Amr Alzhouri Alyafi

Van Bao Nguyen

Yann Laurillau

Patrick Reignier

Stéphane Ploix

Gaëlle Calvary

Joëlle Coutaz

Monalisa Pal

Jean Philippe Guilbaud

From Usable to Incentive Building Energy Management Systems

Keywords: Contextual explanations, incentive system, persuasive technology, system intelligibility, humancomputer interaction, smart building, energy management

Reducing energy consumption is an individual and collective challenge that requires people to be proactive and fully involved. However, most approaches and solutions to this problem promote automated and autonomous systems that take full control of the decisions. Although these systems relieve users from setting the temperature in offices and homes, the level of thermal comfort chosen by the technology may not meet the individuals' requirements. Automating control is an obvious solution but it keeps the human out of the loop. In this work, an alternative approach is promoted based on system-human cooperation that allows people to take the final decision. However, to make sound decisions, users need to understand the system functioning and rationale and to be convinced and motivated to change their habits with regard to energy consumption. Our approach is based on an e-coach system, called Involved, that provides users with contextual explanations along with a user interface designed to persuade and keep the user involved. The results of this research are the development of an early prototype that provides end-users with a 24 hour-plan of recommended actions along with contextual explanations that justify each action. This plan satisfies the inhabitant's preferred compromise between thermal comfort, air quality and financial cost specified by the inhabitant (i.e. user) using a novel interaction technique, the Trade-Off-Pareto sliders. Users can edit the plan (e.g. suppress an action), skip some actions, perform additional actions, or even change their preferred compromise, and be informed in real time of the consequences on energy consumption and comfort.

Introduction

According to statistics from the French Ministry of Environment, Energy and Sea published in 2017 [START_REF]Chiffres clés de l'énergie -Edition 2016[END_REF], 45% of the total energy consumption in France can be attributed to the residential and tertiary sectors. In the global context of control and reduction of energy consumption, the residential sector is thus an important domain to consider. With poorly insulated houses, whatever the inhabitant does, energy is wasted. On the other hand, modern homes are increasingly efficient. They are equipped with complex heating and cooling devices and they are able to produce their own energy. As components of smart grids, modern homes will soon have to provide energy flexibilities to even more complex systems. As this occurs, the main source of energy waste and flexibility will not be the home per se, but inhabitants' inappropriate behaviors.

Traditional approaches to complex building management promote automation as a doing instead-of paradigm (i.e., the system has full control). Using a mathematical model of the thermal characteristics of the house and of its devices, optimization approaches based on objective functions typically generate a daily "Pareto optimal plan of actions" used as input by an energy manager to control the home. The plan is both "Pareto optimal" and "nonoptimal" as it is a compromise between some level of comfort and the amount of energy necessary to reach this level of comfort. From the end-user's point of view, the house acts autonomously. In addition, end-users might not understand the system behavior and even feel that they have to fight against their home to reach their objective. A typical example of this situation is a user who closes the blinds to adapt light conditions for watching TV. As a result, the system automatically switches the lights on, which is inappropriate in the current situation. Moreover, a couple of minutes later, the system may re-open the blinds to heat the room on a sunny winter day! Although the equations that model the home and the objective functions appear to be complete from the point of view of physics, they do not take into account human factors such as intentions. As a result, the system has nice properties from the theoretical perspective of energy consumption but may be inappropriate for the inhabitant's daily living.

Rather than doing instead-of, we promote a doing together approach where the inhabitant (i.e. user) is involved in the final decision and actions. However, sound decisions and actions require that users understand the system functioning and rationale. Users may not be able to answer questions such as "for better thermal comfort and heating performance, shall I shut the kitchen window now? When leaving for work in the morning, shall I switch off the heater and switch it on when I return, or shall I only decrease the temperature set point?"

In this article, we describe Involved, an e-coach that supports end-users in finding optimal compromises between tightly coupled, and possibly conflicting, criteria such as thermal comfort, air quality and financial cost. Based on the specification of user requirements, Involved is able to produce contextual recommendations for actions along with explanations presented in a suitable way. Using the Involved "what-if" feature, the user can edit the daily plan of recommended actions (such as suppressing the "Close the kitchen window by 10:00 am" recommendation) while being informed of the consequences on energy consumption and comfort. As demonstrated by Karsenty and Brézillon [START_REF] Karsenty | Cooperative problem solving and explanation[END_REF], it is reasonable to hypothesize that contextual explanations coupled with the capability to explore the possible configurations in a "what-if" manner will allow users to better understand the functioning and rationale of the energy management system, and, as such like nudges, will be prompted to act in a more virtuous manner while remaining motivated in the long run. Actually, Involved, as a proof of concept of persuasive e-coach, demonstrates a new interactor dedicated to navigating among conflicting criteria, as well as an explanation engine. The prototype is currently being tested with users. This article is structured in the following way: an overview of the background knowledge related to persuasive interactive systems is presented in the following section. Based on the models and design principles developed for supporting sustainable behavior change, the concept of explanation is presented in detail in Section 3. Involved is then described according to two complementary perspectives: the functional perspective with a focus on the generation of contextual explanations in Section 4, followed in Section 5 by the interactional perspective, with a focus on the user interface.

Persuasive interactive systems

Persuasive technology refers to "interactive technology that changes a person's attitudes or behaviors" [START_REF] Fogg | Persuasive Computers: Perspectives and Research Directions[END_REF]. According to Ajzen [START_REF] Ajzen | The theory of planned behavior[END_REF] attitude is one determinant for behavior whereas for Festinger [START_REF] Press | A Theory of Cognitive Dissonance | Leon Festinger[END_REF], behavior and attitude may both be changed for the sake of consistency. Fogg introduced the concept of captology to denote persuasive technology as a research area. Captology does not include computer-mediated persuasion nor non-intentional persuasion [START_REF] Fogg | Persuasive Technology: Using Computers to Change What We Think and Do[END_REF]. Oinas-Kukkonen and Harjumaa [START_REF] Torning | Persuasive System Design: State of the Art and Future Directions[END_REF] prefer the term Behavior Change Support Systems (BCSS). Contrary to captology, BCSS can play the role of a mediator between two persons. In both cases, coercion and betrayal are excluded from the field, for ethical reasons.

Persuasive interactive systems result from applying Persuasive Technology to the engineering of interactive systems. These systems are expected to sense inappropriate or undesirable behavior such as over smoking, and then enact functions, such as recommendations, suitable to support users' changes. The field draws upon a large body of models and theories such as the technology acceptance model [START_REF] Davis | Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology[END_REF], and the Motivation -Opportunity -Ability model [START_REF] Macinnis | Enhancing and Measuring Consumers' Motivation, Opportunity, and Ability to Process Brand Information from Ads[END_REF]. In the following, we will limit the presentation to two seminal models that currently serve as references for the development of interactive persuasive systems: the Fogg Behavioral Model (FBM) and the TransTheoretical Model of change (TTM). We will then summarize the design principles drawn from these models and illustrate the discussion with representative examples of persuasive interactive systems related to energy management and water usage. Fogg's Behavior Model characterizes human behavior according to three dimensions [START_REF] Fogg | A Behavior Model for Persuasive Design[END_REF]: motivation to adopt a particular target behavior, ability to perform the target behavior, and triggers. As shown in Figure1a, motivation and ability define a 2D-space where both human behavior and resistance to change can be characterized. Any trigger received by an individual when being above the activation threshold in the 2D-space should make this person adopt the behavior. In turn, motivation can evolve along three dimensions: pleasure/pain, hope/fear, and social acceptance/rejection. Learning new skills being not frequently accepted by people, ability can simply rely on the simplification of human behavior.

FBM and TTM: two reference models for persuasive interactive systems

The TransTheoretical Model of Change (TTM) [START_REF] Prochaska | In search of how people change. Applications to addictive behaviors[END_REF], [START_REF] Prochaska | The transtheoretical approach: crossing traditional boundaries of therapy[END_REF] decomposes behavior change into a 6-stage cycle (Figure 1b):

• Pre-contemplation: subjects are not considering the idea of change, maybe because they are unaware or not informed or possibly frustrated by a previous failed change attempt. They do not intend to take action in the next 6 months.

• Contemplation: subjects are aware that they should change behavior, and they consider to attempt the change in the next 6 months. In this stage, they try to get informed about the problem, but they are not ready to take a concrete action for changing.

• Preparation: subjects are ready to take change in the near future (usually measured as the next month), they are trying to develop a plan to take their first concrete action in the direction of change.

• Action: subjects have passed to action and have modified their behavior within the past 6 months.

• Maintenance: subjects try to keep the behavior change, and struggle to prevent relapsing. In case of failure at this stage, a relapse will occur and regress them to an earlier stage. They will have to restart the progress from one of the first stages.

• Relapse: subjects fail at the target behavioral change.

Persuasive design principles

According to Fogg, technology can play three roles [START_REF] Fogg | Persuasive Technology: Using Computers to Change What We Think and Do[END_REF]: as a tool, as a media, and as a social actor.

