Jonathan Ben-Naim
email: jonathan.ben-naim@irit.fr

Dominique Longin
email: dominique.longin@irit.fr

Emiliano Lorini
email: emiliano.lorini@irit.fr

Formalization of Cognitive-Agent Systems, Trust, and Emotions

A cognitive agent is an agent characterized by properties that are generally attributed to humans. Cognition is viewed here as a general mechanism of reasoning (in contrast with reactive agents) about knowledge. Such agents can perceive their environment, reason about fact or epistemic states of other agents, have a decision making process, etc. This article presents the main concepts used in cognitive agents formalizations, and speak about two particular concepts related to humans: trust and emotion. The language used for cognitive agents is here a logical language because it particularly fits well for both knowledge representation and reasoning formalization. But, even if trust and emotion can be both easily formalized by logical languages, we show that some numerical models are also well adapted.

Introduction

To characterize an agent is never easy because a lot of languages can be used, the properties attached to this agent can be various, some concepts may have different names in different contexts, the set of concepts that we need in some context must be different of the set needed in another context, etc. In the following, agents are defined as entities having some properties such as: autonomy (they can act without any human action but only with respect to their internal states); reactivity (they can interact with otherhuman or artificial-agents by using a communication language, or perform some actions that are needed by the environment); pro-activation (they can adopt a behavior following from their goals by taking the initiative); etc. As it is summarized by Wooldridge [2000], agents are viewed here as computer systems "deciding for themselves what to do in any given situation" More specifically, in the area of artificial intelligence (AI), the agents properties are often described by using concepts usually associated to humans such as: mental attitudes (belief, knowledge, goal, desire, intention, etc.); social attitudes (commitment, common belief or common intention, acceptance, etc.), time and action. The properties can also be themselves more specific to humans. We can cite for instance: rationality (in a very wide sense, it means that agents do not act in a contradictory manner: they do not believe both something and its converse, they act with respect to their goals, etc.); sincerity (agents do not aim to communicate something they thinks false), etc. These properties depend on the context where agents evolve. For instance, is it suitable to have a sincere agent playing poker or an insincere agent supposed to report weather forecasting? Certainly not. So, all the properties used by system designers are selected depending on a particular application.

In the following, we call "cognitive agent system" (or "cognitive system" for short) a system which has a behavior predictable only from its mental attitudes. So, the problem is to determine the mental attitudes that are needed to formalize the properties that we want to attribute to the agents of the system. An advantage of such systems is that they can describe everything, even functional objects (cars, locks, etc.). These systems are very popular in AI because they have interesting properties: they are philosophically well-founded, the formal tools are mathematically well defined, the high abstraction level that is used allow to distinguish how something works in the real workd from the general concepts that will used to model it. Finally, these systems have a strong explanatory power (an action mathematically following from both their properties and the agents' mental states that are members of these systems).

In the following, we first speak about cognitive agent systems formalization (Section 2). Such an agent is supposed to be able to: represent its physical environment (including the other agents); represent the manner that it wants this environment evolves; reason about these representations in the aim to perform an action.1 Logic is a tool that fits very well both this formalizing task and this reasoning task, and this section will only present logical tools (more precisely, modal logics), including three types of operators: belief or knowledge (environment representation), desires, goals, preferences, etc. (representation of the wished evolution of this environment), action and time. 2Finally, we present two particular concepts strongly related to cognition: trust (Section 3) and emotion (Section 4). We will focus on the cognitive structure of these concepts, that is, on mental states that are necessary to trust or to trigger an emotion. But logic is less appropriate to the representa-tion of their intensity than numerical models. It explains why there are both logical models and numerical models representing trust and emotion. We will give a short overview of these two approaches.

Cognitive-Agent Formal Systems

Short History of BDI Systems

One can say that the story of formal systems as they are today is as long as that of philosophy. Indeed, since Aristotle, philosophy investigated a certain number of concepts: modal logics (logics of necessary and possible), epistemic or doxastic logics (belief and knowledge), deontic logics (obligation, interdiction, permission), temporal, conditional, dynamic logics (explicit or implicit actions), etc.

Our main subject is modal logics, that is, logics including operators that are not truth-functional. So, if is a modal operator, then the formula ϕ (where ϕ is also a formula of the modal logic) is true independently of the truth-value of ϕ. This operator can represent beliefs, goals, intentions, etc. For example, if Bel i sunny means that Agent i believes it is sunny, then i can believe it is sunny or not, independently of the weather. (See Chapter ?? of the same volume for more details about modal logics.)

All these formal works, as well as certain others, in particular in philosophy (see [START_REF] Searle | Speech acts: An essay in the philosophy of language[END_REF] and especially [START_REF] Bratman | Intentions, plans, and practical reason[END_REF]), have contributed to the construction, between end of 80's and beginning of 90's, of the logic BDI of Cohen and Levesque, where: first, intention is defined, in a non-primitive way, from beliefs and goals [START_REF] Cohen | Intention is choice with commitment[END_REF]; and second, the formal framework is also used to characterize the capacities of the agents with regard to communication [START_REF] Cohen | Intention is choice with commitment[END_REF]. One can say that those works have been the corner stone of cognitive-agent systems3 . Indeed, it suffices to see theories of agents (in particular, those of the language of the agents) as theories of action4 . Those works have been followed by those of Rao and Georgeff who, based on the logical principals adopted by Cohen and Levesque, have looked forward to a more rigorous formal framework in a temporal logic accompanied with a semantics and an axiomatization [START_REF] Rao | Modeling rational agents within a BDIarchitecture[END_REF]. It is worth noting that in those works intention is defined in a non-primitive way. In the same research avenue, we can mention the work of Wooldridge, who introduced the logic LORA (LOgic of Rational Agent) in [Wooldridge, 2000]. The goal of Wooldridge was not only to formalize an agent architecture of the type BDI, but also its evolution in time.

