Ingrid Falk

Samuel Cruz-Lara

Nadia Bellalem

Lotfi Bellalem

LINGUISTIC INFORMATION FOR MULTILINGUALITY IN THE SEMBYSEM PROJECT

Keywords: knowledge representation, ontology engineering, multilingual linguistic representation, ontology and lexicon

. In this paper we explore these models under the prospect of putting one or both in praxis in the setting of the SEMbySEM project.

INTRODUCTION

The SEMbySEM project aims at providing a framework for universal sensors management using semantic representations. A detailed description can be found in [START_REF] Brunner | SEMbySEM: a Framework for Sensors Management[END_REF], here we give a brief overview and concentrate on the aspects related to language and linguistic information. A sensor system supervises and manages the data coming from various sensors with varying technical specifications and placed on various objects. The sensors collect and transmit data and a sensor management system must make sense of and visualise this data. To achieve this the SEMbySEM system will be organised in a three layered architecture as shown in Figure 1. The interaction with the sensors (registering and processing events from the sensors) is done in the basic layer, the Façade Layer. The information from the sensors is unified and processed and may then trigger an update of the semantic model of the system. The semantic model together with a rule system make up the middle layer, the Core Layer. End-users connect to the system through the top layer, the Visualisation Layer. They have access to tailored view points designed by expert users and HMI experts through which the data from the semantic model is displayed. From the linguistic point of view the relevant modules are the Core and the Visualisation Layer. It was decided against using OWL and Description Logic which are habitually employed to represent semantic information in this setting [START_REF] Brunner | SEMbySEM: a Framework for Sensors Management[END_REF]. The main reasons were that they were difficult to handle by business users and that OWL fails to express specific business needs in some use cases. The business-oriented model developed instead (MicroConcept) is designed to meet the additional requirements and use existing standards wherever possible in order to leverage existing design tools eg. the lexicalisation tools to be discussed later in this paper. The ontology design is intended to be done at design time, as well as the viewpoints and HMI modeling. The latter will not change at runtime.

LINGUISTIC NEEDS IN SEMBYSEM

SEMbySEM needs (multilingual) linguistic information on the conceptual level (cf. the Core Layer, Fig. 1) and on the GUI or visualisation level. It only needs to be provided at design time and does not need to be updated at runtime. At the conceptual level it is needed to help at the design and maintenance of the semantic model.With regard to the visualisation level the needed (conceptual) information comes from two sources: from the domain ontology on one hand and from elements pertaining to the HMI or GUI. The latter objects can also be modeled by an ontology thus allowing for a uniform data representation. These two ontologies could then be lexicalised using one of the two representation models we will describe in Section 3 and 4. The result of the lexicalisation will be one or more lexical repositories, which can then be used in the visualisation process, ie. at the design of the viewpoints and HMIs which are employed in the Visualisation Layer (cf. Figure 1).

RELATED WORK

Linguistic information for ontologies The need to ground ontology elements in natural language has become evident on the basis of some or all of the following reasons: Ontologies are developed by several people from different communities, over a longer period of time and are meant to be reused -linguistic information is needed to establish and assure the consistence of the human linguistic and cognitive systems with the ontological machine-readable conceptualisation system; Precise linguistic information allows for automatic procedures for ontology-based information extraction from text which in turn help at semi-automatic ontology population; Richer linguistic models capture how concepts and relations are realised in language and therefore help to verbalise and explain ontology elements. We identified two emerging best practices which we could use to attach linguistic and lexical information to ontology elements: LexInfo [START_REF] Buitelaar | Towards Linguistically Grounded Ontologies[END_REF] and LIR, the Linguistic Information Repository [START_REF] Montiel-Ponsoda | Multilingual and lozalization support for ontologies[END_REF]. In both representations domain knowledge and linguistic information are clearly separated while the articulation between language and ontolog-ical systems remains flexible. They both explicitly take into account multilingual aspects. The linguistic information is represented as lexical ontologies. Both systems explicitly adhere to the integration of other existing standards as eg. LMF [START_REF] Francopoulo | Lexical Markup Framework: ISO standard for semantic information in NLP lexicons[END_REF], LingInfo [START_REF] Buitelaar | Linginfo: Design and applications of a model for the integration of linguistic information in ontologies[END_REF] and LexOnto [START_REF] Cimiano | LexOnto: A Model for Ontology Lexicons for Ontology-based NLP[END_REF] but the implementations as ontologies differ mainly in that LIR focuses on representing aspects related to the meaning of lexical entries (eg. synonymy, antonymy, semantic relatedness, variations in meaning conditioned by cultural or regional differences) whereas LexInfo allows for accurate and elaborate representations of morphological relations between terms, morphological and syntactical decomposition of terms and complex linguistic patterns (eg. the mapping between subcategorisation frames1 and predicate-argument structures2 ). We will further illustrate the two linguistic models and their possible integration with SEMbySEM in Section 4.

LINGUISTIC MODELS AND THEIR APPLICATION TO SEMBYSEM

Here we briefly describe the linguistic models LexInfo and LIR and explore ways to use them to associate linguistic information to the semantic model of SEMbySEM. In both frameworks the procedure is the following: (1) Starting from the domain ontology . . . (2) the system builds an empty or default lexical ontology, the main building blocks of which are the lexical entries (LEs) which roughly correspond to the domain ontology components i.e. the classes and properties. The domain ontology elements are linked to at this stage possibly empty LEs which in turn are associated to the corresponding ontology elements. LEs are constructed based on linguistic analysis of the domain ontology labels, comments and/or identifiers;

(3) The lexicon is enriched (semi-)automatically using domain relevant texts and/or external lexical resources eg. WordNet3 or Wikipedia to search for further information (eg. definitions, translations); (4) The lexical ontology is further completed manually.

LexInfo models linguistic information in an ontology combining three previously proposed approaches: LingInfo [START_REF] Buitelaar | Linginfo: Design and applications of a model for the integration of linguistic information in ontologies[END_REF], LexOnto [START_REF] Cimiano | LexOnto: A Model for Ontology Lexicons for Ontology-based NLP[END_REF] and LMF (Francopoulo et

2007

). At the time of writing, it mainly handles ontological properties which are in most cases realised in language as verbs and relational nouns 4 . For example starting from the following property definition from a SEMbySEM use-case:

<owl:ObjectProperty rdf:about="ontologyNS#engineOf"> <rdfs:domain rdf:resource="ontologyNS#Engine"/> <rdfs:range rdf:resource="ontologyNS#Train"/> </owl:ObjectProperty> the tool would generate a lexicon for English which would link to 3 types of elements of the lexical ontology: a lexical entry for the engine component of the property identifier #engineOf, a predicate entry representing the predicate engineOf and to one or more subcategorization frames representing possible linguistic realisations of this predicate.The predicateargument structure of the engineOf property en-gineOf, Domain, Range may be inferred from its ontological representation and is represented in Lex-Info as shown in Figure 2, the rectangle with gray background. A possible linguistic realisation is represented by the subcategorisation frame NounPP which is shown in Figure 2 as the rectangle with filled nodes. The mapping between the semantic predicate argument structure and the syntactic frame is modeled as can be seen again in Figure 2. Finally, the link between lexicon entries and ontology elements is provided through the hasSense property (not shown in the figure). In this example we started from the representation of a property in a domain ontology from which LexInfo inferred a (linguistic) semantic representation (the predicate argument structure) which then was mapped to a syntactic construction (the subcategorisation frame) representing a possible realisation in language which, in a subsequent step, can help detect linguistic realisations of the involved ontological elements in relevant texts.

Localisation. Once the English lexicon is constructed, similar lexica must be built for each other 4 Most nouns as eg. train refer to an ontology class. The nouns we call relational, eg. speed, may be used to express an ontology property. required language. Within LexInfo lexical information pertaining to a given language is grouped in one Lexicon, so there would be one lexicon for each language.

LIR (Linguistic Information Repository) is a model for associationg lexical information to OWL ontologies proposed within the NeOn project. The linguistic information pertaining to a given domain ontology is modeled as an OWL ontology. In contrast to Lex-Info, LIR concentrates mainly on ontology classes, which are in general represented as plain noun or noun phrase class labels. As for LexInfo we start from an ontology element (in this case a class):

<owl:Class rdf:about="ontologyNS#Train"> <rdfs:label xml:lang="fr">Train</rdfs:label> <rdfs:comment xml:lang="en">Train</rdfs:comment> </owl:Class> Localisation is performed at the lexical entry level. As Fig. 3 shows, the ontology class is connected via the hasLexicalEntry relation to English and French lexical entries (LEs). LEs in different languages may be linked through the hasTranslation relation and within the same language through synonymy or antonymy relations. Their sense is typically represented through a definition from an external resource, which may also come from a different language. In LIR it is possible to express the fact that two words are synonym in most cases by linking their sense definitions through the isRelatedTo relation. Finally, within LIR all lexical entries, irrespective of the language they belong to, are members of the same lexical ontology.

