still in her working memory, or perhaps her 'visual sketchpad' (see [START_REF] Baddeley | Working memory and language: an overview[END_REF] since she is reading books with her mother. These examples are therefore at best proto-'DISP' situations. But such situations help her to learn to distance herself from the here and now, which she does in an unusual and surprising way in example (4). At that point, she seems aware that it is possible to refer to something absent and that this is usual in storytelling.

In example (5), the situation is repeated, but with two important differences: she is no longer in a book-reading activity but rather is talking about something real (her sister's coming home). To do so, she uses a temporal expression 'ce soir' (this evening) that marks exactly what she is talking about, and the time to which she is referring. These markers provide a way of distancing the event from the here and now without using tenses such as the future or the imperfect, which the child does not produce yet (Madeleine's first future and imperfect verb forms will appear during the next session, at age 2;02). Note that example ( 5) is probably reproduced from adults' previous speech in similar situations. But this is not the case in example (6), which is non-adult in its form but contains all the elements ('un jour' [one day] associated to the 'passé composé') that allowed the coders to identify it as 'DISP': it has a clear temporal reference, a clear situation, and it is an auto-biographical narrative. The fact that Madeleine clearly constructs the utterance herself shows that she is in the process of mastering the uses of 'DISP' situations. In the next session, she will once again produce 'DISP' utterances within storytelling but using inflectional future and 'imparfait' tenses. By age 2;04, she starts producing a lot of 'DISP' utterances.

Anaé's first uses of 'DISP' are also very interesting, especially because they appear in a different setting than Madeleine's, which shows that storytelling situations, as produced by Madeleine, are but one type of situations where 'DISP' can be produced. For Anaé, the first recurring situations are not storytelling ones, but when talking about 'what actually happened' with verbal stimulation from her mother. For example:

(7) Anaé, 2;02 (Omer, the family dog has wrecked a stone wall in the garden.) Such marking in both parent and child speech may be the crucial clues that allow the children to learn to express displacement from the here and now, in a cognitive co-construction process grounded in discourse.

The data we have presented thus underlines how children's productions are interpreted in context as referring to complex events and a variety of temporal realities and situation types from very early on.

Linguistic forms are not always produced and indeed not required. But in some cases, especially when shared knowledge is insufficient, explicit markers become necessary. Our interpretation is that they are perceived as reliable cues because they are useful, especially in broader social contexts than the family environment, with less shared knowledge and familiarity.

CONCLUSIONS

We have shown that, as predicted in the literature, French children start to produce present/imperative forms, closely followed by 'passé composé' and periphrastic future forms, with gradual progress in the production of the actual morphosyntactic marking. It is only later (in our study after age 2;00) that they start to produce less frequent forms, such as 'imparfait' and future.

The relative infrequency of linguistic forms for expressing displacement from speech time is consistent with most previous research, which proposes that children mark aspect before tense and are restricted to referring to the here and now.

Our coding of other features however, suggests a different story.

Children appear to be able to refer to past, present, future, and to different aspectual meanings, from quite an early age, but in order to observe this, it is necessary to go beyond language forms and to give attention to communicative meaning. Culioli (2000:25) describes children's productions in the following way: 'the system seems poorer on the surface, but contains virtual elements that will progressively become overt markers'4 .

Interestingly enough, detecting these 'virtual elements' seems to be what their interlocutors actually do, and it probably helps the children in the language developmental process. Our proposal is that functions appear first, or are interpreted by the interlocutors before the development of conventional forms. Our analysis of the 'DISP' value also underlines the role of narrative and non-shared knowledge in communication [START_REF] Nelson | Language in cognitive development[END_REF]. Thus, full understanding of language development calls for usagebased pragmatics and semantics as well as usage-based syntax (see also Rossi and Parisse, this volume). It takes a certain amount of experience for children to use the forms borrowed from their input productively. When the value of explicit grammatical marking becomes clear to them, the children can achieve more confident agreement about meaning and function with their interlocutors. But even after children begin to produce clear grammatical forms, we must keep in mind the fact that it does not guarantee that they have the same form/function mappings as their interlocutor.

Gradual co-adjustment is needed between children and adults for meaning to be co-constructed in discourse. But of course, this process continues at various degrees, in all types of interactional contexts, and at all ages.

  , 'verbal patterns are constructed in close connection to cognitive development'. Children's grammars undergo shifts at crucial stages of cognitive reorganization. Before the 'concrete operational stage' children are egocentric; they live in the here and now and speak predominantly in the present tense and about present objects, people and activities. They are unable to talk about time other than the present time.

( 4 )

 4 Madeleine, 1;11: MOT and CHI are reading a book. CHI: est passé le train. [*went by the train*.] MOT: est passé le train? ah ben non, y'a pas d' train là. [*went by the train*? no there is no train here.] In this other situation of storytelling, Madeleine refers to something that does not belong to the story, as attested by the mother's reaction. So there is a clear discontinuity between what Madeleine says and what is happening in the here and now. Whether Madeleine talks about the past, the future or a hypothetical situation is unknown because there is no clear temporal marking.

  MOT: elle était où Marie, Madeleine? [where was Marie, Madeleine?] CHI: est au collège. [is in school.] MOT: au collège? [in school ?] CHI: oui. [yes.] MOT: elle t'a téléphoné? [she called you?] CHI: oui. [yes.] MOT: elle rentre? [she's coming back?] CHI: elle rentre ce soir. [she's coming back tonight.] MOT: ce soir? à quelle heure? [tonight? at what time?] CHI: euh et demi. [uhh *half past*.]