Concerning french work, we can mention the work of Sadek (see his PhD thesis or KR'92), who, in a formal framework of the same family, defined rationality rules in order to guide the behaviour of a rational agent in a system of rational interactions. By the way, his theory has influenced a language of agent communication (agent communication language or ACL) that became an international reference, which has been used or gave rise to numerous works in the agent community: the FIPA language5 .

In the mid 90's, more operational languages appeared, in the sense that the goal is not only to have a logical formalism able to capture the concepts useful to construct the agent systems of interest, but also to implement them. So, BDI systems formalized in situation calculus appeared (see for example the works of Shapiro, Lespérance, and Levesque in Toronto). Programming languages based on primitives of the BDI type also appear: one can mention e.g. GOLOG or ConGolog. This community gave rise to what can be called nowadays cognitive robotics, whose laboratory of the same name in Toronto is the most prominent representative.

Certain formalisms also aims at describing normative systems, that is, systems where the agents have not only to consider what they believe (or know) and what are their goals, but also what they must do. This aspect uses (also also inherits theoretical questions from) deontic logic. For example, we can mention the BOID architecture (where O represent the obligation component of the BDI system) of van der Torre et al. (see e.g. the paper published in AGENTS'01).

Next, BDI systems not only manipulate mental attitudes (in addition to time and/or action), but also social concepts or external constraints. Obligation can be seen as an internal norm (it is then formalized by an operator indexed by an agent or a group of agents), or as an external law every agent must obey (it is then formalized by a non-indexed operator).

By the end of 90's, the BDI systems, as they are then formalized, are heavily criticized, because they are based on strong hypotheses about mental states, in particular sincerity. So, in FIPA for example, an agent believes everything it is told by another agent, because it always assumes the latter tells the truth.

To avoid this problem, certain works describe the effect of a linguistic action by separating what the speaker wants to mean from what the listener believes on the basis of hypotheses made by the latter about the sincerity and competence of the former. Other works looked forward to alternative concepts allowing us to free us from those hypotheses about the internal states of the agents. For example, there are numerous works on social commitment aiming at capturing the public commitment of an agent generated by what that agent says. For instance, when someone says something, he (or she) is committed to the truth-value of that proposition: he could not say he did not said it, and cannot say or do something that opposes what he said (see e.g. the work of Singh [START_REF] Singh | An ontology for commitments in multiagent systems[END_REF] and de Colombetti in Switzerland). Nevertheless, those approaches also have drawbacks: other hypotheses are made (for example, the public aspect of linguistic actions and the fact that they are correctly interpreted by their targets). In addition, it is not obvious that this concept is devoid of links with the mental states of the committed agents.

Finally, this notion has not been studied in a satisfactory way as a nonprimitive concept6 , despite the fact it apparently contains a normative and conventional component, as well as violation condition. In such circumstances, those approaches are almost not BDI systems, since they do not involve mental states: there is an intuitive link, but it has to be formally established.

Other traditional concept have been confronted to that problem, e.g., common belief. The latter is generally defined as the infinite conjunction of the alternative beliefs between agents. For example, if there is common belief between agents i and j about ϕ, then i believes ϕ, j believes ϕ, i believes j believes ϕ, j believes i believes ϕ, i believes j believes i believes ϕ, etc.

Thus, the problem in an implemented system is to decide whether there is common belief without having access to the minds of the agents. At best, we can construct a subjective notion of common belief, i.e., the fact that an agent believes there is common belief (maybe it is not the case). A number of philosophical works are related to this question (see e.g. [START_REF] Gilbert | On Social Facts[END_REF]). They led to notions like acceptance (see e.g. [START_REF] Lorini | The logic of acceptance: grounding institutions on agents' attitudes[END_REF]).

In parallel, certain prior AI problems have been transfered to the BDI framework and gave rise to a rich literature: the frame problem (how to describe environment in a concise and exhaustive fashion?), the problem of characterizing actions (what are the necessary and sufficient conditions to execute a given action?), the problems of revision (how to have an agent's knowledge evolves with time?) and action ramification (how to describe the impact of an action on the domain, including the mental states of the agents). For example, the advent of BDI systems was followed by the problem of revising mental states (see e.g. [van der Hoek et al, 2007]).

More recently, this problem has become the heart of a branch of the domain: dynamic epistemic logics (see below). Put simply, the goal is to integrate into the semantics of these logics the fact that the beliefs (or knowledge) of an agent can evolve: that agent can change his mind, learn that certain propositions are true, learn that others are false, etc. At the cost of certain technical constraints, the logics of public announcements give an adequate answer to the hard question of mental-states evolution. For an overview on that subject see e.g. [START_REF] Van Ditmarsch | Dynamic Epistemic Logic[END_REF].

Finally, agent testbeds have been developed, like e.g. AgentSpeak by Rao, Jason by Hübner and Bordini, or 2APL by Dastani. Those testbeds allow the implementation of agents and multi-agent systems, but do not yet exhaust all the expressive power of the BDI logics. In particular, they are not equipped with a complete set of boolean operators and do not use theorem provers, which by the way already exist for certain (families of) well-known logics.

Concepts proposed in the domain of BDI systems have also been used in other domains of AI. For example, this is the case of argumentation, where e.g. Amgoud used argumentation methods to generate desires and plans in an autonomous agent [START_REF] Amgoud | An Argumentation-based Approach for Practical Reasoning[END_REF] (see also Chapter ?? of the same volume).

Basic Concepts

In what follows, we present the basic concepts generally used in the formalization of cognitive-agent systems in terms of mental states. Of course, all systems do not use all concepts simultaneously, because the way an agent system is characterized depends on the domain of that system.