Discussion. LexInfo and LIR are both conceptualisations of lexicalising a domain ontology in the form of an ontology structure and they both aim at integrating the same existing standards (LMF). Still the resulting ontological structures are quite different. Firstly they are different from a syntactic point of view. Second, they also differ semantically: LexInfo rather emphasises the representation of properties and in particular the syntax ↔ semantics interface. For example with LexInfo it would be possible to express that the sentences The train speeds at 100 km/h. and The speed of the train is 100km/h. are linguistic realisations of the same meaning. LIR adopts a more traditional lexicographic position: one could express for example that train and rame are both possible French translations of the English train, that they may be used as synonyms in most cases but are not entirely synonymous. LexInfo is arguably more suitable at verbalising ontologies or translating natural language queries to database or web search queries, whereas LIR would be more useful to human knowledge engineers or lexicographers for building and maintaining a domain and lexicon ontology. It is in principle possible to translate one lexicon format to the other, but the syntax -semantics mapping information of Lex-Info can not be extracted from LIR and conversely, the lexicographic aspects represented in LIR can not be generated from LexInfo. On this note the two models are complementary. This difference in perception also implies different (semi-)automatic acquisition methods from texts: to enrich a LexInfo lexicon one needs deep syntactic and semantic linguistic analysis whereas for LIR one would make use of statistic semantic similarity measures and high-quality linguistic semantic resources as (Euro)WordNet or Wikipedia. From the SEMbySEM position a point in favour of LexInfo is that it generates a separate lexicon for each language whereas the fact that SEMbySEM needs lie more on the side of ontology building (by humans) speeks in favour of LIR. These differences also entail different APIs and differences in the manipulation of the lexical ontologies.

CONCLUSIONS

In this paper we presented the SEMbySEM semantic model and explored ways of associating multilingual information to its elements. Two state-of-theart techniques for representing and associating linguistic information to ontological structures are Lex-Info and LIR. We presented and compared the principles of these models and investigated whether and how they could be integrated with the SEMbySEM semantic model. LexInfo and LIR both are designed as lexical ontologies building on a domain ontology represented in OWL. Although the SEMbySEM semantic model will not be represented as an OWL ontology, it will be designed following the same basic principles and it will therefore be possible to represent the linguistic information using LIR or LexInfo. We showed that LIR and LexInfo take up different positions mainly with respect to the kind of linguis-tic information they focus on: the syntax -semantics interface for LexInfo and more traditional lexicographic aspects for LIR. These differences entail different acquisition methods, different APIs and differences in the handling of the obtained lexical ontologies. Both present advantages compared to the current way of representing linguistic information by the rdfs:label and rdfs:comment elements, in that they clearly separate domain knowledge from lexical knowledge. Thus domain and lexicon ontology can be developed separately by domain and linguistic experts and can be more easily maintained and reused. However, at this stage of the project we have not yet decided which of them to use.

Figure 1 :

 1 Figure 1: SEMbySEM architecture.

Figure 2 :

 2 Figure 2: Syntax ↔ semantics mapping in LexInfo.

Figure 3 :

 3 Figure 3: Linguistic representation with LIR

Figure 3

 3 Figure 3 schematically shows the way it is represented linguistically within the LIR framework.

A subcategorization frame of a word describes a syntactic construction this word may be used in.

 2 The predicate-argument structure of a sentence represents the meaning of this sentence as a combination of a predicate and its

arguments 3 http://wordnet.princeton.edu/

ACKNOWLEDGEMENTS

This work is carried out by the EUREKA ITEA2 project SEMbySEM partly funded by French, Spanish, Finnish and Turkish governments. We would also like to thank Elena Montiel-Ponsoda and Philipp Cimiano for providing very helpful insights regarding the LIR and LexInfo model respectively.


S Demont-Guignard

P Benquet

G Coiret

U Gerber

F Wendling

Interpretation of intracerebral-EEG epileptic spikes from detailed modeling of neural networks

Keywords: computational modeling, hippocampus, CA1, local field potentials, epilpetic spikes

This paper deals with the interpretation of the macroscopic features of epileptic spikes recorded in human hippocampus based on a neural network model of the CA1 subfield. The network consists of principal cells (pyramidal neurons) and local interneurons and uses GABAergic and glutamatergic synapses. For pyramidal cells, this paper introduces a novel two-compartment model that was developed using published data and our own experimental data (intracellular recordings, in vitro). For interneurons, singlecompartment models published elsewhere were implemented. The forward problem was solved to calculate the local field potential generated by the network. Our results show that: i) the 'reduced' model approach allows for simulations including a relatively large number of cells, ii) for appropriate changes in model-parameters (related to synaptic transmission), the model can generate "spike" events that closely resemble actual epileptic spikes and iii) some features of spike shape (amplitude, duration) can be explained by the degree of excitatory and inhibitory drive to pyramidal cells.

INTRODUCTION

Epilepsy is a neurological disorder that affects about 1% of the population worldwide. In 30% of the cases, this pathology remains drug-resistant and surgery may be indicated. The recording of electrophysiological signals with depth electrodes (intracerebral EEG) during the pre-surgical evaluation can provide reliable information about brain structures involved during epileptic discharges. This information consists of specific "events" recorded either during interictal periods (epileptic spikes) or during ictal periods (seizures). However, for both types of events the underlying mechanisms of generation are not completely understood. Further advances are necessary to allow a better interpretation of intracerebral EEG signals in relation to cell-related or network-related parameters, possibly altered in epileptogenic conditions. In this study, we strictly focused on epileptic spikes observed in patients during intracerebral recording. We limited our study to the hippocampus, a sub-cortical structure commonly involved in temporal lobe epilepsy. The main objective was to develop a physiologically and biophysically plausible neural network model (CA1 subfield) at the cellular level that would provide a link between field activity (as recorded by depth electrodes) and activity generated in interconnected neurons and interneurons (pyramidal, basket and OLM cells) included in the modeled hippocampal network. From this model we simulated events that closely resemble actual epileptic spikes. We also identified specific model parameters that affect the amplitude and duration of epileptic spikes. In particular, the shape of the early fast component and the late slow component of the epileptic spike could be linked to the relative contribution of glutamatergic and GABAergic synaptic currents in pyramidal cells, controlled, in the model, by modifying membrane conductance.

II. DETAILED MODEL OF CA1 SUBFIELD

A. Model of the CA1 pyramidal neuron

Multi-compartment models of pyramidal cells were first proposed during the 1980s in the pioneering work by Traub and colleagues [1]. For the CA1 and CA3 subfields, various models have been created ranging from very detailed representations (up to several thousands of compartments) to more simplified approaches (1 or a few compartments). We have followed the latter approach in developing a twocompartment 'reduced' model of the CA1 pyramidal cell in line with Pinsky and Rinzel's work on CA3 cells [2]. Our model is minimal but still biologically-inspired. The objective was to find a good compromise between physiological relevance and computing time. Based on the Hodgkin and Huxley formalism [3,4], the model entails distinct somatic and dendritic membrane properties. According to this formalism, the cell membrane acts as a capacitor C connecting the membrane potential V m to currents passing through the membrane. With I(t) the injected input current, the equation of conservation of electric charge is:

( ) ( ) ∑ + = ion ion m t I dt dV C t I (1)
where ∑ ion ion I is the sum of ionic currents, where I ion is given by ) .( . .

ion ion ion E V y x g I - =
(2) In eq. 2, g ion represents the ionic conductance; x.y (the product of the gating variables) is the open-channel probability and E ion the reversal potential. Special attention was paid to the selection of the main ionic channels (voltage-gated and leak) included in the model. In this respect, it differs from the literature in that it accounts for more currents than classical reduced models. Current equations were taken from more detailed models published elsewhere and summarized in [5]. Currents were selected based on a review of literature. A validation was performed using data recorded in an experimental model (organotypic rat hippocampal slices). A schematic diagram of the neuron model is shown in fig. 1-a. In brief, the shape of the action potential (AP) is mainly controlled by voltage-dependent sodium, potassium and calcium currents (I Na , I KDR , low and high threshold I Ca ). In addition, to replicate physiological firing rates potassium channels activated by intracellular calcium ions were added (after-hyperpolarisation current I AHP ). Similarly, we also included a rapidly inactivated potassium current (I KA , present only in the dendritic compartment [6] to reproduce the change of density of ion channels along the membrane) in consideration of its potential role in epileptiform activity, as well as a hyperpolarization-activated cationic current (I h , dendritic compartment [7]) and a muscarinic potassium current (I m , [8,9]).

Conductance values were identified by parameter sensitivity analysis of the reduced model. As shown in fig. 1-b, parameters were adjusted to reproduce intracellular experimental data both under control and in 'epileptic' conditions induced with 4-aminopyridine (4AP). As depicted in fig. 1-c, blocking I KA caused the model to switch from normal to burst activity, as also observed experimentally.

B. Models of CA1 OLM and basket interneurons

The neural network model reproduces some of the cellular organization of CA1, by integrating basket and orienslacunosum moleculare (OLM) interneurons. These cells are represented by single compartment models taken from the literature [10].