As a tool, technology can make activities easier or more efficient to perform. The corresponding design principles are then 'reduction', 'tunneling', 'tailoring', 'suggestion', 'monitoring' and 'self-monitoring', and 'conditioning'. In particular:

• Suggestion: persuasion power can be increased by offering suggestion about behavior change. As described in Section 5, one of the key features of Involved is its capacity to provide users with recommended action plans along with the appropriate contextual explanations;

• Monitoring and self-monitoring: technology "eliminates the tedium of tracking performance". As such, it serves as the basis for revealing behavior or for monitoring progress. Mirroring users behavior and their impact on comfort level and energy savings is part of the Involved solution;

• Conditioning: positive reinforcement can be used to "transform existing behaviors into habits".

As media, technology can shape attitudes and behaviors by providing compelling simulated experiences. The corresponding design principles are 'cause and effect', 'virtual rehearsal', 'virtual rewards' and 'simulations in real-world contexts'. For instance, Fogg [START_REF] Fogg | Persuasive Technology: Using Computers to Change What We Think and Do[END_REF] defines the 'cause and effect' principle as a means to persuade people for a change as simulation can make observable "the link between cause and effect". In Section 4, we will see how this "cause and effect" principle is applied to the generation of contextual explanations as well as the "what if" feature that allows users to simulate the effects of alternative behavior on energy consumption.

As social actor, technology persuades by giving a variety of social cues that elicit social responses from their human users. The corresponding design principles are 'attractiveness', 'similarity', 'praise', 'reciprocity' and 'authority'. Among these principles, focusing on mobility, 'social comparison' is another but related principle [START_REF] Fogg | Persuasive Technology: Using Computers to Change What We Think and Do[END_REF]: performance comparison with the performance of others can increase motivation. In its current version, the social dimension has not been investigated for Involved. On the other hand, special attention has been paid to 'attractiveness'.

Applied to a case study about water consumption, [START_REF] Arroyo | Waterbot: Exploring Feedback and Persuasive Techniques at the Sink[END_REF] identifies seven design principles: 'value-added design', 'automation', 'just-in-time prompts', 'positive reinforcement', 'negative reinforcement', 'adaptive interfaces' and 'social validation'.

In summary, the domain of persuasive technology is an active area of research with the development of a variety of theories, models and design principles. As discussed in sections 4 and 5, a number of these models and principles has been used for the development of Involved. The following sub-section briefly describes a subset of representative persuasive interactive systems for energy and water management. The Power-aware-cord [START_REF] Gustafsson | The Power-aware Cord: Energy Awareness Through Ambient Information Display[END_REF] (Figure 2a) uses a lighting electrical cord that makes the electricity flow tangible. The Water-Bot [START_REF] Arroyo | Waterbot: Exploring Feedback and Persuasive Techniques at the Sink[END_REF] (Figure 2b) is designed to encourage users to reduce water consumption by providing immediate feedback about water usage. A device attached to the faucet keeps track of water usage and reminds users to save water by changing the color of the water flow according to water usage. Petkov [START_REF] Petkov | Personalised Eco-feedback As a Design Technique for Motivating Energy Saving Behaviour at Home[END_REF] (Figure 3a) proposes an approach to reduce energy consumption based on possible savings. It presents the financial gain that users can obtain by using less energy. It also highlights the impact of energy consumption on health, resource, and environment. Using a clock-view representation, eForecast [START_REF] Kjeldskov | Eco-Forecasting for Domestic Electricity Use[END_REF] indicates the peak hours for domestic household as well as the green zone when electricity is cheap (Figure 3b). Elsmore et al. [START_REF] Elsmore | Neighbourhood Wattch -Community Based Energy Visualisation For The Home[END_REF] explore human behavior by combining two domains: energy and sobriety. As shown in figure 4a, the user interface shows 5 households where the overall result is conveyed by the color of the windows, while the number of trees and trashcans reflect electricity consumption and waste respectively. Ubi-green [START_REF] Froehlich | UbiGreen: Investigating a Mobile Tool for Tracking and Supporting Green Transportation Habits[END_REF] uses the metaphor of a Polar bear standing on an iceberg to illustrate household consumption (Figure 4b). The objective is to keep the polar alive and to improve the ecosystem. Informative art is also considered for integrating "information visualization in the everyday human environment" [START_REF] Holmquist | Informative Art: Information Visualization in Everyday Environments[END_REF] (e.g. Mondrian's style for a weather display). In the context of physical activities, it has been found [START_REF] Fan | A Spark of Activity: Exploring Informative Art As Visualization for Physical Activity[END_REF] that aesthetic informative art is motivating and engaging to glance at a display. Also, in the field of persuasive technologies, paintings are investigated to convey emotions about behavior change such as the Mona Lisa Bookshelf [START_REF] Nakajima | Designing motivation using persuasive ambient mirrors[END_REF]. According to Fogg's Behavior Model (FBM) [START_REF] Fogg | A Behavior Model for Persuasive Design[END_REF], the informative art approach could increase motivation as it is related to several motivational factors: pleasure factor increased by the aesthetic aspects; hope and fear factors impacted by the utility services such as current time (e.g. hope to be on time, fear being late) or current weather (e.g. hope having a sunny day). Furthermore, in terms of operant conditioning, a changing aesthetic could be considered as a reward for our past actions. According to the TTM [START_REF] Prochaska | In search of how people change. Applications to addictive behaviors[END_REF], [START_REF] Prochaska | The transtheoretical approach: crossing traditional boundaries of therapy[END_REF], it would support the transition between the pre-contemplation stage to the contemplation stage as well as the maintenance stage (i.e. to maintain interest over time).

Examples of persuasive interactive systems for energy and water management

All of these systems have limitations. First, behavior change is a long-term process rather than a single event [START_REF] Prochaska | In search of how people change. Applications to addictive behaviors[END_REF], [START_REF] Prochaska | The transtheoretical approach: crossing traditional boundaries of therapy[END_REF]. The Power-aware-cord and the WaterBot can only be effective at the TTM Pre-Contemplation stage, as they seek to plant a seed into the user's mind by visualizing energy consumption. Such systems are unlikely to be effective to motivate users to commit to long lasting virtuous behavior.

The second problem relates to motivation incentive in behavior change. Petkov uses potential savings as motivation incentive. However, financial incentive does not lead to sustainable behavior change [START_REF] Petkov | Personalised Eco-feedback As a Design Technique for Motivating Energy Saving Behaviour at Home[END_REF]. Moreover, when the cost of energy is low compared to the individual's income, the motivation is unlikely to be effective. As a consequence, e-Forecast is unable to provide a sustainable solution.

Third, the use of social influence and value-centered design [START_REF] Cockton | A Development Framework for Value-centred Design[END_REF] in energy persuasive systems is mentioned but still remains scarcely exploited. Elsmore et al. explore how community affects individual changes while Ubi-green considers the intrinsic values [START_REF] Ryan | Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being[END_REF] of humans as the key factor to raise awareness about energy consumption. However, like the Elsmore's system, Ubi-green mainly focuses on comparison between households. Some participants will consider the system as a competition resulting in a variety of objectives: some will try to win while others may do whatever it takes to not finish last. In Ubi-green, the possibility of raising altruistic values is presented. The fact that some participants may hold it as a game will negatively impact the original aims of the application.

Last, but not least, user interaction is limited in all of these systems. They make energy visible, but do not support "what-if" interactions. FigureEnergy (Figure 5) [START_REF] Costanza | Understanding domestic energy consumption through interactive visualisation: a field study[END_REF] moves from user interfaces to user interaction, making it possible for the end-user to play with the system.

Explanations and causality

Explanations play different roles and take a variety of forms. Already addressed in the previous section about persuasion, causality is also an important concept involved in the production of explanations. These aspects are discussed successively in this section with a particular focus on the problem of elaborating a formal model of causality from sensory data. This section closes with the qualities that explanations should satisfy.

Explanations in Knowledge Based Systems

The 80's have seen the rise of expert systems (and more generally knowledge-based systems or KBS) and their adoptions in corporations as part of the information system. Expert systems are usually based on an explicit high-level symbolic knowledge database and an inference engine to exploit them. They are able to answer questions and take decisions in their expertise domains. And beyond the decision-making aspect, the question of the generation of corresponding explanations was quickly raised and became an important field of study (see [START_REF] Gregor | Explanations from Intelligent Systems: Theoretical Foundations and Implications for Practice[END_REF]- [START_REF] Paris | Generation and Explanation: Building an Explanation Facility for the Explainable Expert Systems Framework[END_REF] for instance).

Gregor and al. [START_REF] Gregor | Explanations from Intelligent Systems: Theoretical Foundations and Implications for Practice[END_REF] stated that explanations in intelligent systems are important for several reasons. An expert user trusting its KBS will need explanations from the system mainly when he will detect anomalies, (when he will disagree with its propositions). At contrary, a novice user will use more the explanation capacity of the system but with a short-term or long-term learning objective. By providing explanations, a system becomes more transparent. It will also appears more competent and trust in an automated systems is related to user's perception of its competence (see [START_REF] Muir | Trust in automation. Part II. Experimental studies of trust and human intervention in a process control simulation[END_REF] for instance).