As soon as we need nested operators, modal logics are particularly adequate, because a formula of a modal logic in the range of a modal operator forms a new formula of that logic. So, we can have an arbitrary large degree of nestedness in the formulas of the object language. This property is particularly important in the domain of cognition, because we can have beliefs about almost anything, including other beliefs: Agent i believes Agent j believes Agent k believes Agent i believes p, etc. (see Chapter ?? on knowledge representation of the same volume).

Belief Operators

The notion of belief has been deeply studied in the domain of doxastic and epistemic logics, since the early 60's (see [START_REF] Gochet | Epistemic Logic[END_REF] for an exhaustive overview). This is probably one of the most studied notion in Logic, in all its forms (classical logic, modal logic, with or without degrees representing the strength of the beliefs or knowledge of an agent 7 ).

A commonly used logic is the propositional modal logic without degrees where "Agent i believes ϕ is true" is denoted by Bel i ϕ, where Bel i (for every agent i) is called the modal operator of Agent i's beliefs, and where ϕ is some formula. Traditionally, the fact that Bel i ϕ is true in a certain world w 0 is interpreted as the fact that ϕ is true in all worlds that are accessible from 7 In the present work, we only consider qualitative approaches to the notion of belief.

We do not discuss the quantitative approaches formalizing degrees of belief (see e.g. [START_REF] Laverny | From knowledge-based programs to graded beliefbased programs, part ii: off-line reasoning[END_REF]). w 0 according to Agent i. Note that i has no certainty that the real world belongs to this set of epistemic worlds (i may be wrong). To represent this, the semantics includes an accessibility relation for every agent. So, the fact that i believes ϕ is true in the real world w 0 is denoted by w 0 Bel i ϕ. Semantically, this means ϕ is true in all worlds that are accessible from w 0 via the relation corresponding to i and denoted by B i .

There is a consensus in the literature that the logic of beliefs in the normal modal system KD45 [START_REF] Chellas | Modal Logic: an Introduction[END_REF], even though this logic constitutes an idealization of certain principles. For example, this logic assumes an agent instantly knows all beliefs implied by its own (omniscience) and it is conscious of all those beliefs (positive introspection). Nevertheless, those criticisms are mitigated by the fact that they constitute idealizations (not aberrations), which are not necessarily counter-intuitive for an artificial agent.

Fig. 1 shows the semantics of the belief operator of agent i. The set of all worlds that are accessible from w 0 is denoted by B i (w 0 ), where B i is the accessibility relation between worlds for Agent i and is graphically represented by arrows.

w 0 B i B i (w 0 )

Temporal Operators

There are many temporal logics, depending on the way one wants to represent time (ramified or linear, with or without explicit temporal indexes, etc.). Temporal logics are relatively well-studied in the domain of modal logics and theoretical computer sciences [van Benthem, 1991]. There semantics is based on transition relations between possible states and are thus equivalent to (potentially infinite) automates (see Chapter ?? of the same volume for more detail about temporal reasoning).

Here, we focus on a very simple notion: linear time. Since this notion is combined with the beliefs of the agents, this means that the latter are not about epistemic worlds, but about linearly-ordered sets of worlds called "stories". This allows us to simulate a tree-based nature of time, since each story corresponds to a development of future events (the agent believes possible).

For example, Fig. 2 represents the four stories believed by Agent i. The dots on the stories represent the present moment and the dashes the past and future moments. So, the agent right now believes that p is true (Bel i p); it consider the possibility that r is right now true but becomes false thereafter (¬Bel i ¬(r ∧ F ¬r)); etc. w 0 s p,r ¬r p s t p s p,q s q q ...

B i B i B i B i B i (w 0 )

Fig. 2 Linear time and epistemic worlds

We can define the operators H and P (about the past) in the same way we defined the operators G and F .

Technically, time is defined in a modal logic of linear time of Type S4.3 t (see [START_REF] Burgess | Basic tense logic[END_REF] for more details). Nevertheless, those operators can be semantically defined with a tree-based structure (which is by the way what is done in [START_REF] Rao | Modeling rational agents within a BDIarchitecture[END_REF]).

Finally, we sometimes use the two operators X and X -1 such that X ϕ means "ϕ will be true right after the present moment is the considered story" and X -1 ϕ means "ϕ was true right before the present moment in the considered story". Obviously, there exists formal links between those operators and the temporal ones defined previously.

Goal Operators

The notion of goal has been widely studied in the literature and has been used in very different senses (see e.g. the notion of goal in Cohen and Levesque [START_REF] Cohen | Intention is choice with commitment[END_REF] or [START_REF] Rao | Modeling rational agents within a BDIarchitecture[END_REF], the notion of choice in the PhD thesis of Sadek or KR'92). We focus on the notion of chosen goal (or preferred goal), with regard to the coherent subset of proposition the agent wants to make true. The primitive operators of goal are denoted by Choice i (where i ranges over all agents) and Choice i ϕ means that "Agent i right now choose to make the goal ϕ right now true".

There is no restriction on the formula ϕ, so it can represent the present state of affairs. This is the difference with the operators of goals to be achieved (abandoned when the desired state of affairs comes true) or to be maintained (an agent looks forwards to keep a certain state of affairs true). As we did it with beliefs, we interpret Choice i ϕ in a world w 0 as the fact that ϕ is true in all the preferred world of the agent from w 0 . Most generally, goals are partial pre-order, but, for the sake of simplicity, we do not consider this point: we focus on coherent non-ordered binary goals.