C. Network features

Network simulations used glutamatergic (AMPA and NMDA) and GABAergic synapses. Simulated cells were connected to reproduce the CA1 circuit (fig. 2-a and2-b) in accordance with commonly accepted assumptions (location of synapses and receptors, synaptic strength, connectivity patterns). The number of cells was gradually increased to check for scalability effects. The number of pyramidal cells (resp. interneurons) was 80% (resp. 20%) of an arbitrary-chosen total number of cells. Regarding connectivity patterns, the number of connections per cell and the maximum distance between two connected cells were fixed according to the literature. The probability of connection was based on a Gaussian distribution: physiologically, the probability of connection between two neurons is larger when the two cells are close, and is null beyond the maximum distance. Pyramidal neurons and interneurons evenly distributed in a 3D space, as shown in fig. 2-c. Finally, the whole network was stimulated with an afferent volley of quasi-synchronous action potentials coming from an "external array of cells" (not represented in fig. 2). The objective was to mimic the input from CA3 to CA1.

III. RECONSTRUCTION OF LOCAL FIELD POTENTIALS

The dipole theory was used for the calculation of the model local field potential (LFP) with the following assumptions. First, the main contribution to the LFP comes from pyramidal cells due to their spatial arrangement 'in palisades'. Second, each pyramidal cell is considered as a point source (current dipole formed by a sink and a source) positioned within a volume conductor characterized by a homogeneous conductivity. Third, according to the superposition theorem, the contributions of all pyramidal cells sum up instantaneously at the level of the extracellular recording electrode, placed at the center of the modeled network (typically, at the middle of the dendritic tree along the somatodendritic axis, see fig. 2-c). According to these postulates, the potential V i of the electric dipole corresponding to cell i is:

2 4 . i i i i r u d V σ π = ( 3
)
where σ is the conductivity, r i is the distance between cell i and the measurement point (i.e. the recording electrode), i u is a unit vector on the line going from the origin of dipole vector i and the recording point, i d is the dipole moment. Moreover, the total potential V engendered at the level of the recording electrode is given by:

∑ = = N i i V V 1 (4)
where N is the total number of pyramidal cells. In order to compute V, the dipole moment i d (eq. 3) must be estimated. In our reduced two-compartment model of the pyramidal cell, we assuming that the sink and the source are located at the level of the somatic compartment and the dendritic compartment, respectively. Therefore, the magnitude of the dipole moment i d , which corresponds to the value of the longitudinal current flowing along the somatodendritic axis, can be estimated as a function of the dendritic and somatic membrane potential obtained by numerical integration:

i i c i d i s i S l g V V d . . . - =
where i is the cell index, i s V and i d

V , respectively, denote the somatic and dendritic membrane potential, g c is the coupling conductance between the somatic and dendritic compartments, i l is the distance between the sink and the source, and S i is the total membrane surface. Regarding the numerical values, we chose g c = 1 mS.cm -2 , i l = 350 µm (half of the size of the dendritic tree). For S i , we assumed that the soma approximates a sphere of radius R = 8 µm (S soma = 4.π.R²) and that the ratio S soma / S i = 0.15 as in [2].

IV. RESULTS: MODEL-BASED INTERPRETATION OF EPILEPTIC

SPIKES

Simulations were run for networks of 640 pyramidal cells, 80 basket cells and 80 OLM cells. Software was written in C and objective-C language. Differential equation systems were solved using a 4 th order Runge-Kutta algorithm (fixed step). Computation time was about 7 minutes for 800 ms of activity at a sampling frequency of 25 kHz, on a PC-type computer (quad-core running under MS Win. XP).

A. Real versus simulated spikes

Figure 3 shows examples of real epileptic spikes recorded in human hippocampus. One can note that the amplitude of the early fast component (spike) and the duration of the late slow component (negative wave) strongly differ from one event to another. In a first step, we increased the conductance values associated with glutamatergic currents and verified that the model was able to produce a "spike" with an "average" shape similar to epileptic spikes observed in the depth-EEG signals (fig. 3-c). In a second step, we quantified the effects of these conductance values on two "macroscopic" features of the spike: the peak-to-peak amplitude (A) and the duration (D) as defined in fig. 3-b.

B. Effects on spike amplitude

Fig. 4-a shows the effect of the AMPAergic synaptic current. This current is required for spike generation. When the conductance value increased from 5 mS/cm² to 15 ms/cm², the amplitude increased by a factor of 30. This amplitude increase also appeared when the NMDA conductance value was increased but to a lesser extent (fig. 4-b). The effect of changing the GABA conductance value is very weak (fig. 4-c).

C. Effects on spike duration

Increasing the AMPA conductance was found to shorten spike duration (fig. 4-d). Conversely, GABAergic synaptic current had a major impact on spike duration with an increase of 600% when the conductance value was multiplied by 7 (fig. 4-e). The NMDA synaptic current also played a role: the spike duration varied linearly with an increase of 130% over the same conductance range as in a) (fig. 4-f). V. DISCUSSION AND CONCLUSION Intracellular recordings are reasonably well described in terms of the properties of excitable membranes. However, the interpretation of extracellular signals, in particular those reflecting the activity of neuronal networks, has proven to be a challenging and still unsolved issue. Difficulties mainly stem from the complexity of the recorded networks of neurons. The predominance of nonlinear mechanisms give rise to complex interactions that complicate the relationship between network activity and recorded activity. Computational modeling provides insights into this complexity as biologically-inspired models can act as bridges between subcellular/cellular/network parameters and electrophysiological observations [11]. In the context of epilepsy, the present study is an attempt to identify relationships between "macroscopic" features (amplitude, duration) of interictal events and the basic parameters involved in excitatory and inhibitory synaptic transmission (conductances associated with glutamatergic and GABAergic currents) in neuronal networks. The main findings of this study are summarized below. First, for a physiologically relevant stimulation (an afferent volley of quasi-synchronous action potentials mimicking the input from CA3 to CA1), the model was able to reproduce spikes relatively similar to epileptic spikes. Simulated events showed peak-to-peak amplitudes ranging from several hundreds of µV to 1 mV. These values are compatible with actual amplitude values and confirm that the assumptions we introduced for solving the forward problem (section III) are reasonable. In this respect, our study differs from studies published elsewhere in which authors used the total transmembrane current to calculate the field potential [12][13][14].

Here the contribution of each pyramidal cell was represented by an equivalent current dipole that reflects longitudinal current along the somato-dendritic axis. Second, the model reflects the major role of the AMPA conductance in both the generation of the spike and its amplitude. Our model also shows a slight influence of the NMDA conductance on spike amplitude. Conversely, the GABA conductance value was found to have no effect. These results corroborate experimental findings showing that the non-NMDA receptor antagonist CNQX (20 µM) as well as NMDA antagonists abolished interictal spikes [15]. Third, regarding spike duration, a distinction must be made between the early fast component and the late slower component. The duration of the former was mainly influenced by the AMPA conductance value ("sharpness" of the spike) whereas the latter was affected by both the GABA conductance value and, to a lesser extent, by AMPA/NMDA conductance values. These results are also in line with experimental data showing that the duration of the late part of the extracellular IS was reduced by the NMDA receptor antagonist APV [16]. In this study we restricted our analysis to the effects of specific network-related parameters on the shape of the spike. There are many other parameters to be studied in the model. For instance, connectivity patterns could also be considered as free parameters. Indeed, recent studies showed that network excitability is enhanced for particular configurations of connections between cells [17]. The influence of cell-related parameters should also be studied, as several reports showed that the properties of ion channels can be altered in epilepsy. Indeed, upregulation of excitatory glutamatergic receptors in the dendate gyrus has been observed in both human and animal models of hippocampal sclerosis and may contribute in the development of chronic seizures through increased excitatory transmission [18,19]. Our approach allows these issues to be addressed in future studies as the model represents all of the main ion channels, and the 'reduced' pyramidal cells and interneurons maintain the computation time for solving the differential equations at a reasonable level.

Figure 1 .

 1 Figure 1. a) Reduced pyramidal neuron model (two compartments). Transmembrane currents are defined and discussed in section 2.A. Coupling strength between soma and dendrites is ensured by conductance gc. b)Left: real AP recorded in a CA1 pyramidal cell (patch-clamp technique, currentclamp, whole cell mode, organotypic hippocampal slice culture) stimulated during 10 ms at 0.3 nA on the cell body. Right: The model was stimulated with a current pulse of 60 pA/cm² during 10 ms injected at the soma. Both plots represent the time course of the somatic membrane potential. c) Voltage somatic responses to step current injections of 300 ms in control and in presence of 4AP. The model was stimulated with a current pulse of 300 ms. The inactivating potassium conductance value (gKA) was 15 mS/cm² (4AP) and 55 mS/cm² (control).

Figure 2 .

 2 Figure 2. Network features and calculation of the field potential. a) The network model reproduces essantial features of the CA1 subfield (hippocampus) b) The network includes pyramidal cells (PYR) decribed by a two-compartment model as well as basket (BAS) and oriens-lacunosum moleculare (OLM) cells each described by a single-compartment model. The respective percentages of cells and the connectivity patterns (synaptic interaction only) were obtained from the literature. c) The field potential is calculated by solving the forward problem from the network to the measurement electrode (V) using dipole theory.

Figure 3 .