Explanations are also required by the users when they will lack some knowledge needed to contribute properly in a problem-solving process. Both the KBS and the user cannot solve the problem alone but they have to co-operate. Users have their own expertise that may differ from the expertise of the KBS. And they know the context where the problem occurs. "Computational technology should be used, not to make or recommend solutions, but to help users in the process of reaching their decision" [START_REF] Karsenty | Cooperative problem solving and explanation[END_REF]. This is what Woods and al. called a "Joint Cognitive System" [START_REF] Woods | Cognition, Computing, and Cooperation[END_REF]. The system and the user are engaged in a cooperation process relying on explanations.

Karsenty and Brézillon have studied cooperative dialogs in natural working conditions [START_REF] Karsenty | Cooperative problem solving and explanation[END_REF]. Two different types of dialogs were considered: validation dialogs and design dialogs. Validation dialogs are between an expert and a user. The expert is proposing a solution validated or modified by user. Expert and user have complementary knowledge: the expert have the technical knowledge and the user have the domain expertise. In design dialogs, a first solution is not proposed by one of the experts but the preliminary solution is proposed from the problem definition by a close cooperation between both, each one bringing its technical expertise.

Context plays a central role in the man-system cooperation process when solving a problem. It's an important element to produce more pertinent explanations and thereby, enhancing cooperation. Defining context has been a challenging problem for the last 20 years (see [START_REF] Brézillon | Context in Human-Machine Problem Solving: A Survey[END_REF] for instance for an early survey). Its definition may even depends of the context [START_REF] Brézillon | CONTEXTUAL KNOWLEDGE SHARING AND COOPERATION IN INTELLIGENT ASSISTANT SYSTEMS[END_REF]. In the ubiquitous computing domain, Dey has proposed a definition focusing on man-machine interaction: « Context is any information that can be used to characterize the situation of an entity. An entity is a person, place, or object that is considered relevant to the interaction between a user and an application, including the user and applications themselves » [START_REF] Dey | A conceptual framework and a toolkit for supporting the rapid prototyping of context-aware applications[END_REF]. Context can be both considered from a representational or interactional point of view [START_REF] Brézillon | CONTEXTUAL KNOWLEDGE SHARING AND COOPERATION IN INTELLIGENT ASSISTANT SYSTEMS[END_REF], [START_REF] Dourish | What we talk about when we talk about context[END_REF]. Context as representation is an information. It can be separated from activity. Context elements can be selected and described before the interaction occurs and are not modified by the interaction: activity happens within the context [START_REF] Dourish | What we talk about when we talk about context[END_REF]. Context as interaction is a relation between activities or objects. It only exists during the interaction (task or problem solving) and evolves dynamically.

As we have mentioned in the introduction, building a fully automated energy manager (doing instead) may be inappropriate for users. We are in the same situation as described by Woods and al. or Karsenty and al.: the system has some knowledge and competence to solve the problem, with the notable difference that this knowledge is numerical (physical knowledge, optimization capabilities etc.) and not symbolic and so more intelligible as in the studies cited above. The user has its own and complementary knowledge (like his own perception of comfort, his intentions etc). The system nor the user can solve individually the whole problem but they have to cooperate (joint cognitive system). And this cooperation corresponds to what Karsenty and al. have described as a validation as opposed to a design dialog [START_REF] Karsenty | Cooperative problem solving and explanation[END_REF]: the expert has the technical knowledge, the user as the domain knowledge. The expert is proposing a solution that is accepted or modified by the user who makes the final decision.

Cooperation is based on explanations. On a fully cooperative system, the e-coach is modifying the user's perception of the problem but there is also the reciprocity [START_REF] Karsenty | Cooperative problem solving and explanation[END_REF]. The user can modify the e-coach by providing his own explanations to the system. The approach we are presenting in this paper is focusing on the first aspect. The e-coach is making propositions (energy plans) and provides explanations. We have not considered yet the user feedback modifying the e-coach perception of its environment.

In the next sections, we will first make a quick review of various forms of explanations. We will then present our approach for generating explanations from the observed data in a smart home.

The roles of explanations

An explanation is a communication act between one or several persons. Its main objective is to directly increase the comprehension of the receiver. Beyond direct knowledge increase, an explanation may have several other objectives, as stipulated in [START_REF] Keil | Explanation and Understanding[END_REF] (a survey article that has mainly inspired this section):

• To be able to predict similar events in the future [START_REF] Heider | The Psychology of Interpersonal Relations[END_REF].

• To be part of a diagnostic process [START_REF] Graesser | How does one know whether a person understands a device? The quality of the questions the person asks when the device breaks down[END_REF]. Diagnosis is used to repair a malfunctioning system. It can also be used to reinforce an efficient or inefficient action to solve a particular problem. This association may help to choose, or not to choose, the same action(s) to solve the same problem in the future. • To justify an action.

All of these objectives, except the "diagnostic process for repair", are relevant to our goal. Helping users to predict the future and emphasizing the efficiency of their actions will help them to act correctly in similar situations.

Different forms of explanations

Historically, explanations, as a scientific domain, were primarily studied in social sciences (behavior explanations) and in philosophy (scientific explanations) [START_REF] Lombrozo | The structure and function of explanations[END_REF]. For instance, Aristotle identified two types of scientific knowledge: the "knowledge about that" and the "knowledge about why". "Knowledge about that" is descriptive whereas "knowledge about why" is explanatory. "It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why" [START_REF] Salmon | Four Decades of Scientific Explanation[END_REF].

Aristotle considered that a scientific explanation should be a list of deductive arguments. This early influential vision has led to the widely used Deductive-Nomological model (D-N) [START_REF] Hempel | Studies in the Logic of Explanation[END_REF]. A D-N model of explanation is similar to a logical proof. It involves three sorts of statements: statements about the initial conditions, statements about laws and theories (both of them being called the explanans), and the observed statements that describe the phenomena to be explained (the explanandum). The explanandum is validly explained if it can be validly deduced from the explanans and the explanation is the deduction. In this process, all the statements must be true: the explanandum (which is obviously true because it is observed), the initial conditions and the laws. For instance, "all gases expand when heated under constant pressure" is a law. An initial condition can be "a bladder balloon is heated" and the observation is "the size of the bladder balloon is increasing". The observation can be deduced from the initial condition and the law is the explanation. One of the limitations of this approach is the definition of the "law". A law should be a true generalization that does not suffer exception. Typically, a probabilistic phenomenon is not qualified as a law. The singular causal explanation of Michael Scriven [START_REF] Scriven | Explanations, Predictions, and Laws[END_REF] is also an example of a statement that will not meet the law criterion because it is not a generalization: "the impact of my knee on the desk caused the tipping over of the inkwell".

New models of explanations have then been proposed to address the limitations of the D-N model. In particular, the logic formalism has been relaxed toward a variety of forms including textual representations, diagrams, and simulations. These forms may not capture the full complexity of a phenomenon but they serve as useful approximations of a phenomenon. Here, causality plays a central role.

Causality is usually present in every-day life explanations. Philosophers of science have used this notion to illustrate why some things explain others and not the opposite. Causal relationship can be deterministic (like 2 pieces of a mechanism), or probabilistic (as in economy, psychology, etc.). However, explanations do not rely solely on causal relationships. For instance, one can explain how a mathematical result is achieved, or why China is bordered by 14 different countries [START_REF] Keil | Explanation and Understanding[END_REF]. Nevertheless, when both causal and noncausal elements are present in an explanation, the causal elements dominate the patterns of judgment [START_REF] Murphy | The role of theories in conceptual coherence[END_REF].

There are at least four kinds of causal explanations:

• Common cause. The same cause has several effects, like a cold may cause fever and stuffy nose. It is often used in diagnosis.

• Common effect. Several causes converge to the same point. This is often the case in History. For instance, World War I was not caused only by the murder of François Ferdinand.

• Linear chain. There is a unique series of steps between an initial cause and a final effect. Linear chains are easy to understand but not very frequent in real life.

• Causal homeostasis. This is a causal relation that forms a stable cycle that reinforces itself.

Another way to differentiate various types of explanations (D-N, textual, causal, a-causal, etc.) is the use of stances [START_REF] Dennett | The Intentional Stance[END_REF]. A stance is one way to set the frame for an explanation. A stance can be mechanical, design or intentional. The mechanical stance considers that the phenomenon to explain is composed of entities and is the result of their organization and interactions [START_REF] Bechtel | Explanation: a mechanist alternative[END_REF]. The explanation can be the mechanism itself (ontic) or the description of the mechanism (epistemic) [START_REF]Mechanistic Explanation: Ontic vs Epistemic[END_REF]. The design stance considers that entities have functions and have been created on purpose. The explanation is based on that purpose and not on the mechanical functioning of the entity. Finally, in an intentional stance, the entity whose behavior is to be predicted is treated as a rational agent which, given its supposed beliefs and goals, will very likely act in order to reach these goals.