A difficult and non-studied question is the following: how those goals emerge? From a cognitive point of view, it looks like they emerge from a deliberative process about more primitive attitudes: desires, ideals, and imperatives (see [START_REF] Rao | Modeling rational agents within a BDIarchitecture[END_REF][START_REF] Conte | Cognitive and social action[END_REF][START_REF] Castaneda | The role of beliefs in goal dynamics: Prolegomena to a constructive theory of intentions[END_REF]). The set of goals we characterize is the one obtained from a process of selection of ideals and desires. It is meant to resolve conflicts between those two concept and to eliminate impossible cases. Then, the chosen goals of an agent satisfy the two following fundamental rationality principles: they are consistent (an agent cannot choose two contradictory goals); the chosen goals are related to the beliefs of the agent that chose them. In [START_REF] Cohen | Intention is choice with commitment[END_REF], the relation between beliefs and goals is an inclusion relation: if an agent right now believes ϕ is true, then it necessarily right now has ϕ as a goal (this notion is called strong realism). We can also impose a relation of weak realism, where it is only required that there is a non-empty intersection between the epistemic worlds that are possible and those that are preferred. Some recent works aim to explain the goals building process by the way of desires. Desires and goals are often combined (see for instance [START_REF] Dubois | The strength of desires: A logical approach[END_REF]).

Ideals

There exist many normative systems in logic with very different characteristics, more or less complex, adapted to a class of problems or another. Those norms may have different origins: state laws, institution rules, moral (be it religious or not), etc.

Certain particular norms, specific to a given agent, are called ideals. We introduce a new set of operators such that Idl i ϕ means: "ϕ is an ideal state for Agent i". This means that i gives an order to itself, a kind of "must make true" for ϕ (when ϕ is false at the present moment) or "must keep true" (when ϕ is already true) [START_REF] Castaneda | The role of beliefs in goal dynamics: Prolegomena to a constructive theory of intentions[END_REF].

There are different ways to explain how a state ϕ becomes an ideal state for a certain agent. A possible explanation is that ideals are just social norms that have been internalized (or adopted) by this agent [START_REF] Conte | Cognitive and social action[END_REF]. Assume an agent believes in a certain group (or institution) there is a certain norm (e.g. an obligation) saying that a state ϕ must be true, whilst the agent sees itself as a member of that group. In such a case, the agent adopts this external norm (that does not originate from the agent and has not yet been acknowledge as a norm by the agent) and that norm becomes an ideal for that agent. For example, if Agent i believes in France, it is obligatory to pay taxes and that agent considers himself (or herself) as a French citizen, then he adopts this obligation and pays his taxes.

Semantically, the ideals are represented from the possible worlds considered as ideal by the agent having internalized those ideals. There is no particular relation with the other operators, besides belief, if we assume an agent is conscious of its ideals (see Chapter ?? of the same volume for more details about normative operators). (See also [START_REF] Gabbay | Handbook of Deontic Logic and Normative Systems[END_REF]] pour for more details about normative and deontic systems and [START_REF] Berreby | Modelling moral reasoning and ethical responsibility with logical programming[END_REF][START_REF] Lorini | A logic for reasoning about moral agents[END_REF] about moral systems.)

Explicit Action

When one tries to define "Agent i is capable of executing Action ϕ", one has to consider logics of action (see Chapter ?? of the same volume on reasoning about action and change). Generally speaking, those logics formalize actions with state-transition systems. There are essentially to schools of thought, one where action is explicit and one where it is implicit (see the next section).

The main logic of explicit action is propositional dynamic logic (PDL), which studies the interact between an action and its effects [START_REF] Harel | Dynamic Logic[END_REF]. It has been shown (e.g. in [START_REF] Van Linder | Formalising abilities and opportunities[END_REF]) that dynamic logic is particularly adapted to the characterization of the concepts of capacity and power. There is a rich literature on the integration of dynamic logic into logics of beliefs and goals (see e.g. epistemic dynamic logic [START_REF] Baltag | Logics for epistemic programs[END_REF] or doxastic dynamic logic [START_REF] Segerberg | Getting started: Beginnings in the logic of action[END_REF][START_REF] Segerberg | Belief revision from the point of view of doxastic logic[END_REF]).

PDL distinguishes between actions like α and formulas like ϕ and ψ, and its set of non-logical constants is constructed from those two categories. The formula After α ϕ expresses the fact that ϕ will be true after any possible execution of Action α. So, After α ⊥ means α is not executable8 .

Several extensions have been proposed where an agent is added to the arguments of the PDL operators. In such extensions, the formula After i:α ϕ means that ϕ is true after any possible execution of Action α by Agent i. For any action α and agent i, After i:α is an action modal operator.

Semantically, action is treated as a transition from a real world to a set of other real worlds (certain semantic constraints can force this set of worlds to be a singleton). Fig. 3

Implicit Action

Action is implicit in logics of agency, which study the interaction between an agent and the effects caused by it. The peculiarity of those logics is that they do not represent the actions that caused the effects (only results matter). For example, in the logic STIT [START_REF] Belnap | Facing the future: agents and choices in our indeterminist world[END_REF], actions are formalized by formulas involving an agent and speaking about the effects caused by that agent. So, the action described in "i buys the product p" is formalized by the following formula of agency: "i sees to it that Product p is bought by Agent i".

Formulas of agency are of the form STIT i ϕ, which means "The action chosen by Agent i at the present moment ensures that ϕ is true, independently of what the other agents do". In short, "i sees to it that ϕ". The modal operator STIT i is called the operator of agency.