 3 Figure 3. Epileptic spikes recorded from the hippocampus in a patient with TLE in comparison with simulated spikes a) Spikes were visually extracted from a 1-hour depth-EEG recording and were sorted according to increasing amplitude.Although spikes are commonly characterized by a fast early component followed by a slower late component, this figure shows the variability of interictal events in terms of amplitude (A) and duration (D), as defined in b). c) Example of simulated spike (local field potential).

Figure 4 .

 4 Figure 4. Influence of synaptic current conductance values on the spike amplitude (a, b, c) and duration (d, e, f). Each parameter is varied independently from the others, starting from the control condition.

ACKNOWLEDGMENT S. Demont-Guignard is supported by the Region Bretagne.


Introduction

Understanding the background productions in searches for new physics is very challenging at hadron colliders. Therefore, measurements of differential cross sections represent important milestones in the discovery road. In this note, we present measurements of Z/γ * + jets production and photon plus heavy flavor jets at the Fermilab Tevatron with the DØ detector [1].

The production of vector bosons is an important signal at hadron colliders, providing unique information about the production mechanism of heavy bosons with additional hard partons. The electron and muon decay modes are distinct experimental signatures, and can be identified with low background rates.

Photons produced in association with heavy quarks (c or b) at hadron colliders provide valuable information about the heavy quark and gluon content of the initial state hadrons, . Although the background rates are not negligible, the statistics are high enough to constrain accurately the parton distribution functions (PDFs).

Z/γ * +jets

The DØ collaboration has studied the production of Z/γ * + jets in both the electron channel and the muon channel [2,3,4]. The jets were reconstructed using a seeded mid-point cone algorithm [5] with cone size of 0.5, and they are required to have |y| < 2.8 and p T > 20 GeV.

The muons were selected to have opposite charge, p T > 15 GeV, |η| < 1.7 and the di-muon invariant mass ranging between 65 GeV and 115 GeV. Isolation requirements were used to reduce the background rates to negligible levels. The electrons were selected to have opposite charge, p T > 25 GeV, |η| < 1.1 or 1.5 < |η| < 2.5, and the di-electron invariant mass ranging between 65 GeV and 115 GeV. In the muon decay channel, we measured differential cross section in the leading (transverse momenta) jet p T and the Z/γ * p T [2]. In Figure 1, the NLO pQCD predictions and from three event generators (ALPGEN [6], using PYTHIA [7] for the showering; SHERPA [8]; PYTHIA, with all jets coming from the parton shower) are compared to data.

The ∆ϕ between the Z/γ * and the leading jet were also measured in the muon channel using two different p T thresholds (25 GeV and 45 GeV), since the production of additional jets is essentially uncorrelated with the Z/γ * production [4]. We compared the measurement with NLO pQCD and LO pQCD predictions, and the event generators: SHERPA; HERWIG using JIMMY [9] for multiple parton interactions; PYTHIA with tune QW and with the Perugia tune using the p T ordered shower; ALPGEN, using the mentioned PYTHIA tunes and HERWIG for the showering (Figure 2).

In the electron decay channel, we measured the jet p T spectra normalized to the Z/γ * (→ e + e -) + X cross section in different jet multiplicities [3]. The measurements were compared to different theory predictions: NLO pQCD; LO pQCD; PYTHIA using tune QW; PYTHIA using Tune S0; HERWIG using JIMMY; ALPGEN using PYTHIA tune QW; and SHERPA (Figure 3).

The pQCD NLO prediction describes the DØ measurements within uncertainties while the event generators show varying agreement. With more data, these results can be extended and tighter constraints can be placed.

Z = M F µ = R µ CTEQ6.6M PDF ALPGEN Z T p ⊕ Z = M F µ = R µ CTEQ6.1M PDF -1 DØ Run II, L=1.0 fb ) + jet + X µ µ → *( γ Z/ | < 1.

Photon+heavy flavor

Using the DØ detector, we studied events with at least one photon candidate and at least one heavy-flavor jet candidate [10]. The photons were selected to have p T > 30 GeV with |y| < 1.0 and the leading jet p T > 15 GeV and |y| < 0.8. To suppress background events coming from cosmicray muons and W leptonic decays, the total missing transverse energy was required to be less than 70% of the photon p T . The remaining background from dijet events, containing π 0 and η mesons that can mimic photon signatures, is rejected using an artificial neural network (ANN) with the requirement that the ANN output be > 0.7. Light jets are suppressed using another dedicated ANN (b-ANN), trained to discriminate light flavor from heavy flavor jets. The leading jet is required to have a b-ANN output value > 0.85.

The fraction of c and b jets in the final data sample is determined using a fitting technique, where the discriminant is P b =ln ∏ i P i , where P i is the probability of a track in the jet cone to originate from the primary vertex, omitting the least likely track to have come from this vertex. The measured normalized cross section for the leading jet in Z/γ * + jet + X events (upper left) compared to the predictions of NLO and the ratios of data and theory predictions to NLO compared to various event generator models. The measured normalized cross section for the second leading jet in Z/γ * + 2 jets + X events (upper right) compared to the predictions of NLO and the ratios of data and theory predictions to NLO compared to various event generator models. The measured normalized cross section for the third leading jet in Z/γ * + 3 jets + X events (bottom) compared to the predictions of LO and the ratios of data and theory predictions to LO compared to various event generator models.

The measured differential cross sections and their ratios to theoretical predictions are presented in five bins of p γ T and two regions of y γ y jet (y γ y jet > 0 and y γ y jet < 0), and can be seen in Figure 4 for photon + b jets and photon + c jets. Theoretical predictions are from NLO pQCD calculations using the CTEQ 6.6M PDFs. For photon + c jets, comparisons with CTEQ 6.6M PDFs based on the models with an intrinsic charm component (IC) were also done.

The NLO pQCD prediction agrees with the measured cross sections for photon+b production over the entire p γ T range, and with photon+c production for p γ T < 70 GeV. For p γ T > 70 GeV, the measured photon + c cross section is higher than the NLO pQCD prediction by about 1.6 -2.2 standard deviations (including only the experimental uncertainties) with the difference increasing with growing p γ T .

Conclusion

Important measurements have been performed with the DØ detector, testing NLO pQCD, and the modeling of these complex final states by event generators. The understanding of the discrepancies observed between data and predictions is vital to the sensitivity to new physics at the Tevatron and LHC. T for both rapidity regions. The data points include the overall uncertainties from the measurement, and the theoretical predictions are displayed as dotted lines. The uncertainties from the theoretical predictions include those from the CTEQ 6.6M PDFs (yellow band) and from the choice of scale (full line). The ratio of two intrinsic charm models to the standard theoretical predictions are also included (dashed lines).

7 µFigure 1 :

 71 Figure 1: The measured cross section (a) and the ratio of data and predictions to ALPGEN (b) are shown in bins of leading jet p T (left) and in bins of Z/γ * p T (right).

Figure 2 :

 2 Figure 2: The measured normalized cross section in bins of ∆ϕ(Z, jet) for Z p T > 25 GeV (left) and for p Z T > 45 GeV (right).

Figure 3 :

 3 Figure 3:The measured normalized cross section for the leading jet in Z/γ * + jet + X events (upper left) compared to the predictions of NLO and the ratios of data and theory predictions to NLO compared to various event generator models. The measured normalized cross section for the second leading jet in Z/γ * + 2 jets + X events (upper right) compared to the predictions of NLO and the ratios of data and theory predictions to NLO compared to various event generator models. The measured normalized cross section for the third leading jet in Z/γ * + 3 jets + X events (bottom) compared to the predictions of LO and the ratios of data and theory predictions to LO compared to various event generator models.

Figure 4 :

 4 Figure 4: The γ + b and γ + c differential cross sections as a function of p γT for both rapidity regions. The data points include the overall uncertainties from the measurement, and the theoretical predictions are displayed as dotted lines. The uncertainties from the theoretical predictions include those from the CTEQ 6.6M PDFs (yellow band) and from the choice of scale (full line). The ratio of two intrinsic charm models to the standard theoretical predictions are also included (dashed lines).


Guillaume Piolle

Yves Demazeau

Addressing Temporal Aspects of Privacy-Related Norms

Agents interacting in open environments such as Internet are often in charge of personal information. In order to protect the privacy of human users, such agents have to be aware of the normative context regarding personal data protection (applicable laws and other regulations). These privacy-related norms usually refer to deadlines and durations. To represent these regulations, we introduce the Deontic Logic for Privacy; this logic represents privacy-related obligations while providing the required temporal expressiveness.

INTRODUCTION

Any personal agent designed to evolve in an environment like Internet and to assist a human user with her online activities should then be aware of privacy issues and regulations, in order to protect the user's personal information. These regulations appear as laws, contracts, company policies, user requirements... Six dimensions have been identified that can be used to analyze regulations dealing with personal data protection [START_REF] Piolle | Privacy management in user-centred multi-agent systems[END_REF][START_REF] Piolle | Une logique pour raisonner sur la protection des données personnelles[END_REF]. These are user information, user consent, data update, justification of data collection and usage, data retention and data forwarding.