Our primary objective is to help users to better understand how they can modify their behavior and how they can improve their decisions with respect to their own comfort criteria. Due to the complexity of the building physics as well as to unconscious routines, users have difficulties in understanding what is happening and why they need to change their routines to improve their comfort, or how to make appropriate compromises between comfort and cost. Users do not need explanations as logical proofs (D-N), but as approximations that provide them with sufficient information about the current phenomena (epistemic mechanical stance). Explanations must not be generic but strictly related to their behavior as well as to the characteristics of their housing. As mentioned above, causality plays a central role. Generation of contextual and causal explanations is therefore at stake.

From sensory data to causality

End-user's housing is equipped with sensors that measure environmental variables such as temperature, humidity, CO2 level, weather conditions, and the number of persons in a room. Sensors also measure the user's actions such as turning on the heater or opening doors and windows. In our case, generating an explanation requires the analysis of the data flow provided by the sensors as well as the identification of the causal relationships between the actions of the users and variation of the environmental variables. In the next part of this section, we will considerer that a phenomenon is the value or the variation of the value of a variable. Some of the phenomena might be characterized as causes, some others as effects of these causes.

Problem statement

Causality from sensory data is difficult to model mathematically. Effects can be directly observed, but causal relationships cannot. Considering phenomena as events, a cause (C) always precedes the observation of an effect (E) but an effect (E) observed after (C) and correlated with it, does not necessarily mean that (C) is the cause for (E). The "car allergic to vanilla ice cream" scenario illustrates this case [START_REF]Help! My car is allergic to vanilla ice cream; a study in problem solving. The complete case -Kepner-Tregoe[END_REF]: a man used to buy ice cream after dinner for his family. He complained to General Motors that every time he would buy vanilla ice cream, he had difficulties to start the car engine (other ice cream flavors were fine). General motors engineers finally found that the cause of the problem was vapor lock. Actually, it took less time to buy vanilla ice cream than for other flavors. As a result, the engine remained too hot for the vapor lock to dissipate. The co-occurrence of buying vanilla ice cream and the car not starting did not mean that buying vanilla ice cream was the cause of the car failure.

As illustrated in Figure 6, the co-occurrence (with a potential time delay dt) of 2 phenomena calls for several interpretations: precedence only (6a), direct causal relationship (6b), consequences of a third phenomenon that may be outside of perception (6c). For instance, having the flue may first cause fever and then coughing. Ignoring the existence of viruses may lead to believe that fever is the cause for the cough.

Building a causal model from a bottom up approach?

Extracting a causal model solely from time-correlated observations is a promising approach to the elaboration of a truly adaptive system. As almost no initial expert knowledge is necessary (everything is extracted from the data flow), such a system can be deployed in any housing and can learn a model of the environment from its interactions and observations. Constructivist or Developmental Artificial Intelligence is an example of such approach. It has been originally applied to robotics but there are some examples in the context of ambient intelligence (see [START_REF] Mazac | Approche décentralisée de l'apprentissage constructiviste et modélisation multi-agent du problème d'amorçage de l'apprentissage sensorimoteur en environnement continu[END_REF] or [START_REF] Najjar | Constructivist Ambient Intelligent Agent for Smart Environments[END_REF] for instance).

However, learning a causal model from a purely bottom-up approach is a complex task. In particular, one cannot be sure that all the necessary phenomena are observed in order to infer "common cause" causal relations. For a common causal relation (Figure 6c), is it necessary to find the common cause. If this common cause cannot be determined or observed, we might conclude the existence of a direct temporal relation between the two phenomena (as for Ph1 and Ph2 in Figure 6b). Direct relations are helpful for predictions. If Ph1 is observed, it is known that Ph2 will then be observed. But because one have a partial view of the world, one cannot predict when this relationship might fail. In addition, since the model is based on observations but not intrinsic to a mechanism, it cannot be used to determine which external intervention will modify its behavior. For instance, it can be observed that every morning, the rooster wakes up, sings and soon after, the sun rises. There is of course no direct causal relationship between those phenomena but it can be used to predict sun rising. Even so, there is no point in waking up the rooster earlier to get a longer day.

Injecting knowledge in the building process

Complexity rises from the size of the possibility space (all the possible causal models to explain the observed phenomena). One open question is how our brain is able to build complex representations with just sparse data? As stated by Tenenbaum et al. [START_REF] Tenenbaum | How to grow a mind: Statistics, structure, and abstraction[END_REF], "yet children routinely infer causal links from just a handful of events [START_REF] Gopnik | Mechanisms of theory formation in young children[END_REF], far too small a sample to compute even a reliable correlation!". As suggested by Plato, another source of information (as abstract background knowledge) must be available to help this inductive learning process. "Psychologists and linguists speak of constraints; machine learning and artificial intelligence researchers, inductive bias; statisticians, priors." [START_REF] Tenenbaum | How to grow a mind: Statistics, structure, and abstraction[END_REF]. This abstract knowledge, or over-hypothesis, restricts the hypothesis or the model space at a less abstract level, reducing the complexity to find an appropriate model for explaining the data. Where does this over-hypothesis come from? Some authors suggest that over-hypothesis can be learned simultaneously with the model (the blessing of abstraction as opposed to the curse of dimensionality) using, for instance, hierarchical Bayesian approaches [START_REF] Tenenbaum | How to grow a mind: Statistics, structure, and abstraction[END_REF], [START_REF] Goodman | Learning a theory of causality[END_REF], [START_REF] Kemp | Learning overhypotheses with hierarchical Bayesian models[END_REF] . Hierarchical Bayesian approaches are relevant in the context of our work. One of the problems with these techniques is the quantity of data needed to obtain good results. Data is specific to every housing and cannot be easily mutualized. It is sparse and it may be necessary to have the system initially running for a long period of time to acquire enough data to get an initial usable causal model. As a result, the use of a knowledge model of the environment as a high-level predefined expert knowledge has to be investigated.

In the context of our work, a knowledge model is a set of equations that describe a housing, modeling the thermal properties of the walls, floors and ceilings in terms of thermal resistance and thermal inertia, windows surface areas and orientation, etc. These models are able to predict the evolution of the physical variables (e.g. inside temperature, CO2 concentration and humidity), by considering the value of these variables at the previous time step as well as the value of other environmental variables such as weather conditions, doors and windows opening. These thermal models rely on the analogy with electrical circuits. For instance, electrical resistance and capacitance represent thermal resistance and inertia. The electrical circuit is based on the characteristics of the housing. The CO2 model is a differential equation that uses room volumes, number of occupants and CO2 concentration on adjacent rooms. The various parameters of the thermal models are determined using genetic algorithms to fit the measurements of the sensors [START_REF] Scanu | Model Tuning Approach For Energy Management Of Office and Apartment Settings[END_REF].

Quality of an explanation

Keil and al [START_REF] Keil | Explanation and Understanding[END_REF] propose three dimensions to evaluate the quality of an explanation: circularity, relevance, and coherence. Others such as Kim et al. refer to the credibility of an explanation [START_REF] Kim | From symptoms to causes: Diversity effects in diagnostic reasoning[END_REF].

• A circular explanation is an explanation where the conclusion is used as part of the explanation. For instance, "This diet pill works because it helps people lose weight" (extracted from [START_REF] Keil | Explanation and Understanding[END_REF]). Complex circularities might be difficult to detect [START_REF] Rips | Circular reasoning[END_REF].

• Considering an explanation as a speech act, an explanation is relevant for a given goal if it has the appropriate level of details while not providing unnecessary or unrelated information. Particular care must be taken against ego-centrism as explanations may be based on what we believe the other person knows: the estimation of the other person's knowledge is often extrapolated from our own level of knowledge [START_REF] Nickerson | The Projective Way of Knowing: A Useful Heuristic That Sometimes Misleads[END_REF], which could be misleading, resulting in irrelevant explanations.

• Coherence means that the explanation is composed of a set of elements with some of them positively constraining others toward the effects.

The credibility of an explanation is related to the causal structure and is called "the causal diversity effect" [START_REF] Kim | From symptoms to causes: Diversity effects in diagnostic reasoning[END_REF]. A single cause might create several effects that in turn create several effects, etc., resulting in a causal tree. The causal diversity effect indicates that the further apart are two final effects in the tree, the more they are considered as a good justification of the initial cause. In 1847, the philosopher of science, William Whewell, called this "consilience" [START_REF] Whewell | The philosophy of the inductive sciences, founded upon their history[END_REF].

Another concept related to the evaluation of explanations, is the Illusion of Explanatory Depth (IOED). The IOED refers to the fact that people usually think, after having received an explanation about a system, that they understand it deeper than they really do [START_REF] Rozenblit | The misunderstood limits of folk science: an illusion of explanatory depth[END_REF]. Rose et al. have shown that the more people see or visualize a system component, the more they build mental simulations, and the more they believe they understand it.