Dynamic of Mental States

Last years, a certain number of researchers working in the domain of logics for autonomous-agent formalization and in multi-agent systems have proposed logics for the dynamic of mental states. They belong to the large family of dynamic epistemic logics (DEL), see e.g. [START_REF] Hv | Dynamic Epistemic Logic[END_REF]. DEL is a term used in a very large sense to include dynamic extensions of logics of belief and knowledge, but also logics of preferences and norms (deontic logics) [START_REF] Baltag | Logics for epistemic programs[END_REF][START_REF] Kooi | Expressivity and completeness for public update logic via reduction axioms[END_REF][START_REF] Van Benthem | Dynamic logic of preference upgrade[END_REF]. In those logics, modal operators are introduced to describe the effects, on the mental states of the agents, of various types of informative events (transmission of public or private messages, orders, etc.).

Here, we consider the most known dynamic epistemic logic, namely public announcement logic (PAL) [START_REF] Hv | Dynamic Epistemic Logic[END_REF]. Informally, a fact p is publicly announced if and only if: every agent learns that p is true; every agent learns that every agent learns that p is true; every agent learns that every agent learns that every agent learns that p is true, etc., up to infinity. In the PAL logic, public announcements are events that update the beliefs and knowledge of the agent: the role of a public announcement is, first, to reduce the set of possible worlds to the worlds where the publicly announced fact holds, and second, to restrict the epistemic accessibility relations to those worlds. PAL uses the notation p! for the public announcement of p, and introduce modal operators of the form [p!] to describe the effect of a public announcement on the mental states of the agents: the formula [p!]q means that q will be true after the public announcement of p. We take below an example to illustrate those dynamic operators. [p!]q signifie que q sera vrai après l'annonce publique de p. Nous présentons ici un exemple pour illustrer le fonctionnement de ces opérateurs dynamiques. Marie, Paul et Alice sont assis autour d'une table sur laquelle sont posées trois cartes. Sur la face non visible de chaque carte est écrit un numéro compris entre 1 et 3 différent de celui marqué sur les deux autres. Ainsi, chaque carte est identifiée par un numéro entre 1 et 3 (carte 1, carte 2, carte 3). Marie, Paul et Alice prennent une carte chacun et on suppose que Marie prend la carte 1 (que l'on notera m 1 ), Paul prend la carte 2 (noté p 2 ) et Alice prend la carte 3 (a 3 ). Chaque joueur regarde sa carte sans que les autres joueurs ne la voient et la repose face cachée sur la table. Chaque joueur ne connaît donc que sa carte.

Dans Supposons qu'il soit annoncé publiquement que Alice a une carte avec un numéro impair. Cette annonce est représentée par l'événement a 1 ∨a 3 ! (Alice a la carte 1 ou bien Alice a la carte 3). Figure 4, le modèle à droite de la flèche représente les croyances de Marie, Paul et Alice après cette annonce. Grâce à cette dernière, Marie apprend que Paul a la carte 2 et que Alice a la carte 3. En fait, l'effet de l'annonce publique est de restreindre l'ensemble des mondes possibles aux mondes dans lesquels Alice a une carte avec un numéro impair et de restreindre les relations d'accessibilité à ces mondes. Donc, dans le monde réel après l'annonce, Marie connaît la distribution des cartes : Marie a la carte 1, Paul a la carte 2 et Alice a la carte 3, et Marie le croit. Ce dernier fait est représenté par la formule m 1 ∧ p 2 ∧ a 3 ∧ Bel m (m 1 ∧ p 2 ∧ a 3 ) qui est vraie dans le mondé réel du modèle de droite. Au contraire, l'annonce publique ne fait rien apprendre à Paul et Alice : après l'annonce publique, Paul et Alice restent incertain Fig. 4 Example of cards Marie, Paul, and Alice are seated around a table on which are laid three cards. The cards are face down, but, on every card, is written a distinct number between 1 and 3. So, the cards can be called Card 1, Card 2, and Card 3. Marie, Paul, and Alice take one card, each. We assume Marie took the card 1 (denoted by m 1 ), Paul the card 2 (denoted by p 2 ), and Alice the card 3 (a 3 ). Each player confidentially looks at his (or her) card and put it of the table face down. Therefore, each player only knows the number written on his card.

In Fig. 4, the model on the left represents the beliefs of Marie, Paul, and Alice in the initial situation. There are 6 possible worlds and the one in grey is the real one. The arrows represent the accessibility relations B between epistemic worlds, for each player. For example, in the real world, Marie considers as possible the world where Marie has Card 1, Paul Card 2, and Alice Card 3, as well as the world where Marie has Card 1, Paul Card 3, and Alice Card 2. So, in the real world, Marie has no certainty about the card distribution.

Assume it is publicly announced that Alice has a card with an odd number. This announcement is represented by the event a 1 ∨ a 3 ! (Alice has Card 1 or Card 3). In Fig. 4, the model to the right of the arrow represent the beliefs of Marie, Paul, and Alice after this announcement. Thanks to the latter, Marie learns that Paul has Card 2 and Alice Card 3. Indeed, the effect of the public announcement is to reduce the set of possible worlds to those where Alice has an odd card and to restrict the accessibility relations to those worlds. So, in the real world, after the public announcement, Marie knows the card distribution: Marie has Card 1, Paul Card 2, and Alice Card 3. This fact is represented by the formula m 1 ∧ p 2 ∧ a 3 ∧ Bel m (m 1 ∧ p 2 ∧ a 3 ), which is true in the real world of the model on the right. In contrast, the public announcement does not make Paul and Alice learn anything: after the public announcement they still have no certainty about the card distribution.

Up to know, we gave an overview of the concepts related to cognitive-agent systems and a way to formalize them. In what follows, we present two particular complex concepts that can be described in terms of mental states, time, and action. Cognitive-agent systems are thus very adapted to the formalization of these two concepts. Nevertheless, the latter are also formalized in more numerical ways and, in what follows, we give an overview of this.