Many privacy-enhancing technologies, protocols and architectures try to address parts of the issue [START_REF] Deswarte | Current and future privacy enhancing technologies for the internet[END_REF]. The Platform for Privacy Preferences (P3P), for instance, aims to deal with the first two dimensions, by providing websites with means to communicate on their privacy policies [START_REF]Platform for Privacy Preferences specification 1.1[END_REF]. However, none is able to provide a cognitive agent with means to reason on the regulations themselves, so that it could adapt to the context of a transaction in a dynamic and autonomous fashion.

In this paper, we propose a logic designed in order to specifically represent privacy-related regulations concerned with all six dimensions. This Deontic Logic for Privacy (DLP) is able to deal with obligations regarding personal data processing and its temporal organization. We explain why specific operators are needed to represent dated norms, we identify the requirements for expressing obligations with deadlines, we build such an operator on the base of existing propositions and we put it in the context of privacy norms.

THE DLP LOGIC

When dealing with privacy management, norms are often linked with notions of delays, deadlines, precedence between actions; an explicit representation of time would then provide valuable reasoning means. Much work has been done on temporal deontic logics in general [START_REF] Åqvist | Combinations of tense and deontic modalities[END_REF], but to the best of our knowledge none of them deals with privacyrelated norms in a specific way. A prominent temporal feature of privacy regulations is the notion of deadline. We will examine how existing proposals can be of use in privacy-based reasoning, but we must first introduce a common formalism to compare them. This is why, in the light of this background, we present here the DLP language, a temporal deontic logic able to represent specific privacyrelated norms, and in particular the deadlines associated to them.

DLP is a language where the SDL obligation modality Ob is freely mixed with LTL operators. The well-formed formulae ϕ of the DLP language are defined as follows, where p is a proposition from a language LDLP to be specified later:

ϕ = p | ϕ " ∨ " ϕ | "¬" ϕ | "Ob" ϕ | ϕ " U " ϕ | ϕ " S " ϕ ; (1)
We have chosen the U S temporal language (U and S being the strict versions of "until" and "since" connectives) for its expressiveness, but we will use the common abbreviations F , G, H, P . We also define U -and F -as the loose versions of U and F including the present. The X i operators, based on a "neXt" operator X and its counterpart in the past X -1 , can be used to travel step-wise along a time flow. The DLP logic is interpreted over bidimensional Kripkelike structures, where a world is defined by its history h (the linear flow of time it belongs) and a date ti in the time flow. The temporal accessibility relation relates a world in a history to its successor in the same history, and the deontic accessibility relation relates a world to all its acceptable deontic alternatives (in all histories).

OBLIGATIONS WITH DEADLINES

We have said that in order to express privacy-related norms, we need the notion of deadlines, to which obligations will be attached. Indeed, it is often argued that obligations without deadlines are void [START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF]: one can not fulfill them, and yet never be in violation of a norm (since one can always postpone and pretend the obligation will be fulfilled later). In order to deal with deadlines, we introduce specialized constants in our language, which we call dated propositions. They are noted {δi} i∈N , δi being true only at date ti.

Our aim here is to build an operator Ob(ϕ, δ) expressing the obligation for ϕ to be true before the date represented by δ (i.e. before the propositional date δ becomes true). We have identified six requirements that an operator in our formalism should meet in order to bear the right meaning in privacy-related norms:

1. Failed obligations should be dropped after the deadline; 2. Violations should be made punctual, not persistent in time; 3. Deadlines that are not dated propositions have no meaning; 4. Obligations on ⊥ should be impossible to fulfill; 5. Obligations on ⊤ should be trivially respected; 6. It should be impossible to express obligations with past deadlines; 7. The operator must comply with the propagation principle [START_REF] Brunel | A state/event temporal deontic logic[END_REF], saying that an obligation must be maintained until the deadline is reached or the obligation is fulfilled; 8. The operator must comply with the monotony principle [START_REF] Brunel | A state/event temporal deontic logic[END_REF], saying that an obligation with a given deadline implies an obligation with a further deadline.

Some work has been done already on obligations with deadlines; our first six requirements regard choice points already discussed by Dignum et al [START_REF] Dignum | Meeting the deadline: Why, when and how[END_REF]. However, our conclusions slightly differs from theirs, for instance on the fact that they take violation as a state rather than as an event. In their own work, they introduces an operator that defines an obligation jointly with its violation. Because of their strictly temporal definition, dated obligations can then be derived whenever they seem to be respected, which is a significant drawback for us. From another point of view, it is not monotonic and deadlines with a value of ⊤ can be defined, resulting in an immediate obligation. Brunel et al [START_REF] Brunel | A state/event temporal deontic logic[END_REF] extend a temporal deontic logic with explicit quantification on time, in order to reason on delays rather than on deadlines. For that reason, it cannot be directly expressed in DLP. Furthermore, it is not monotonic. The operator proposed by Demolombe et al [START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF], although not expressed in temporal deontic logic, can be translated. It satisfies some kind of semi-monotony, ensuring the property provided that the obligation is not violated. This key property makes it our best candidate. The operator matches most of our other requirements, but needs to be adapted to dated propositions in order to comply with the third and sixth points. We integrate these conditions to a DLP translation of the original proposition, and end up with the dated operator Ob(ϕ, δ) (2). The authors propose a persistent violation for their operator; we transform it into a punctual one (3) in order to match our second requirement. One can see that semi-monotony has a nice side-effect: it prevents us from deriving multiple violations for the same initial obligation, while still ensuring monotony if the obligation is fulfilled.

Ob(ϕ, δ) def =  F (δ ∧ G¬δ ∧ H¬δ) Ob(F -(ϕ ∧ F δ)) U -(ϕ ∨ δ) (2) viol(ϕ)
def = δ ∧ P (Ob(ϕ, δ) ∧ ¬ϕ U -δ) (3)

APPLICATION TO PRIVACY NORMS

Our deontic and temporal formalism can be used to express privacyrelated norms by its application on a base language LDLP . LDLP is based on predicates related to the six dimensions of personal data protection mentionned in the introduction. Argument domains are finite or countable sets, so we end up with a countable set of propositional terms. LDLP includes for instance a predicate perform representing the actual process involving personal information, a predicate consent representing the user's authorization, a predicate forget representing data deletion3 ... As an application, let us see how the an example regulation about data retention (One must not keep somebody else's credit card number more than one week after a transaction) translates into DLP (4). It is an interesting example since it involves antecedence and a deadline. Formally, it says that whenever an agent A performs a process of type transaction to which is attached an information of type creditCardNum owned by an agent B (and not by agent A), if δ represents a date one week in the future, then there is a dated obligation that A should forget this information before the deadline δ. perform(A, ID) ∧ owner(ID, creditCardNum, B) ∧¬owner(ID, creditCardNum, A) ∧ actiontype(ID, transaction) ∧ X 7 * 24 δ → Ob(forget(A, ID, creditCardNum), δ) (4)

CONCLUSION AND FUTURE WORK

We have proposed the DLP language, based on temporal deontic logic, to represent privacy-related norms. DLP is expressive enough to represent obligations with deadlines, as well as other (more classical) temporal notions, in an acceptable way. DLP is based on a propositional language specifically oriented towards personal data processing. Some work remains to be done on this logic, including a better basis for the temporal operators of the language. Currently, it is based on the U, S logic, which is very general but somewhat too expressive. Indeed, we must then question inclusion of "since" in the logic, since we do not seem to need it, and it has already been argued that adding it to an until-based logic is not trivial from the point of view of complexity [START_REF] Reynolds | The complexity of the temporal logic with until over general linear time[END_REF]. An automated procedure is to be proposed to generate DLP formulae on the basis of information exctracted from P3P policies [START_REF]Platform for Privacy Preferences specification 1.1[END_REF]. DLP, along with these associated tools, are then to be integrated in a privacy-aware cognitive agent that should be able to model and reason on its privacy-related normative context.

Université Joseph Fourier, Laboratoire d'Informatique de Grenoble, France, email: guillaume.piolle@imag.fr

CNRS, Laboratoire d'Informatique de Grenoble, France, email: yves.demazeau@imag.fr

Due to page limitations, we are not able to include the full specifications of L DLP here.

ACKNOWLEDGEMENTS

This research has been supported by the Rhône-Alpes region Web Intelligence project. We would also like to thank Andreas Herzig and Philippe Balbiani for their valuable comments on our work.


Guillaume Piolle
email: guillaume.piolle@imag.fr-yves.demazeau@imag.fr

Obligations with deadlines and maintained interdictions in privacy regulation frameworks

We aim at providing artificial agents with logical tools to reason specifically on privacy-related regulations, in order to comply with them. In order to express these regulations, we propose a deontic and temporal logic based on predicates dealing with personal data management. Using an example, we show the need for specific operators to express obligations with deadlines and maintained interdictions. We define a set of eight specific requirements for such operators, we evaluate the existing proposals with respect to these requirements and we adapt our own ones, to better suit to our formalism.