Having presented the background knowledge related to persuasive technology and explanations, we now turn to the description of the Involved e-coach system, starting with the generation of explanations.

Generation of explanations in the Involved e-coach system

To illustrate our approach, we will use our laboratory office as a real life experimental setting. This office is a single room with two outside windows, an inside window and an inside door connecting to an adjacent corridor. It is equipped with 27 sensors: doors and windows contact sensors, CO2 concentration, temperature within the office, in the adjacent corridor and outside, humidity, power consumption, etc. The office layout and the corresponding physical model are shown in Figure 7. The equations of the housing model are elaborated by experts whose goal is to predict the evolution of physical variables, not to model causality. These equations, which are not designed to produce explanations, do not represent causal relationships explicitly. As a result, causal relationships cannot be determined automatically from the analysis of the equations. The following example illustrates the difference between a causal model (represented as a diagram) and a mathematical equation (extracted from [START_REF] Pearl | The Art and Science of Cause and Effect[END_REF]). Two representations of a mechanism are considered: a set of two equations and a diagram that represents a chain of transformations (first, a multiplier, then an adder) between 3 variables (X, Y, Z), going from X to Z:

The equations and the diagram are not equivalent representations. The two equations above can be transformed into two equivalent mathematical equations that now correspond to the following new mechanism: a subtractor followed by a divider, going from Z to X.

Finally, the first two equations and the second two equations can be summed up, providing 2 new mathematically equivalent equations shown below. These two new equations represent constraints on the X, Y and Z but do not provide any indication about how they influence each other.

More precisely, consider an external intervention that imposes Y=0. This post intervention can be modeled by adding a new constraint Y=0, imposing Z=1 (Eq 1). It can also be easily modeled in the second mechanism by imposing X=0 (Eq 2). However, if Y=0 is enforced in (Eq 3), nothing can be concluded for X and Z

The example above shows that causality cannot always be extracted from a formal analysis of the equations of the housing model. Instead, causality must be elicited by making virtual experiments on the mechanism described by these equations. Making a virtual experiment means defining a scenario, selecting variables values (e.g. outside temperature) and use the physical equations to compute the missing values like air flow, heat flow, etc. The goal is to extract useful information from different measured and computed data and to represent them in a way that makes sense for the user.

In the next two sections, the virtual experiment approach is presented to generate direct differential explanations as well as differential explanations with influence.

Direct differential explanations

To reduce the risk of false causalities or circular explanations, the available variables modeling phenomena have been organized into four groups (see Figure 8):

• Action: list of user's actions on the environment that have an impact on the comfort level (in our experimental setting, opening/closing doors and windows). Door or window opening is the percentage of time a door or a window has been opened during a one-hour time slot.

• Context: context can be representational or interactional [START_REF] Brézillon | CONTEXTUAL KNOWLEDGE SHARING AND COOPERATION IN INTELLIGENT ASSISTANT SYSTEMS[END_REF], [START_REF] Dourish | What we talk about when we talk about context[END_REF]. There is no absolute definition and it depends of the context of the problem. A representational approach has been selected because it is related to the current setting state. The ecoach context contains variables having a role in the final decision while ensuring the stability property, that is not modified by the user energy related decisions. It is for instance the outside temperature Tout, the solar intensity, the temperatures in the neighbor zones (e.g. temperature of the corridor Tcor), the number of occupants, etc... A sequence of actions executed on two days but in a same context should have the same result. Opening the window on two similar summer days will have the same effect: heating the room. Opening the window on a summer day or a winter day will have opposite effects.

• Intermediate: these variables are either measured (e.g. indoor temperature Tin, CO2 concentration) or estimated like the heat flow and air flow. These variables correspond to what physicists consider to be important in the causal chain.

• Effect: the conclusion of explanations directly related to human perceptions (indoor temperature and air quality, costs). These are the variables such as thermal dissatisfaction and air quality dissatisfaction experienced by the users.

Natural tendency of causal relations between the groups of variables are also predetermined as expert abstract knowledge [Tene11].

Figure 8. Variable categories and main causal relations

Users may not act "optimally" with respect to their own comfort criteria. In energy management, optimality is defined as "Pareto optimality" where any criterion (or objective) of a multi-criteria optimization problem cannot be minimized without increasing the others. In other words, compromises have to be made between conflicting criteria. In energy management, comfort levels and energy and environmental costs are typical conflicting criteria. For example, in winter, absence of heating would be optimal with regard to cost but not acceptable in terms of thermal comfort. As another example, good air quality may imply opening the window which in turn may lead to poor thermal comfort in winter and high energy cost. Our hypothesis is the following: by generating "differential explanations", endusers will be able to find the preferred optimal tradeoff between conflicting criteria. A differential explanation is constructed by analyzing the difference between two scenarios defined in a same context (scenarios are said context-similar) for the sake of meaning: (1) a past scenario for instance can be compared with an alternative scenario, possibly optimal, or (2) a forecasted scenario compared with an alternative scenario. The main objective is to evaluate the difference of perceptions associated to the difference of actions between both scenarios (the difference of perceptions is the difference of effects associated to the difference of actions because both scenarios are in the same context). By carefully selecting the two scenarios that are compared, various explanations can be computed. The two following scenarios are firstly be considered: the "history recorded scenario" includes: (1) the set of actions performed in real life by the users during the day (doors and windows opening in our experimental setting), (2) contextual environmental information (weather, time, etc.) and (3) measured effects (air quality and temperature). The "Pareto optimal scenario" is selected from the Pareto front, i.e. from the set of optimal solutions computed using a differential approach for the following criteria: air quality, thermal comfort, and energy cost (see [START_REF] Pearl | The Art and Science of Cause and Effect[END_REF] for details). 2. Difference in terms of effects: the difference on air quality and temperature comfort for each corresponding time slot of scenario 1 and scenario 2.

3. Difference in terms of intermediate effect variables. Some of the intermediate effect variables (e.g. air or heat flow) are not directly measured by sensors. Therefore, they are not available in the "History recorded scenario". Instead, we draw on the the physical model, which uses sensory data as input, to estimate the intermediate effect variables.

It is then necessary to transform the quantitative values into qualitative information. For instance, the sentence "shutting the door at 2pm will cause an important decrease of the airflow and a significant decrease in the air quality level" is easier to understand than "a difference in airflow of 30% will lead to a difference in CO2 concentration of 400 ppm (parts per million)". The transformation from quantitative data to qualitative information is performed by dividing the value domain of a variable into 7 sub-domains (3 positive, 3 negative and 1 no-change levels). An example of the differences between the "history recorded scenario" and the "optimal Pareto scenario" is illustrated in Figure 9. The explanation that can be extracted from the difference between the history-based and the Pareto-optimal scenarios is what Aristotle called "knowledge about that". It is descriptive, not causal. For instance, from 8 am to 12 am, the system points out that the windows and doors should have been opened for a longer, or a shorter, period of time. At 12 am, the temperature and air quality would have been increased but there is no explicit link between these two. This explanation informs the users about how they should change their behavior along with the gain they can expect from this change. On the other hand, the explanation does not provide any indication about which action is really responsible for a given effect. For instance, is it really important to close the door between the office and the corridor between 10 am and 11 am? If the end-user is out of the office at this time and if he does not intend to come back to close the door, will it ruin the air and comfort qualities later in the day? To answer these questions, we need to go deeper in the explanation process and compute the impact of each action and its resulting effects. This problem is addressed with "differential explanations with influence".

Differential explanations with influence

The actions proposed by the system in the previous section do not have the same importance in terms of impact. Some of them might be skipped if necessary, some of them should be performed because of their strong influence on a particular criterion. To evaluate the influence of an action A, we compute the difference between the Pareto optimal scenario and the Pareto optimal scenario where A is replaced by the action that has been performed effectively by the user. Both scenarios are simulated using the physical model of the housing. The difference between the effects indicates the influence of not performing the recommended Action A. The result of this influence computation is displayed in Figure 10. Using the equations of the knowledge model, it is possible to generate cause-effect relations between actions and final effects, but the causality between the different levels of the intermediate variables and the final effects are unreachable because their changes cannot be monitored with a knowledge model (see figure 11). Knowledge model are based on physics (see [START_REF] Scanu | Model Tuning Approach For Energy Management Of Office and Apartment Settings[END_REF] for instance). Integrating relations between the intermediate and the final variables is important to provide users with complete explanations. This can be achieved by injecting expert knowledge in terms of rules that represent potential causalities as well as impossible ones. For instance, heat flow may have an influence on air temperature but not on CO2 concentration. This can easily be done because the expert has a very good knowledge about the nature of those variables.

By integrating calculated influence and potential influence, a full diagram for the whole system can be automatically elaborated. Part of this diagram is represented in figure 12.

Natural language text generation

Reading complex tables and graphs such as those presented in Figures 10 and12, may be a rather abstruse experience for the user. Users may prefer statements expressed in natural language provided that these statements are well written and smart enough such as not using the same wording repeatedly.