Formalization of Trust

Trust systems (or trust models) are used in certain multi-agent systems to help users to choose the agents to interact with. Indeed, agents may be incompetent or malicious. But, the agents are typically so numerous that it is impossible for a central authority to test them all. Consequently, the goal of a trust system is to evaluate the agents on the basis of relations between them. More precisely, for a user u, the evaluation of the peers of u is based on two kinds of information:

• the result of past interactions between u and the other agents;

• the feedbacks other agents have provided about their peers. The value (a score, a position in a ranking, etc.) of an agent a can naturally be seen as the trust of u in a.

Trust systems can be motivated by several large-scale applications where no central authority can test all agents. As examples, we can mention: ecommerce (Ebay, Amazon, etc.), large wikis (Wikipedia, Planetmath, etc.), social networks (Facebook, Tweeter, etc.), webpages and hypertext links, papers and citations.

Various trust systems have been developed. To validate and compare them two kinds of approaches are possible: a theoretical and an experimental one. The first approach consists in establishing desirable properties (or axiom, postulates) that a trust system could satisfy. The second approach consists in developing a testbed where different trust systems can compete.

As far as we know, there are two kinds of trust systems: logic-based systems (essentially modal-logic-based systems) and numeric systems. Two position papers that cover a large number of models are for example [START_REF] Sabater | Review on Computational Trust and Reputation Models[END_REF] and, more recently, [START_REF] Pinyol | Computational trust and reputation models for open multi-agent systems: a review[END_REF].

Logic-based Trust Models

In the logical approach, the goal is to characterize the notion of trust in a certain formal language. Similarly, the objective is to formalize in such a language the notion of trusting someone, as well as the mental state of an agent trusting someone.

One of the main models of trust is the cognitive one from Castelfranchi et Falcone (denoted by C&F) [Castelfranchi and Tan, 2001]. Contrary approaches that are more computational, the C&F model is more than subjective probabilities updated in the light of direct interactions with the trustee (the agent to be trusted) and feedbacks from interactions between the trustee and other agents.

Informally, the C&F model defines trust as an personal belief of the truster (the agent that has to decide whether or not to trust the trustee) that the trustee is reliable with regards to various aspects (capacity, intention, readiness, etc).

According to C&F and the analysis conducted in [START_REF] Herzig | A logic of trust and reputation[END_REF], the notion of trust is based on four components: a truster i, a trustee j, an action α of j, and a goal ϕ of i. According to their definition, "i trusts j that j will perform α in order to achieve ϕ" if and only if: ϕ is a goal of i; i believes j is capable of performing ϕ; i believes that performing ϕ will makes ϕ true; and i believes that j intends to do α.

For example, assume i trusts j to send a certain product p in order to possess p. Then: possessing p is a goal of i; i believes j is capable of sending p; i believes sending p will make him (or her) possessing p; and i believes j intends to send p.

In other words, trust is formally defined as follows:

Trust(i, j, α, ϕ) def = Goal i ϕ ∧ Bel i (Capable j (α) ∧ After j:α ϕ ∧ Intend j (α))
where every operator used above is either a basic one or a compound one defined from the basic ones (cf. Section 2.2):

• Goal i ϕ def = Choice i F ϕ means "Agent i chooses to make F ϕ true at the present time";

• Capable j (α) def = ¬After j:α ⊥ means "Agent j is capable of executing Action α if and only if α is already executable"; 9

• Intend j (α) def = Choice j Does j:α means "Agent i intends to execute Action α if and only if executing α (right here, right now) is a chosen goal of i". A relatively recent paper allowing an agent to reason about its trust model, by providing a method for incorporating a computational trust model into the cognitive architecture of the agent is [START_REF] Koster | Opening the black box of trust: reasoning about trust models in a BDI agent[END_REF].

We turn to approaches where the notion of trust is not based on modal logic, but more numeric objects.

Numerical Models of Trust

Previously, trust was seen essentially as a particular belief of the truster about certain aspects of the trustee. Depending on whether i trusts j or not about a proposition ϕ, i was in position to decide whether or not to believe what j says about ϕ.

The situation is similar with numeric approaches. The first question is to decide how to represent trust in a numeric way. Various solutions have been proposed, for example, trust can be represented by a number, an interval, or a fuzzy interval.

First, trust can be represented by a simple number. One of the first approaches of this kind is [START_REF] Marsh | Formalising Trust as a Computational Concept[END_REF]. Another important approach is that of Pagerank [START_REF] Page | The PageRank Citation Ranking: Bringing Order to the Web[END_REF], the system at the basis of the well-known Google search engine. More precisely, a webpage can be seen as an agent and a hypertext link from x to y as a positive feedback. Pagerank associates every agent with a real number between 0 and 1 on the basis of these feedbacks. Theses numbers can be seen as the degrees of trustworthiness of the agents.

It is worth noting that Pagerank evaluates the trustworthiness of an agent for an external user. Most trust systems evaluates the trustworthiness of an agent for another agent x. In such a case feedbacks from direct interactions with x are obviously more important than feedbacks from interactions where x is not involved.

A relatively exhaustive study of questions related to Pagerank and its alternatives can be found in e.g. [START_REF] Langville | Deeper Inside PageRank[END_REF]. A version of Pagerank adapted to peer-to-peer systems as been constructed in [START_REF] Kamvar | The Eigentrust Algorithm for Reputation Management in P2P Networks[END_REF].

In certain approaches, an agent is either trustworthy or not, and a model can associate an agent x with a number indicating the probability that x is 9 One could think that this should be a sufficient but not necessary condition. Indeed, it suffices that Agent i believes Agent j will be capable of executing Action α in time to achieve Goal ϕ. Nevertheless, it is worth noting that we formalize a notion of trust "right here, right now", not a notion of potential trust.

trustworthy. In other approaches, a model can associate an agent x with a number indicating the degree of trustworthiness of x. In other words, depending on the model, the same number x is associated with can mean different things. For example, assume x is associated with 0.5. It can mean that x perfectly achieves one goal out of two, as well as x achieves every goal halfsuccessfully.