Introduction

Commercial service providers tend to put a stress everyday more significant on personalization, thus collecting more and more personal data from users. In consequence, they have to provide them with guarantees on the protection of their private information. The users' concern for privacy has indeed grown jointly with the thirst for personalization. Intelligent agents aiming at interfacing their human user with distant or distributed services should then be provided with tools for protecting private information, in application of the privacy regulations relevant to their execution context.

In the general domain of privacy, research has first focused on the so-called Privacy-Enhancing Technologies (PETs), the technical means used to protect individuals' information. The ISO, for instance, gave in 1999 a set of "common criteria" to be met by such systems, in terms of technical features [START_REF]Information technology -security techniquesevaluation criteria for it security, part 2: Security functional requirements[END_REF]. In 2006, Yves Deswarte classified existing Internet-oriented PETs with respect to their aims (identity management, IP anonymization...) [START_REF] Deswarte | Current and future privacy enhancing technologies for the internet[END_REF] while we proposed the same year a classification of privacy-related regulations along six dimensions (user information, user consent, data update and retractation, process justification, data retention and data forwarding) [START_REF] Piolle | Privacy management in user-centred multi-agent systems[END_REF]. Regarding the needed reasoning means on these regulations, much work has been done on the representation of security policies using deontic logic. One could cite for instance the early works of Ortalo [START_REF] Ortalo | Using deontic logic for security policy specification[END_REF] or the proposals of Cholvy and Cuppens on the consistency of such policies [START_REF] Cholvy | Reasoning about norms provided by conflicting regulations[END_REF]. These works seem to provide us with means to represent the normative context of an agent. So far, none of the logic-based proposals include privacy-specific reasoning features, even though some of them deal with closely related fields like information exchange policies [START_REF] Cholvy | Raisonner avec une réglementation incomplète : le cas d'une politique d'échange d'informations. In 16e congrès francophone AFRIF[END_REF].

The need for temporal dynamism is particularly prominent in privacy regulations, which often deal with notions such as durations and deadlines. Such norms may state, for instance, that a piece of information should be deleted before a given date or after a given duration, or that user information must take place at least N days before her data are used. Techniques for dealing jointly with deontic and temporal notions has often been studied, most notably by Lennart Åqvist [START_REF] Åqvist | Combinations of tense and deontic modalities[END_REF], and some authors have been working "in the abstract" on the general notion of deadlines in deontic obligations [START_REF] Dignum | Meeting the deadline: Why, when and how[END_REF][START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF][START_REF] Brunel | A state/event temporal deontic logic[END_REF]. This notion is actually crucial to the representation of privacy norms, and we need to thoroughly analyse how these contributions can help us in our work. What we propose here is to build a deontic and temporal logic dedicated to the representation of privacy regulations and to make sure that it is expressive enough for notions such as obligations with deadlines and maintained interdictions.

In the following section, we present the Deontic Logic for Privacy (DLP), designed to deal with privacy-specific notions. In section 3, we specify the requirements for an "obligation with deadlines" operator, see how three operators already proposed match these requirements once translated into DLP, and how a more suited one can be built on this basis. We also show how the notion of interdictions maintained over time can be expressed in DLP. In section 4, we use these operators to translate a fictional privacy regulation into a DLP norm. In the following, we will consider a service agent, in charge of a process (or service) involving personal information, and a user agent, willing to obtain that service and responsible for the personal information of its human owner.

The DLP logic

The DLP logic is a normal deontic and (linear) temporal language, the corresponding modalities being applied on a base language L DLP designed to represent information and actions about personal data usage and protection.

Privacy-related information

In L DLP , processes making use of personal information are identified through a unique ID. Processes have one or more ACTIONTYPEs to define their nature. Each process is related to a set of personal information chunks, each of them being identified by a DATAID (local to the process) and characterized by one or more DATATYPEs. In the current version of the language, ACTIONTYPEs and DATATYPEs take their values in the various sets and type trees defined by the P3P standard schemata [START_REF] W3c | Platform for Privacy Preferences specification 1.1[END_REF]. The language is based on three sets of predicates, on which the connectives of propositional logic (¬, ∨) are applied1 :

• Informative predicates, designed to represent the service agent informing a user agent with respect to a given process. Information can be about the type of the process (informActionType predicate), the potentitial recipients of a given piece of information (inform-Forward), the information retention time (informDuration) or the agent to contact for further data update or deletion requests (informContact).

• Performative predicates, designed to represent some actions taken by the agents. Service agents can request for a piece of data in order to provide the service (request), ask for the consent of the user agent with respect to a process (requestConsent), execute the process (perform), update an information (update), delete it (forget) or forward it to another service agent (forward). User agents can consent to a process (consent), send a piece of information (tell), request a data update (updateRequest) or a data deletion (forgetRequest).

• State predicates, used to memorize information in the form of relational tuples. With these predicates, processes are associated to their ACTIONTYPEs (ac-tionType), the service agent responsible for them (responsible) and the associated contact agent (contact). Pieces of information are linked to their DATATYPEs (dataType), their owner (owner), their potential recipients (forwardList) and their registered retention duration (duration).

Any instance of these predicates can be true or false at a given instant in the timeflow, thus allowing a precise description of past and planned events. One must notice though that L DLP is not an agent communication language. Its only aim is to internally represent the information about the speech acts taken by the agents, not to embody them.

For each predicate in the language, each argument takes its value in a domain which is a finite or countable set. Therefore, the set of all possible L DLP predicate instances is countable and can be mapped onto a set of (virtual) propositional atoms. In the case one of the arguments is not bound in an expression, then the predicate represents a propositional schema (like axiomatic schemata), covering a whole set of propositional atoms. One should note that there are no explicitly quantified formulae in the language. This is why, even though we use the form of predicates to express our information, we can consider a modal logic based on L DLP as a propositional modal logic.

DLP Syntax

DLP is a language where the obligation modality Ob of Standard Deontic Logic (SDL [START_REF] Wright | Deontic logic[END_REF]) is freely mixed with temporal operators from Propositional Linear-time Temporal Logic (PLTL [START_REF] Pnueli | The temporal logic of programs[END_REF]). The well-formed formulae ϕ of the DLP language are defined as follows, where p is a L DLP proposition2 :

ϕ = p | ϕ " ∨ " ϕ | "¬" ϕ | "Ob" ϕ ϕ" U " ϕ | "H" ϕ | "X -1 " ϕ ; (DLP-1)
We have chosen a temporal language allowing much expressivity on the future, through a strict "until" operator U. A loose until U -is defined as well, including the present (DLP-2). Since this logic is to be used by an agent to reason about its own behaviour and the plans it chooses to execute, more expressivity is needed in the future than in the past, where a "since" operator has not proved essential. We thus rely on an universal modality H on the past, and a X -1 operator pointing to the previous time step (DLP is to be interpreted over non-dense timeflows). Its symmetric operator in the future is a "next" modality X, defined as an abbreviation (Xϕ def = ⊥ U ϕ). We will use the usual temporal abbreviations G (universality in the future), F (existential dual of G) and P (existential dual of H), none of them including the present. We define their loose counterparts G -, H -, F -, P -including the present.

ϕ U -ψ def = ψ ∨ (ϕ ∧ ϕ U ψ) (DLP-2) F ϕ def = ⊤ U ϕ (DLP-3) Gϕ def = ¬F ¬ϕ (DLP-4) P ϕ def = ¬H¬ϕ (DLP-5)
We also define a class of indexed X i operators, based on X and X -1 , which can be used to travel step-wise along a timeflow:

       X 0 ϕ def = ϕ ∀n ∈ Z * + , X n ϕ def = XX n-1 ϕ ∀n ∈ Z * -, X n ϕ def = X -1 X n+1 ϕ (DLP-6)

DLP Semantics

DLP formulae are interpreted over Kripke-like bidimensional structures which we call DLP models.

Definition 1 (DLP model)

A DLP model M is a set {H, T , ❀, O, v} where: • H is a countable set of objects (h, h ′ , h ′′ ... ∈ H) called histories; • T is a countableset of objects (t, t ′ , t ′′ ... ∈ T ) called dates. A couple from I = H × T (i, i ′ , i ′′ ..

. ∈ I) is called an instant (or a world, for DLP interpretation is based on them);

• O is a (serial) binary relation among instants (O ⊂ I × I) called the deontic accessibility relation;

• ❀ is a binary relation (serial, left-unbounded, linear in both directions) among dates (❀⊂ T × T ) called the temporal accessibility relation;

• v is an application from L DLP to ℘(I) called the valuation function.