Natural Language Generation (NLG) is a Natural Language Processing (NLP) sub-field concerned with the generation of texts from non-linguistic data [START_REF] Reiter | Building Applied Natural Language Generation Systems[END_REF]. Typical systems take a high-level representation of input data, select and structure the final information to convey (macro-planning), make a lexical and syntactic transformation to this structured information (micro-planning) and to finally linearize it as text (surface generation). This classical pipeline has mainly been approached by expert and grammatical rules [START_REF] Portet | Automatic Generation of Textual Summaries from Neonatal Intensive Care Data[END_REF], statistical models [START_REF] Mcintyre | Learning to Tell Tales: A Data-driven Approach to Story Generation[END_REF] or machine learning [START_REF] Vinyals | Show and tell: A neural image caption generator[END_REF] in areas as diverse as complex medical data summarization [START_REF] Portet | Automatic Generation of Textual Summaries from Neonatal Intensive Care Data[END_REF], prose generation [START_REF] Mcintyre | Learning to Tell Tales: A Data-driven Approach to Story Generation[END_REF] or image captioning [START_REF] Vinyals | Show and tell: A neural image caption generator[END_REF].

A NLG system is both a dialogue system and a Machine Translation (MT) system. Most recent stochastic MT systems perform NLG through shallow language models but there are also MT systems that propose deep general-purpose NLG module using a high-level internal representation. This high level internal representation is extracted from a linguistic analysis of the target language analysis and used to generate a text that complies with its grammar rules.

We have chosen the Ariane-Heloise MT system, a reengineering version of the widely known Ariane MT system [START_REF] Boitet | DSE-1'-Le point sur ARIANE-78 début 1982[END_REF]. Ariane-Heloise links together several transducers that transform a source text into a decorated tree, then transform this tree into a linguistic tree structure, and generate a target text from this structure. During the process, various linguistic operations are carried out: morphological and structural analysis, lexical transfer, syntactic and morphological generation. The decoration of each node of a tree is a combination of values for a set of declared variables and allow for coding linguistic properties and relations. The following is an example of a generated textual explanation (in French): "Dans le créneau horaire 12h-13h, si vous aviez laissé la porte ouverte beaucoup plus longtemps, le confort thermique aurait augmenté beaucoup, la qualité de l'air un petit peu et le créneau 13h-14h aurait été impacté, il y aurait eu un courant d'air sensible vers le couloir". More details can be found in [START_REF] Alyafi | Explanations engine for energy management systems in buildings[END_REF].

Interaction with the Involved e-coach system

Given the explanation engine presented above, a user interface is mandatory to convey the explanations and to support the user in the energy management process. However, information display and interactivity are not enough to involve the user in such a process. If the user is unaware, or not motivated, or unable to control her/his energy consumption, such a system is useless. Therefore, a user interface has been designed for Involved that supports awareness, aiming at persuading and helping users to change their behavior in order to reduce their energy consumption while feeling comfortable. In the following, we focus on such a user interface and illustrate our design principles. The user interface of Involved is intended to be deployed on a tablet installed on a wall of the living room or in the entrance hall. Thus, several issues have to be considered: (i) standing in front of the tablet may not be comfortable compared to sitting at a desk; (ii) depending on the period of the day, the user may not be available to interact with the system (e.g. leaving home in a hurry to go to work); (iii) over time, users may not pay attention to the device any more.

User interface requirements

To address these issues, the user interface (UI) must satisfy the following two design requirements: (R1) The UI must catch the eye; (R2) Multiple levels of interaction for different contexts of use (e.g. key moments of the day) must be supported. According to FBM (cf. Section 2), these two requirements aim at maintaining motivation and ability high. For example, by embedding utility functions such as time and weather forecast, the UI should catch the eye for key moments of the day (e.g. looking at the clock before leaving home). Consequently, it should maximize (i.e. make the user aware of) the persuasive features of the systems such as reminders of actions to reduce energy consumption as well as greetings and rewards in order to maintain appropriate behaviors.

Designed for daily life: catching the eye, at the right time (R1)

One compelling approach to potentially impact the motivation of individuals is to offer an interactive system for daily life. Our suggestion is to bring daily activities and objects such as consulting time, checking weather or decorative elements into the UI. Figure 13 illustrates the design concept in a "Mondrian" style. To satisfy requirement R1, it is hypothesized that an artistic-like user interface (e.g. a painting) that embeds daily utility services (e.g. a clock) would catch the eye at any moment of the day and be attractive. The location of the device is also important. In their long-term field study of the Digital Family Portrait1 , Rowan and Mynatt [START_REF] Rowan | Digital Family Portrait Field Trial: Support for Aging in Place[END_REF] installed the device at the entrance of the participant's kitchen. They observed that the choice of the location was key to be readily visible and therefore, effective.

Three levels of user interaction for three contexts of use (R2)

To meet requirement R2, the user interface has been designed to support different contexts of use. Here, "context of use" is defined as "time or period of the day, and user's expertise and interest in energy management". Depending on the moment of the day, users may not have enough time to use the system. Therefore, the UI must be designed to support very brief user interactions as well as longer periods of interaction. We hypothesize that such an adaptation to the context of use is a means, according to the FBM, to increase ability as well as motivation by providing customized messages such as explanations. These functionalities would also support maintenance. Three classes of UI properties have been selected for three classes of use: Glanceable or "no click" UI. A glanceable display is designed to provide easy and quick feedback to the user [Gouv16]. Going one step further, we envision our user interface to provide the user with synthetic and relevant information depending on the moment of the day (e.g. checking before leaving home). For instance, about the Digital Family Portrait [START_REF] Rowan | Digital Family Portrait Field Trial: Support for Aging in Place[END_REF], the key moments were the departure for and return from work. At a glance, the appearance and size of the butterfly icons informed the participants about the relative's current level of activity.

One-click UI. The user achieves a very short user interaction with the system (e.g. requesting details, validating a suggestion). In terms of persuasion, this level of interaction constitutes 'baby steps' to involve the user in the process. For instance, the e-coach engine may require the user to indicate an appropriate compromise between comfort level and energy cost.

Zoomable UI. The user performs longer interaction for exploring the state of the home or the capabilities of the management system. It is assumed that it is achieved for a suitable (e.g. comfortable) context of use (e.g. sitting at a desk). To address this situation, the overall design of the UI is based on the principles of zoomable user interfaces [START_REF] Hornbaek | Navigation Patterns and Usability of Zoomable User Interfaces with and Without an Overview[END_REF]. A zoomable user interface offers users the capability to continuously change the scale and level of details of some information without loosing the informational context.

With these three types of UI properties (glanceable, one-click, and zoomable UI), it has been hypothesized that we can target a wide range of users with different levels of implication or different interests in energy management as well as with different levels of expertise.

User interface in detail

As shown in Figure 13, a Mondrian's style has been adopted as the baseline for the aesthetics of the UI. Similar to Microsoft Windows 8, one property of this style is to split the screen space into tiles. Here, the tiles represent a block of information that corresponds to a specific task. At the center of the interface, a 24-hour clock provides an overview about the energy consumption of the last 24 hours. At a glance. A zoomed-out tile provides synthetic information that requires no or very little user interaction. If more detail is needed, using semantic zoom interaction techniques, a tile is expanded providing more space at the expense of the other tiles. Three major tiles are identified: a spatial view of the habitat (blue tile on the left hand side), a temporal view of the energy consumption (clock-based white tile), and the e-coach view (yellow tile). The white and yellow tiles both support sliding gestures to present complementary views. On the left hand side, the blocks filled in blue provide information about the outside conditions (top-left blue rectangle: air quality, humidity percentage, weather conditions) and about inside the habitat. The latter is represented through a map of the home where a rectangle represents a room or a corridor. As detailed in the following, red and green circles indicate the global status of the home as well as the status for each room.

At the center of the screen, the white tile displays a clock (a utility service) associated to time-based synthetic visualizations. The spiral-based visualization presented here is only one possible illustration. Additional complementary visualizations can be obtained by a sliding gesture performed at the bottom of the tile. These visualizations represent information about energy consumption, domestic activities, daily objectives, etc.

The yellow tile (center-bottom) is dedicated to the interaction with the e-coach. For instance, a synthetic view may be a representation of the suggested next actions to be achieved within the current hour slot of the day. In a click, the user can obtain detailed explanations about the action and its consequences. Use of everyday life metaphors. When people face something new and want to understand it, they usually try to compare it to things that they already know in order to fit it into their knowledge structure. Thus, the use of everyday life metaphors in a UI may facilitate learning. The metaphors can be based on an activity or an object that are familiar to the user. In our UI, we have used the traffic light metaphor to promote a glanceable (i.e. concise) user interface: "at a glance, I can check if everything is ok in my home".