( 6 )

 6 Madeleine, 2;01 MOT : pourquoi as-tu peur de l'escalier ? [why are you afraid of the staircase ?] CHI : un jour l'est tombé dans l'escalier et de mon lit. [one day * she fell* off the stairs and off my bed.] MOT (to OBS) : oui parce que deux jours après elle est tombée de son lit. [yes, because two days later she fell off her bed.]

  *MOT: il a encore mangé le mur. [he ate the wall again.]

	uses the 'imparfait' with the nonstandard form 'était bougé' (for 'avait
	bougé', it had moved, using the auxiliary be instead of have), but it is also
	thanks to the semantic frame induced by the word 'caddy' (trolley) that the
	observer can reconstruct the reference to what happened in the supermarket.
	(8) Anaé, 2;08
	CHI: euh le caddy il était bougé aussi. [so the trolley *was* moved
	too.]
	OBS: le quoi? [the what?]
	*OBS: mangé le mur ! [ate the wall !] CHI: euh, le caddy de moi, il était bougé. [the caddy *of me* *was*
	*MOT: <hum hum>. [uhh -nodding and smiling.] moved.]
	*CHI:	l'a mangé [lə] mur. [(he) ate the wall.]
	In this example, Anaé follows her mother's prompt, repeating a part of what
	her mother has said before. But during the same session, she was able to
	answer her mother's (simpler) questions by herself. She is thus able to do
	more than replicate the adults' language, but her use of 'DISP' is still very
	uncertain. Her borrowings from the preceding adult productions continue in
	the rest of our recordings, but she replicates the adults' utterances less and
	less and she produces one utterance, coded as 'DISP', of her own initiative
	in our data:
	(8) Anaé, 3;01
	CHI: on a trouvé, hier on a trouvé peut-être. [we found yesterday,
	we found maybe.]

OBS: t'es allé au supermarché aujourd'hui? [you've been to the supermarket today?]

Table 1 :

 1 Extract from the coding grid.

	session line	speake	Utterance		form	Time	Aspect	Gram verbal	DISP
			r							form
	Mad-	951	CHI	l'a perdu sa maman	a	past	completed	passé	no
	1_11			[lost her mummy]		perdu			composé
	Mad-	1056	CHI	attends. [wait]		attends present directive	imperative	no
	2_06
	Mad-	1144	CHI	elle	montre	la	montre present ongoing	présent	no
	2_06			grenouille. [she shows
				the frog]
	Mad-	1669	CHI	et on a pas trouvé des	a pas	past	completed	passé	yes
	2_06			plus petits pour moi	trouvé			composé
				[and we didn't find
				smaller models for me]
	Mad-	4011	CHI	maintenant on fait la	fait	future	directive	présent	no
	2_06			galipette [now we jump
				up and down]
	Mad-	4280	CHI	on lui dira quand ce sera	dira	future	potential	inflect fut	yes
	2_11			plus un secret [we'll tell
				her when this will no
				longer be a secret]

Table 2 :

 2 Percentages of production of grammatical verbal forms

			completed	directive	ongoing	potential
	Anaé	1;06-2;00 2;01-3;00	22 16	23 25	32 38	22 21
	Madeleine	1;06-2;01 2;02-3;01	19 13	31 26	42 49	8 11
	Adults	Anaé Madeleine	3 18	36 19	31 40	30 23

Table 3 :

 3 Percentages of use of 'situation type'

			past	present	future
	Anaé	1;06-2;00 2;01-3;01	16 13	78 80	6 7
	Madeleine	1;06-2;01 2;02-3;01	16 8	78 85	7 7
	Adults	Anaé Madeleine	3 21	84 69	13 10

Table 4 :

 4 Percentages of reference to time

This does not mean that references to the past and to the future are limited to utterances containing lexical verbal forms -especially for young children who do not yet master the full grammatical tools of their language. However, in this chapter, we focus on the development of the relationship between lexical verbal forms and functions, and do not address the issue of the development of reference to time in general

See Slobin, 1985, and[START_REF] Weist | Tense and aspect: temporal systems in child language[END_REF], for a summary and for the presentation of the 'Semantic Predisposition Hypothesis' and the 'Aspect before Tense hypothesis'.

Our translation.

ACKNOWLEDGEMENTS

This work was supported by a grant from the Agence Nationale pour la Recherche, France. We would like to thank Nancy Chang for insightful comments, suggestions and thorough editing of this paper, Martine Sekali for her enormous work as editor of this special issue and the CoLaJE team

In this example Anaé is talking about something that she did before playing with the toy she is manipulating in the situation. Whether she is talking about a real fact is not important here, but she uses 'hier' (yesterday) to locate her actions in time. Without this indication, there would have been no clue that this puzzling utterance should be coded as 'DISP'. This emphasizes the role of explicit linguistic elements: without grammatical elements (such as temporal adverbs), we cannot easily interpret Anaé's ability to refer to displaced time, outside well-formatted situations.

At first glance, the story of the emergence of 'DISP' is very different from the one about time and situation types described in Section 3.1. We first explained how we frequently encountered situations in which the children produced words that could be interpreted as expressing time and various situation types. The regularity of these situations suggested to us that children might express these features without using the corresponding conventional language forms. It is much more difficult, however, to identify the 'DISP' value -actual displacement and lack of anchoring in the present situation -with certainty. The occurrences are much less frequent, and only the specific properties of the ongoing situation (story-telling, eating a meal, playing a specific game) allow the adult to resolve the intended referent and identify it as clearly displaced from speech time. When those properties are insufficient, the identification of a 'DISP' value depends on the presence of explicit linguistic marking in discourse, as shown in example (8). The child for all their feed-back during the research process. We are very grateful to our three anonymous reviewers for their constructive comments and tried to follow their suggestions. Any errors and other shortcomings are, of course, our own responsibility.