A DLP model is then a bi-dimensional grid where an instant i is the point defined by a couple of coordinates (h, t). A particular date t 0 can be identified as an arbitrary reference point for the timeflow. The truth of L DLP propositions and DLP formulae is defined for instants, which are the elementary worlds of the structure. For each instant i = (h, t), the equivalent notations M, h, t |= ϕ and M, i |= ϕ read, respectively, "ϕ is true at date t in history h of model M" and "ϕ is true at instant i of model M". We define the relation < (resp. ≤) among dates as the transitive (resp. transitive and reflexive) closure of ❀. DLP formulae are interpreted over DLP structures as follows (with p ∈ L DLP , ϕ, ψ ∈ DLP ):

M, h, t |= p iff (h, t) ∈ v(p) (DLP-7) M, h, t |= ¬ϕ iff M, h, t |= ϕ (DLP-8) M, h, t |= ϕ ∨ ψ iff (M, h, t |= ϕ or M, h, t |= ψ) (DLP-9) M, i |= Ob ϕ iff (∀i ′ ∈ I, if iOi ′ then M, i ′ |= ϕ) (DLP-10)
Thus, a deontic obligation on a formula at a given date of a given history means that this formula is true at all instants accessible via O. One could note that O is not a relation among histories: a deontically acceptable alternative is a date in a history, and not the history as a whole. This gives a better granularity to the notion of norm violation. The following formulae give the semantics of the temporal operators: ϕ U ψ is true at a given date of a given history if and only if, in the same history, ψ occurs at some point in the (strict) future, and ϕ is true from the next instant (tomorrow) until then. Hϕ is true at an instant if and only if ϕ has been true at every past instant in the same history, and X -1 ϕ is true at an instant if and only if ϕ was true at the previous instant in the same history. It is then straightforward to check that the semantics of temporal abbreviations is defined as usual.

M, h, t |= ϕ U ψ iff ∃t ′ ∈ T ,    t < t ′ , M, h, t ′ |= ψ ∀t ′′ ∈ T , if t < t ′′ < t ′ then M, h, t ′ |= ϕ (DLP-11) M, h, t |= Hϕ iff ∀t ′ ∈ T , if t ′ < t then M, h, t ′ |= ϕ (DLP-12) M, h, t |= X -1 ϕ iff ∀t ′ ∈ T , if t ′ ❀ t then M, h, t ′ |= ϕ (DLP-13)
We will now examine how obligations with deadlines and maintained interdictions can be defined in DLP. As an example, we will consider the following (fictional) norm: users must be informed at least one week in advance of the nature of any process involving their personal information. This sentence looks rather simple, and not uncommon. It could be part of a corporate regulation, for instance. However, its interpretation is not so straightforward, and could benefit from the notions of obligations with deadlines and maintained interdictions. Indeed, an agent could consider this norm from two different points of view. On the one hand, if a given user has not been informed so far about a given process, then there is a standing interdiction (maintained for one week) to perform that process. On the other hand, if the agent has planned to perform a process more than one week in the future, then it has the obligation to inform the user before a date situated one week before the process. The regulation will then be translated into (a conjunction of) two partially redundant DLP formulae, representing the two sides of the problem 3 . This example norm is pretty rich, showing the need for the dated operators of obligations with deadlines and maintained obligations. Other more intuitive or more common example norms may have resulted in simpler interpretation cases.

In the following, we will consider the building of an operator Ob(ϕ, δ) intended to mean: "it is obligated that ϕ becomes true strictly before δ". Later on we will see how to construct its deontic counterpart, the maintained obligation operator F or(ϕ, δ). We define violOb(ϕ, δ) and violF or(ϕ, δ) as the respective violations of these deontic operators.

Requirements

In order to represent deadlines, we add a special kind of propositions to the language, the dated propositions. The additional predicate date(δ) means that δ is a dated proposition. They are defined as propositions occuring once and only once in the timeflow. Furthermore, for practical reasons, we consider that the dated proposition δ i correspond to the date

t i (∀i ∈ Z, ∀h, M, h, t i |= δ i ). date(δ) def =    δ ∧ G¬δ ∧ H¬δ ∨F (δ ∧ G¬δ ∧ H¬δ) ∨P (δ ∧ G¬δ ∧ H¬δ) (DLP-14)
We introduce and discuss eight requirements that an operator for obligations with deadlines must match, in order 3 There are actually other cases to be examined by the agent, like when a process is planned less than one week in the future and the user has not been informed. In this cases, the unavoidable violation is triggered by the first form of the norm. The reader can check that the remaining possibilities are covered by the two norm descriptions we have given.

to properly represent the notion in DLP logic.

1. Deadlines must be dated propositions: for a deadline to bear a meaning, it must be defined in a clear and distinct fashion. It must exist and be unique in the timeflow. Our dated propositions have been defined for that purpose.

2. The deadline must be in the future: it is obvious for a human that a present or past deadline does not leave any choice or liberty to plan actions.

3.

Obligations on ⊤ must be tautologies: we introduce this principle in coherence with the immediate deontic obligation, for which Ob ⊤ is a theorem. In the same way, Ob(⊤, δ) should be a theorem.

4.

Obligations on ⊥ should be antilogies: for the same reasons, ¬ Ob(⊥, δ) should be a theorem.

5.

Violated obligations should be dropped after the deadline: this choice is rather philosophical in nature, and subject to debate (although it is a consequence of point 1). We think that if the agent could not cope with the obligation on time, then it is too late and the violation must be simply accepted. This principle is not an opposition to the existence of eventual contrary-to-duty norms attached to dated obligations.

6.

Violations should be punctual: we prefer to think of violations as events, not states. It gives a better expressivity and is allowed by the fact that we can reason on the past. Again, this point is specific to the chosen formalism and subject to debate.

7.

The propagation principle must be respected: it says that the obligation with deadline must be maintained from instant to instant, until the obligation is respected or the deadline is reached.

Ob(ϕ, δ) ∧ ¬(ϕ ∨ δ) ∧ ¬Xδ → XOb(ϕ, δ) (P)
8. The monotony principle must be respected: it says that if there is an obligation with a deadline, then an obligation with a further deadline can be derived (M).

Ob(ϕ, δ) ∧ F (δ ∧ F -δ ′ ) → Ob(ϕ, δ ′ ) (M)
The first six requirements have already been pointed out as choice points and discussed by Dignum [START_REF] Dignum | Meeting the deadline: Why, when and how[END_REF]. However, due to their different goals and formalisms, their opinion differ on some aspects. For instance, since they do not reason on past, they define violations as states, not events. Furthermore, they reject obligations on ⊤ since they are not coherent with the STIT operator they use. On some other points, they do not make a clear choice and leave the final decision to the reader, depending on her needs. Propagation and monotony requirements have been introduced by Brunel [START_REF] Brunel | A state/event temporal deontic logic[END_REF], and we have adapted them to our more strict interpretation of the notion of deadline.

Evaluating some existing proposals

Several works have been done on obligations with deadlines, and we evaluate three of them. We choose to examine three proposals made by Dignum [START_REF] Dignum | Meeting the deadline: Why, when and how[END_REF], Demolombe [START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF] and Brunel [START_REF] Brunel | A state/event temporal deontic logic[END_REF]. We will adapt them to our logical formalism (we will note their proposed operators, respectively, Ob a , Ob b and Ob c ) 4 and see how these adaptations satisfy our requirements.

The operator Ob a by Dignum is defined jointly with the notion of violation, and does not rely on a real deontic logic [START_REF] Dignum | Meeting the deadline: Why, when and how[END_REF]. Here, an obligation with a deadline is characterized by the absence of violation before the deadline, and the maintaining of a violation, or its negation, after the deadline, depending on whether the obligation has been fulfilled on time or not. Because of its strictly temporal definition, such obligations can be derived whenever they seem to be respected. This is quite an undesirable feature for building norm-directed agents. Further more, it is not monotonic at all: there are several cases where an obligation with a further deadline cannot be derived 5 . Deadlines with a value of ⊤ can be defined, resulting in an immediate obligation.

The Ob b operator, adapted from Demolombe [START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF], translates better in a deontic and temporal logic. An obligation with a deadline is now the maintaining (until the deadline or the fulfilment of the obligation) of an obligation of anteriority between the target formula and the deadline. Propagation is here built-in in the operator, in the form of immediate obligations allowing us to derive dated obligations. Regarding monotony, if an obligation Ob b (ϕ, δ) is fulfilled on time, then it is possible to check that Ob b (ϕ, δ ′ ) is true for any future δ ′ . However, if it is violated, it is not possible to derive an obligation with a further deadline.We will call this semimonotony. It is interesting to see that this property has a nice side-effect: it prevents us from deriving multiple violations for the same initial obligation, whereas it still allows monotony if the obligation is fulfilled.

The Ob c operator is based on two different dated obligations [START_REF] Brunel | A state/event temporal deontic logic[END_REF]. The first one, Ob c ′ , is used when the obligation is initially activated, and does not allow propagation (although it is monotonic). Brunel, unlike precedent authors, reason on delays of k time steps (k ∈ N) rather than on deadlines.

The final operator has the following meaning: an obligation with a deadline is active at the present time if there was in the past an obligation (of type Ob c ′ , and not fulfilled yet) on ϕ with a deadline not reached already, and also that there was no obligation on the same formula with a shorter deadline. This more complex operator deals efficiently with propagation and is able to express subtle nuances of dated obligations. Yet, it has several noticeable drawbacks in our application context. First, it introduces new quantifiers on delays (when Ob b relies on existing temporal quantifiers, for instance). For this reason it is not directly expressible in our modal language. Plus, the operator does not respect the monotony principle, although it deals properly with other requirements, by reasoning on delays rather than on deadlines.

Table 1 summarizes how the three operators match our eight requirements. An empty square means that the requirement is only partially satisfied, or under some conditions.