As explained above, this part of the user interface (Figure 15) represents a logical representation of the habitat (less accurate than a real 2-dimensional map). The traffic light metaphor is used as follows: if the system detects an undesired event (i.e. lights are on in a room with no presence), a red circle (Figure 14b) is drawn in the related room associated to an icon (e.g. a light bulb means that lights are on; an open door means that, according to the e-coach, a door should stay shut in order to optimize temperature in the room and/or to maintain air quality). The circle located at the top-right corner provides a global overview. Therefore, a green circle means that everything is ok (Figure 14a). Designed for everyday tasks. Another method to keep users motivated is to give them full and easy control of their habitat, in particular, by simplifying the complex notion of multicriteria optimization. Our solution is to hide this complexity in the form of an everyday activity such as navigating on a map or manipulating familiar widgets.

Figure 15 shows the Trade-Off Pareto sliders (in short, TOP-sliders) based on the composition of familiar widgets (here, sliders), extended with the appropriate features, to allow users to find the preferred tradeoff between thermal comfort, cost and energy wastes. A preliminary semi-controlled empirical study with 16 participants using 3 interdependent criteria shows that the TOP-Sliders can serve as a sound basis to support non-expert users in making informed compromises [START_REF] Laurillau | The TOP-Sliders for multi-criteria decision making by nonspecialists[END_REF]. We can make here an analogy with what Brézillon and Pomerol call the asymmetry in an Intelligent Assistant System [START_REF] Brézillon | CONTEXTUAL KNOWLEDGE SHARING AND COOPERATION IN INTELLIGENT ASSISTANT SYSTEMS[END_REF]: the system provides support by proposing satisfying solutions (the Pareto front) and arguing over them. The user makes the final decision.

The TOP-Sliders are composed of a set of parallel sliders, each of which is associated to a criterion of the optimization problem. As with standard sliders, the position of the cursor on a slider denotes the currently selected value for that criterion. The sliders are augmented with tightly coupled visual features to support decision making through a "what-if" process. These features represent [START_REF]Chiffres clés de l'énergie -Edition 2016[END_REF] the interdependence between the criteria, (2) the impact of the modification of the value of one criterion on the others, (3) and for each criterion, the current ranges within which its values may fall, each range resulting from the Pareto front calculated for the current optimization problem.

Color encoding is used to discriminate the three sorts of "Pareto ranges": white denotes a range of values situated on the Pareto front; grey, a range of feasible but non-optimal values, and red for ranges of unfeasible values. For example, in Figure 15, the choice for thermal comfort (21.5°C) and air quality (670 ppm) is optimal whereas financial cost (greater than 122€) is not. The interdependence between the criteria is made explicit with pairs of dashed white lines where a pair pops up when a cursor is selected and links this cursor to the boundaries of the optimal range of the other sliders. For example, in Figure 15, the cursor of the financial cost is currently selected: two pairs of lines have appeared to show the impact of the current choice on the range of the optimal values for the other two criteria. In addition, as the cursor of a slider is moved, the ranges of the other criteria are updated according to the underlying Pareto model. Tight coupling between cursor movements and Pareto ranges makes explicit the impact of a selection of one criterion value on the remaining criteria. In order to allow users to explore tradeoffs that are not necessarily Pareto optimal, moving one cursor does not move the other cursors. To improve affordance and intelligibility for situations where the cursor for a criterion lies outside of an optimal range, an additional textual label coupled with the appropriate icon are displayed below the appropriate interval to explain the situation. In addition, a corrective action is proposed as a speed-up button (see Figure 15 for the Financial Cost slider). When clicked, the cursor is automatically moved to the nearest optimal value The tradeoff between the criteria once defined, the e-coach engine generates a list of recommended actions. Figure 16 shows the actions plan recommended for the day. As explained in section 4, it represents the optimal scenario computed by the explanation engine. Clicking on the "see why" button attached to a particular action gives access to explanations about the action and its consequences2 . Black boxes denote user's actions that are not part of the optimal scenario (e.g. closing the kitchen door between 2pm and 3pm). The interaction metaphor is based on that of the well-known Geographical Information Systems (GIS), typically Google map: the action plan corresponds to the route recommended by the GPS with landmarks on the way as well as the current location, in our case, a temporal location. As shown in Figure 16, it is currently 3.30pm, past actions are greyed out, and next actions to be performed between 3 and 5 pm are zoomed-out. Multiple levels of interaction: zoomable UI. Hornbaek et al. [START_REF] Hornbaek | Navigation Patterns and Usability of Zoomable User Interfaces with and Without an Overview[END_REF] define zoomable user interfaces as interfaces that "organize information in space and scale, and use panning and zooming as their main interaction techniques". This interaction technique has been applied to support the three types of user interface properties and several levels of detail. Scaling is applied on tiles: double-clicking (or tapping) on a tile expands its space; the other tiles are shrunk and organized around to maintain visible the "informational context". Figure 17 shows an expansion of the left hand-side blue tile of Figure 13. The map of the home is augmented with graphs that show the temporal evolution of relevant indicators (e.g. indoor temperature, level of CO2).

Conclusion

The conceptual contribution of this article is threefold: (1) Generation of explanations for the user, including differential explanations; (2) Design principles of persuasive user interfaces (UI) for energy management systems; (3) Mapping of persuasive UI principles into concrete interaction techniques and metaphors.

From the technical perspective, an early prototype of the Involved e-coach system has been developed that provides end-users with a 24 hour-plan of recommended actions along with contextual explanations that justify each action. This plan satisfies the user's preferred compromise between thermal comfort, air quality and financial cost specified by the user. Users can edit the plan (e.g. suppress an action), skip some actions, perform additional actions, or even change their preferred compromise, and be informed in real time of the consequences on energy consumption and comfort.

In practice, in its current version, the generation of explanations has been tested when deployed in a controlled environment (that of an office), and the user-centred evaluation of the UI elements has also been performed in a controlled setting (again, that of an office) where the behavior of the explanations generator was simulated. Whereas these early steps are necessary to detect the basic technical flaws and limitations of a system, they must be completed by longitudinal experiments performed in real world settings. Based on previous research results and field studies on home automation, it is expected that users will be interested in the system recommendations in the very first months of use provided that these are useful, robust, and trustworthy. However, users will play with the TOP-sliders to express their preferred compromise and explore the solution space provided that the required attentional cost [START_REF] Blackwell | Investment of attention as an analytic approach to cognitive dimensions[END_REF] is not too high. In the long run, either the e-coach is not used anymore, or the settings (compromises) are good enough and the system will run in the background as calm and optimal technology until some exception occurs. In this case, the Involved system could be called upon for specifying a new compromise relevant to the current situation, but there is no guarantee that the user will be motivated enough to address the exception. Clearly, these hypotheses on future use need to be validated experimentally.

Beyond those contributions and their coming evaluation, we also argue for integrated research combining expertise from different fields (e.g. physical buildings) as well as for openness towards artistic design for example.

Figure 1 .

 1 Figure 1. (a) Fogg's Behavior model (left). (b)Transtheoretical model of change (right)

Figure 2 .

 2 Figure 2. a) Power-aware-cord (left) b) Waterbot (right)

Figure 3 .

 3 Figure 3. a) Possible savings (top) b) Clock view representation of electricity cost (bottom).

Figure 4 .

 4 Figure 4. a) Elsmore et al.'s user interface (left) b) Ubi-green (right)

Figure 5 .

 5 Figure 5. From user interface to user interaction inCostanza et al. [Cos12]

Figure 6 .

 6 Figure 6. Causal relationships between co-occurrent phenomena

Figure 7 .

 7 Figure 7. Our experimental setting (laboratory office, left hand side of the figure) with part of the corresponding physical model (right hand side).

A

  scenario is compared to a reference scenario (the two scenarios are what has been done and what would have been the best scenario) over a period ranging from 8 am to 8 pm (office hours) divided in 12 one-hour time slots. The doors and windows opening values are the percentage of opening time during each slot. The other values like temperature or CO2 are the average values during the same time slot. The difference between the two scenarios is the computation of three values for every one-hour time slot: 1. Difference in terms of actions: the difference of opening time percentage of doors and windows for each corresponding time slot of scenario 1 and scenario 2.

Figure 9 .

 9 Figure 9. Difference between what really happened during a day in the office and what could have happened if the scenario extracted from the Pareto front would have been followed. For instance, between 2pm and 3pm, the office door should have been opened longer increasing the air flow from the corridor to the office. At the end of day, the air quality and temperature comfort would have been increased.

Figure 10 .

 10 Figure 10. Differential explanations with influence between actions and their final effects. Openingthe door longer at 10:00 will increase air quality and temperature comfort at 12:00 for instance.

Figure 11 .

 11 Figure 11. Missing Knowledge. The physical equations cannot be used to simulate the effects of intermediate variables.

Figure 12 .

 12 Figure 12. Part of the path diagram (relations between all variables) covering one full day.

Figure 13 .

 13 Figure 13. Design concept inspired by Mondrian's style

Figure 14

 14 Figure 14. a) No issues: green light (left), b) Issues highlighted with a red icon (right).

Figure 15 .