Concerning links between trust and other important notions, it is described in e.g. [START_REF] Osman | Trustworthy advice[END_REF] how trust models can be used to distinguish between good and bad advices. Finally, a paper describing how the notion of trust can be integrated with those of negotiation and argumentation is e.g. [START_REF] Bonatti | On the integration of trust with negotiation, argumentation and semantics[END_REF].

Applications of Trust Systems

We present six examples of multi-agent systems where a user (be it an external entity or an internal agent) needs an evaluation of the trustworthiness of the agents: E-commerce (Ebay, Amazon, . . . ).

The agents are the buyers and sellers. A user has to choose the agents to make transactions with. But they are numerous, generally unknown to him (or her), far from him, and some agents are malicious or incompetent. So, the user needs an evaluation of the agents. After each transaction, the buyer can rate the seller, and vice versa. So, a trust system can exploit these ratings to construct an evaluation. We can globally admit that the more an agent is trustworthy, the more he tends to provide honest and accurate feedbacks. The same goes for the buyers. So, in case of cycles the trustworthiness of an agent x depends on that of an agent y, and vice versa, which makes the evaluation hard to construct.

Large wikis (Wikipedia, Planetmath, . . . ).

The agents are the contributors of the wiki, that is, those that create, delete, or modify articles. A user has to choose to trust or not the contributions and thus needs an evaluation of the contributors. It is easy to imagine how to modify a wiki so the contributors can provide opinions about their peers, in particular when they participate in long debates about controversial issues. A trust system could exploit these opinions to construct an evaluation. We can admit that the more an agent provides serious contributions, the more he (or she) tends to provide serious opinions about its peers. So, again opinion cycles constitute a difficulty. Social networks (Facebook, Myspace, . . . ).

The agents are the persons, applications, etc. registered in the network. A user has to choose the agents to establish a formal link with. Such a link gives access to all sorts of personal information about the user. But, some persons or applications are malicious. A friendship link between a and b can be seen as the fact that a recommends b as an honest agent, and vice versa. Those links can exploited to evaluate trustworthiness. There are recommendation cycles and the more an agent is honest, the more it provides honest recommendations.

Web pages and hypertext links.

The agents are the web pages. A hypertext link from a page a to a page b can be seen as a recommendation, that is, as the fact that a provides an opinion that the content of b is important. There are cycles and the more a page a has an important content, the more the hypertext links contained in a are important.

Papers and citations.

An agent is a paper or an author. A citation relation from a paper x to a paper y can be seen as the fact that x supports y. Similarly, an authorship relation between a paper x and an author a can be seen as a support relation for a. The are no relation cycles, but the more a paper x is trustworthy, the more the citation or authorship relations coming from x are important.

Entity-key bindings and certificates.

In the systems based on public key certificates, there are entities willing to send messages to other entities. Since an entity can listen messages that are not intended for it, they are encrypted and decrypted with keys. So, the system generates a set of keys such that there exists a function f transforming any key K into a key f (K) such that the following holds:

(a)f (K) is the unique key that can decrypt the messages encrypted with K, and it can decrypt only these messages; (b)the converse is true, that is, K is the unique key that can decrypt the messages encrypted with f (K), and it can decrypt only these messages.

Next, a set of bindings is published. A binding is a pair E, K where E is an entity and K a key. Such a binding represents a claim that E is the unique entity that knows f (K). If it is indeed the case, then we say that E, K is valid. So, to send a confidential message to an entity, it suffices to find a binding containing it, and use the corresponding key. By (a), only this entity will be able to decrypt the message. The problem is that a malicious entity F can publish a false binding E, K . In other words, E does not know f (K), but F does. So, if this false binding is used, then F can listen some messages intended for E and decrypt them.

To counter this, a set of public key certificates is published. A certificate is a pair D, S , where D is a quadruplet of the form E, K, E , K and S is a digital signature, that is, S is supposed to be the result of encrypting D with f (K). Such a certificate represents a claim that E supports the validity of E , K . Again, the problem is that false certificates can be published. However, it is possible to formally check that the certificate D, S was created by an entity knowing f (K). By (b), it suffices to decrypt S with K and then check that the result is indeed equal to D. Only the certificates that pass this test are considered. Now, we can explain the link with trust systems. An agent is a binding E, K . A user is an entity E that has to choose valid bindings before sending messages. A certificate E, K, E , K , S can be seen as the fact that E, K supports the validity of E , K . These support links can be exploited to evaluate the validity of the bindings. Finally, the problem of evaluating the validity (or trustworthiness) of the bindings is difficult in particular because there are cycles of support links and the following holds: if a binding E, K is valid, then E is the unique entity knowing f (K), thus the certificate E, K, E , K , S was created by E, i.e., this certificate is authentic, so we should attach more importance to it.

Formalization of Emotions

There is a rich literature on emotions, be it in philosophy 10 [ [START_REF] Gordon | The structure of emotions[END_REF], psychology [START_REF] Lazarus | Emotion and Adaptation[END_REF][START_REF] Ortony | The cognitive structure of emotions[END_REF], economy [START_REF] Loewenstein | Emotions in economic theory and economic behavior[END_REF], or cognitive sciences [Lane and Nadel, 2000].

In computer sciences, emotions play an important role in multi-agent systems at different levels. Much work focus on the modelization of facial and gestural results of emotions with animated conversational agents (ACA) (see e.g., [START_REF] Gratch | Lessons from emotion psychology for the design of lifelike characters[END_REF][START_REF] Pelachaud | Modelling multimodal expression of emotion in a virtual agent[END_REF]). ACA also use models of emotions to represent those of the users, to show their affective states, or a particular personality.