Requirement 1 2 3 4 5 6 7 8

Ob a ✷ ✷ Ob b ✷ ✷ ✷ Ob c ✷ Table 1
. Evaluation of existing operators

An operator adapted to DLP

Even though Ob c satisfies more of our requirements, both Ob a and Ob c imply too significant extensions to our logic to be directly usable (namely, the non-deontic nature of Ob a and the explicit quantification on durations in Ob c ). The operator Ob b seems to be a better trade-off, being much more compatible with DLP formalism. It can be improved by the use of dated propositions, so that it satisfies our requirements in a better way. For the reason we have given, we will accept semi-monotony rather than strict monotony for our operator, which is now defined (along with its punctual violation, adapted to the persistent one proposed by Demolombe) as follows:

Ob(ϕ, δ) def =    date(δ) F δ Ob(F -(ϕ ∧ F δ)) U -(ϕ ∨ δ) (def-1) violOb(ϕ, δ) def =    date(δ) δ P (Ob(ϕ, δ) ∧ ¬ϕ U -δ) (def-2)
It is now easy to show that this adapted operator satisfies the eight requirements (with monotony replaced by semimonotony) defined in section 3.1.

Ob(ϕ, δ) ∧ date(δ ′ ) ∧F (δ ∧ F -δ ′ ) ∧ ¬(¬ϕ U -δ) → Ob(ϕ, δ ′ )
Properties 1 and 2: trivial, by definition of the operator. Property 3: once we have date(δ) and F δ, Ob(⊤, δ) re-

duces to Ob(F -(⊤∧F δ)) U -(⊤), then to ⊤ U -⊤, which is ⊤. Property 4: Ob(⊥, δ) implies Ob(F -(⊥)) U -(δ). F -(⊥) implies F (⊥), then ⊥.
By the D axiom of SDL obligations, the original expression then boils down to ⊥ U -δ and then to ⊥. Property 5: Ob(ϕ, δ) → F δ, so F -Ob(ϕ, δ) → F δ, then ¬G -¬Ob(ϕ, δ) → F δ. F δ implies ¬δ, so (¬G -¬Ob(ϕ, δ)) → ¬δ. Modus tollens then leads us to the result. Property 6: violOb(ϕ, δ) implies δ, so it can be true only once in the timeflow. Property 7: the antecedent of the proposition allows us to derive Xdate(δ) and XF δ (through ¬Xδ ∧ F δ). ¬(ϕ ∨ δ) tells us that the deadline is not reached yet, so the whole U -expression will be true at next time step. By conjunction of these points, we get XOb(ϕ, δ). Property 8: the antecedent of the proposition gives us date(δ ′ ) and F δ ′ . ¬(¬ϕ U -δ) implies that ϕ will be true before δ, so before δ ′ . Therefore,

Ob(F -(ϕ ∧ F δ)) U -(ϕ ∨ δ) implies Ob(F -(ϕ ∧ F δ)) U -(ϕ ∨ δ ′ ).
On the other hand, (ϕ ∧ F δ) implies (ϕ ∧ F δ ′ ), therefore by the normal character of modalities we get Ob(F

-(ϕ ∧ F δ ′ )) U -(ϕ ∨ δ ′ ).
The antecedent therefore allows us to derive Ob(ϕ, δ ′ ). ✷

Maintained obligations

It is much easier to defined an operator with good properties for maintained interdiction than for obligations with deadlines. Our operator and its associated violations are defined by the formulae (def-3) and (def-4). It is easy to show that this operator has eight properties corresponding to the ones we have seen (where principle 5 would be the maintaining of interdictions, even violated, until the deadline, and monotony would be the ability to derive an interdiction with a sooner deadline).

F or(ϕ, δ) def = date(δ) ∧ F δ (F or ϕ) U -δ (def-3) violF or(ϕ, δ) def = date(δ) ∧ F δ ∧ ϕ P -F or(ϕ, δ) (def-4)

Application to privacy norms

Now that we have two suitable operators for obligations with deadlines and maintained obligations, we can translate in DLP logic the interpretations we have made of the fictional norm presented in part 3. Formula (ex-1) formally says that if there is an identified type for a given process, and this process uses given data, and the owner of these data has not been informed so far, and the date δ in situated one week in the future, then there is a maintained interdiction to perform the process until δ. Formula (ex-2) says that if δ is in the future and one week before a planned process, and the owner has not been informed yet, then there is an obligation to inform her before δ. actionType(ProcessID, ActionType) H¬informActionType(self, User, ProcessID, ActionType) owner(ProcessID, DataID, User) date(δ) ∧ X 7 * 24 δ

           → F or(perform(self, ProcessID), δ) (ex-1) actionType(ProcessID, ActionType) date(δ) F (δ ∧ X 7 * 24-1 perform(self, ProcessID)) H¬informActionType(self, User, ProcessID, ActionType) owner(ProcessID, DataID, User)                → Ob(informActionType(self,
User, ProcessID, ActionType), δ) (ex-2) If norm (ex-1) is activated (i.e. if its antecedent is verified), then the agent sees that any occurence of ProcessID before δ would result in a violation. A privacy-aware agent willing to comply with enacted regulations would then refrain from performing this action (by generating a BDI desire about it for instance, or by postponing any undertaken plan or intention involving ProcessID). The monotony principle here makes it easier to develop reasoning means to effectively derive short-term and even immediate interdictions on the basis of a maintained interdiction.

If norm (ex-2) is activated, then the agent knows that it has to inform the user before a given and well-known date δ. The propagation principle (and basically the structure of the operator, ensuring the utterance of an immediate obligation at each step of the period) provides a direct way to make the agent feel "concerned" already by this obligation (thus triggering planning mechanisms) rather than postponing the interpretation of the norm.

Conclusion and future work

In this paper we have proposed a language, based on temporal deontic logic, to represent and reason on privacyrelated norms. We have pointed out the need for a specific operator dealing with obligation with deadlines. We have defined eight requirements that such an operator should match in order to bear the right intuitive meaning in our formalism. We have examined three proposed operators for operations with deadlines, ported them onto our logic, and observed that none of them met all our requirements. We have slightly adapted the most suited of these operators to satisfy our requirements and designed another one for dealing with maintained obligations. Finally, we have used these operator in the translation of an example regulation in our logic.

It is interesting to point out that the translation of privacy regulations from natural language to formal expressions cannot be done without a human interpretation phase, and not only because of the natural language processing problems. In the context of artificial agents, it would then be necessary to develop norm designing tools constraining the form of the regulations defined by a human user.

Current work involves finishing off the axiomatization of DLP logic (notably, there is a debate over temporal/deontic converse axioms, which could be an obstacle to the dynamism of the norm base) and characterizing its complexity. The DLP normative conflict detection and resolution engine based on our previous work [START_REF] Piolle | Une logique pour raisonner sur la protection des données personnelles. In 16e congrès francophone AFRIF-AFIA sur la Reconnaissance de Formes et l'Intelligence[END_REF] is to be adapted in order to take into account obligations with deadlines and maintained obligations. Further on, we plan to formally evaluate the characteristics and performance of the implementation and compare them to the formal model of DLP logic as well as to other possible implementations. DLP engines will then be integrated in the cognitive layers of "privacy-aware" software agents. These agents are then meant to be used as personal assistants or as automatic service providers in Internet-based (or other distributed) applications, thus helping human users to deal properly and more safely with their private information.

This research has been supported by the Web Intelligence project of the Rhône-Alpes region ISLE cluster.

  Theorem 3.1 The operator Ob(ϕ, δ) and its associated violation violOb(ϕ, δ) have the following properties:

	1. Deadlines are dated propositions (they occur once and
	only once in the timeflow);
	2. Deadlines are always in the strict future;
	3. Ob(⊤, δ) can be derived for each properly defined
	deadline δ;
	4. ¬Ob(⊥, δ) is a theorem;
	5. Obligations are dropped after the deadline;
	6. Violations are punctual:
	violOb(ϕ, δ) →	G¬violOb(ϕ, δ) H¬violOb(ϕ, δ)
	7. Propagation principle is respected;
	8. Semi-monotony is respected:

For page limitation reasons, we do not give the full argument list and usage of each predicate.

The logic presented here is actually a simplified version of DLP. The complete version makes use of a class of obligation modalities Ob ν a (rather than the single one Ob used here), differentiated by agent and by normative authority. This is to allow normative conflict representation and arbitration, as it has been shown in a previous communication[START_REF] Piolle | Une logique pour raisonner sur la protection des données personnelles. In 16e congrès francophone AFRIF-AFIA sur la Reconnaissance de Formes et l'Intelligence[END_REF], but does not bring anything essential to the problem addressed here.

Operators appear in a different formalism in the original papers, and have slightly different properties in a different context. Ob c , for instance, is originally expressed using (unnecessary) extensions of the temporal language, which we have translated into standard LTL operators.

[START_REF] Demolombe | Formalisation de l'obligation de faire avec délais[END_REF] Namely, if the obligation is fulfilled and then another obligation on the same formula is violated after the first deadline, or if the obligation is violated and then ϕ becomes true after the deadline.