 15 Figure 15. Finding the appropriate compromise between conflicting criteria using the Trade-Off-Pareto sliders (https://pareto-sliders.firebaseapp.com/)

Figure 16 .

 16 Figure 16. Action plan recommended by the e-coach.

Figure 17 .

 17 Figure 17. Zoomable user interface: the focus is currently set on the office room while contextual temporal information and action plan information are still observable

The Digitla family Portrait is a picture of users' elderly relative living remotely, framed with butterfly icons that indicate the level of activity of the relative during the day

At the time of this writing, the "see why" button is not connected to the natural language text generator described in Section 4.3

Acknowledgements

This work benefits from the support of the INVOLVED ANR-14-CE22-0020-01 project of the French National Research Agency. It is also supported by the French National Research Agency in the framework of the the EquipEx program AmiQual4Home ANR -11-EQPX-00 and the "Investissements d'avenir" program (ANR-15-IDEX-02) as the cross disciplinary program Eco-SESA. This work is also partially supported by the project (DST-INRIA/2015-02/BiDEE/0978) of Indo-French Centre for the Promotion of Advanced Research (CEFIPRA|IFCPAR).


domain: math shs

text:
Solomon A Tesfamicael
email: solomon.a.tesfamicael@ntnu.no

Geir H Botten
email: geir.h.botten@ntnu.noøyvind.a.lundeby@ntnu.no

Øyvind A Lundeby

The teaching and learning of relations and functions: A comparative study of Norwegian and Ethiopian textbooks

Keywords: Relations, functions, textbooks, comparative studies

Introduction

Comparative studies in mathematics include studies that document, analyze, contrast or juxtapose similarities and differences across all aspects and levels of mathematics education [START_REF] Jablonka | CERME 7 Working Group 11: Comparative studies in mathematics education[END_REF]. In this project, which is in an early phase, we intend to carry out such a study at the cross-national level. The rationale behind it is to identify similarities and differences between mathematics education in Norway and Ethiopia, to reflect on their practices in the light of international wisdom [START_REF] Clarke | International comparative studies in mathematics education[END_REF], and to lay down grounds for further intervention studies, for example for the Norwegian NORHED project that will start in 2017. (https://www.norad.no/en/front/funding/norhed/news/).

We have started comparing textbooks, since textbooks are the main resources used in mathematics classrooms [START_REF] Pepin | Mathematical tasks and learner dispositions: A comparative perspective[END_REF] in many countries including Ethiopia and Norway. Textbooks are tools, or instruments, that facilitate the daily work of teachers. They also contribute to the field of mathematics by preserving and transmitting skills and knowledge (Rezat, 2008a). In general, Mathematics is a subject that has long been associated with textbooks and curriculum materials [START_REF] Remillard | Examining key concepts in research on teachers' use of mathematics curricula[END_REF]. Therefore, it is important to look at textbooks as a source of comparison.

At this stage, emphasis is given to the teaching and learning of relations and functions as presented in the textbooks, partly due to students' difficulties with learning these topics [START_REF] Denbel | Functions in the secondary school mathematics curriculum[END_REF]. As teacher educators working with students preparing to work in primary and middle school in Norway, we have also observed that many student teachers struggle to grasp these concepts and hence to teach them.

Method

In this study we selected six textbooks in Norway and the one textbook from Ethiopia from lower secondary level which covers the concepts of relation and function. At this early phase of the study, definitions, examples, representations, exercises and problems, activities, group works, contexts and level of abstractions in the textbooks are being identified and compared.

Findings

As mentioned above, the purpose of this poster is to communicate the beginning of our project, which will enable constructive sharing of knowledge and experience about the teaching and learning of mathematics between the two countries, and we hope with the international mathematics education community in the coming years. We report our findings to date as follows.

Thematic Working Group 11 Proceedings of CERME10 Among the selected textbooks, only two of them (one text from Norway and the textbook from Ethiopia) address the concept of relations directly by providing definitions, domain and range of relations and different representations, examples and exercises, without including the topic of function. The other Norwegian textbooks deal with the topic of function by taking for granted that students understand the concept of 'relation' in mathematics. Most of the books follow the teaching of functions by giving context-based definitions and examples, beginning with proportional relationships of variables, building to linear and then quadratic functions.

In The Ethiopian textbook (M9) the definitions of relations and functions are provided in terms of subsets of a Cartesian product of two sets. Examples and problems are consistently abstract and unrelated to any real context. In contrast, we find no single definition and representation in the respective Norwegian textbooks. In addition, the Norwegian textbooks include many real life related contexts that are accessible by the students, and they are full of different representations (graphs, symbols, words, tables and physical figures) for both concepts. With reference to this topic, the textbook M9 has a higher level of abstraction than its Norwegian counterpart. Symbolic and graphic representations are present in M9, but it is devoid of contexts and real life related examples and problems.


text:
Maitane P Istúriz

Ignacio González-Ruiz

Jose M Diego-Mantecón

Tomas Recio
email: tomas.recio@unican.es

José B Búa

Teresa F Blanco
email: teref.blanco@usc.es

Maria Gonzalez
email: mariaj.gonzalez@unican.es

Irene Polo
email: irene.polo@unican.es

Tomas Recio

Tomás Recio

María J González

Kids Inspiring Kids for STEAM (KIKS)

Keywords: STEAM, STEM, collaborative work, motivation and cross-cultural work

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

STEAM

STEM (Science, Technology, Engineering and Mathematics) is an educational approach based on the interdisciplinarity and applicability of scientific and mathematical knowledge to technology and engineering. STEAM integrates Art into STEM in order to promote children's creativity (Fenyvesi, Téglási and Szilágyi, 2014). In many European countries, the number of graduates in science, maths, technology and engineering areas is clearly insufficient for the needs of their companies and industries. To stimulate students' interest in these areas and art, the European Union has dedicated a lot of resources and effort, developing a large number of projects for pre-university classrooms. For a review, see [START_REF] Rocard | Science education now: A renewed pedagogy for the future of Europe[END_REF].

KIKS project

KIKS, Kids Inspiring Kids for STEAM is a European Erasmus+ Project, which involves four European institutions: Metropolitan University of Budapest (Hungary), STEM Team East (Cambridge, United Kingdom), University of Jyväskylä (Finland) and University of Cantabria (Spain). The project started in March 2016 and its main aim is to promote secondary education students' interest on the STEAM areas, by developing activities and presenting them to other students locally and internationally. Many students and teachers do not enjoy or have confidence in maths and STEM: they have anxiety even maths/technophobia and drop it as soon as they can. So we seek to promote the creativity and motivation for learning of these less confident students, working interdisciplinary, using technology, and fostering communication and the transfer of ideas/knowledge across cultures. From a research point of view, KIKS aims to compare cross-culturally the elaboration and resolution of STEAM activities at secondary education level.

Development of activities

Students, in teams of fives and led by at least one teacher, are asked to elaborated STEAM activities or projects under the following approach: How would you get your schoolmate to love Maths? The activities or projects can emerge from a teacher, a pupil, or a KIKS coordinator's idea. Once the idea emerges, it is developed into an activity or project. It should involve different STEAM areas, but its duration and degree of difficulty can vary according to teams' availability. Once an activity is elaborated, the team presents it to their local homologous (in face to face events) and to their international homologous (through video conferences). Schools from different countries are invited Thematic Working Group 11 Proceedings of CERME10 to participate in the project, at the moment we have more than 25 participant schools from different countries and backgrounds.

Products to be developed by the students

Each participant team has to elaborate a written document, an explanatory video, and a presentation of its work. (1) The written document (Word Doc or Power Point) has to include a presentation of the team members, and a description of the activity with the main results and the material used. (2) The edition of the video has to include the practical or technical aspects of activity, which are difficult to explain on paper. For example, the manipulative construction of objects, the use of measurement tools, etc. All the products have to be developed in the English language. The limited scope of this paper does not allow us to include here examples of the activities already developed by our teams, but they can be found at our website (http://www.kiks.unican.es/en/actividades/).

KIKS support

KIKS provides support to the teams through different platforms including Goggle Drive, YouTube, Facebook and a Website (www.kiks.unican.es). The Google Drive and Facebook platforms function as storages of information-where teachers and coordinators can exchange ideas-as well as repositories of documents elaborated by the teams. The YouTube Canal works as repository of videos, and the Website provides different and meaningful information about the ongoing process of the project. Apart from the above, KIKS provides support to the teams proposing activities, helping in aspects related to the English language, and furnishing technical support for video edition, online connections, etc.

Evaluation

Parallel to practical work of the project, we are undertaken a research study aiming to evaluate the strengths and weakness of KIKS. Firstly, this research aims to assess cross-culturally teachers' and students' perceptions about STEAM. Secondly, we aim to characterise the STEAM activities elaborated by the teams, according to the cognitive (competences, capacities, skills) and motivational (attitudes, emotions) dimensions they may develop in the learners. In short we seek to evaluate the impact of STEAM activities in the learning process. Tools for evaluating these two dimensions are currently under construction.

Proceedings of CERME10