The goal is to make such agents so realistic that users have the impression to interact with other humans. First, this goal assumes a great realism in the expressive aspects of the agents (facial and corporal movements, intonations, verbal expressions, etc.). Second, it is necessary, for the agents, to be able to recognize and take into consideration user's emotions in their of reasoning (as well as their artificial own). So, agents can speak and act in a most adequate fashion.

Emotions are fundamental to have natural and optimal interactions between agents and users, because nowadays it is known that we constantly communicate information about our emotional states (be them real or not) without explicating them. For example, a "Hello!" accompanied with a smile constitutes a common and short way to express your greetings to someone and to tell him (or her) you are happy to see him (which could be explicated by "Hello, I am happy to see you").

Logical Formalization of Emotions

Concerning formal models of emotions, we look forward to construct logical frameworks in order to formalize certain specific emotions, their properties, the links between them, etc. (see e.g., [START_REF] Adam | A logical formalization of the OCC theory of emotions[END_REF][START_REF] Turrini | Coping with shame and sense of guilt: a dynamic logic account[END_REF]). The main objective is to take advantage of logical methods to rigorously specify how to implement emotions into an artificial agent. The design of systems containing such agents (capable of reasoning and expressing certain emotions) can benefit from the fact that logic is a tool particularly adapted to the notion reasoning and forcing the designer to disambiguate the different dimensions of emotions (identified in different psychological models of emotions).

Generally, logical definitions of emotions characterize cognitive structures of emotions, rather than emotions themselves. According the theories of cognitive evaluation [START_REF] Lazarus | Emotion and Adaptation[END_REF], the cognitive structure of an emotion is the configuration of the mental state of an agent when it (artificially or not) feels that emotion. The cognitive structure is just a part of the affective phenomenon. In the sequel, we use the word "emotion" for "the cognitive structure of an emotion".

We distinguish between simple emotions and what we call complex emotions [START_REF] Adam | Logical modeling of emotions for Ambient Intelligence[END_REF][START_REF] Lorini | A logic for reasoning about counterfactual emotions[END_REF]. The former are those that can be described only with mental attitudes like beliefs, goals, or ideals. The latter are those requiring more complex reasonings like counterfactual conditionals: "I could have made ϕ true, whilst it is actually false". In that sense, complex emotions are associated with counterfactual reasonings about norms, responsibilities.

For example, the fact that agent i feels joy about Fact ϕ may be expressed as follows:

Joy i ϕ def = Bel i ϕ ∧ Choice i ϕ
According to this definition, Agent i feels joy about ϕ if and only if i believes ϕ is true and wish ϕ to be true. For example, Tom feels joy about a certain test, because he thinks he successfully passed it and it is what he wishes. So, Tom is happy because he believes the state of affairs is as he wishes. Joy has a positive valence, that is, when it is felt, it is associated to a state of affairs corresponding to desires. This is not the case of sadness for example whose state of affairs does not correspond to desires.

Concerning complex emotions, we restrict ourselves to those related to the notion of responsibility (be it that of the agent feeling the emotion or another one). The responsibility of Agent i for the fact that ϕ is true can be defined as follows: ϕ is true and i could have made ϕ false. More formally:

Resp i ϕ def = ϕ ∧ Cd i ¬ϕ
Here Cd i (i could have made) is a basic operator of the formal language, but can be defined from the implicit action operator STIT (for more details, see [START_REF] Lorini | A logic for reasoning about counterfactual emotions[END_REF].) So, when Agent i is responsible for the fact that ϕ is true, whilst i has ¬ϕ as goal, i feels regret (see e.g., [Zeelenberg et al, 1998]). More formally:

Regret i ϕ def = Goal i ¬ϕ ∧ Bel i Resp i ϕ.
Other emotions can be defined in the same way. Emotions constitute a growing domain, because computer science does not have yet exhausted all their possibilities. Existing and implemented systems can often be reduced to simple labels that can be activated or deactivated. Formal models based on logic force designers to explicate the nature of emotions and thus to better understand them.

Numerical Models of Emotions

There exist numerical models of emotions that study the quantitative aspects of those affective phenomena. For example, El-Nasr et al. [START_REF] El-Nasr | FLAME: Fuzzy logic adaptive model of emotions[END_REF] proposed a numerical model of emotions called FLAME (Fuzzy Logic Adaptive Model of Emotions) based on fuzzy logic. The main contribution of this work is a quantification of the intensity of emotions, from appraisal variables like desirability or probability. For example, based on the psychological model of emotions of Ortony, Clore and Collins [START_REF] Ortony | The cognitive structure of emotions[END_REF], in the model FLAME, the intensity of hope with regard to a certain event depends on the degree of desirability of that event and its subjective probability. More recently, several researchers in AI have augmented formal models of emotions with quantitative aspects. For example, Meyer et al. [START_REF] Steunebrink | A formal model of emotions: integrating qualitative and quantitative aspects[END_REF] proposed a model describing how the intensity of emotions decreases with time. Lorini [START_REF] Lorini | The cognitive anatomy and functions of expectations revisited[END_REF] proposed a systematic study of the intensity of emotions on the basis of expectations (hope, fear, disappointment, relief) and the relation between those emotions and the mechanism of belief revision of a cognitive agent.

There also exist numerical models of emotion where the latter is represented by a vector whose numbers correspond to components of emotion. For example, Mehrabian captures mood by a vector representing pleasure, excitation, and dominance (i.e., the capacity of an individual to dominate a stimuli). In other words, mood depends on the values of those three components. We can also mention works on the robot with human-like head WE-4R constructed in the university of Waseda (Japan) by Hiroyasu Miwa and his team. The model of emotion is a space-oriented vector calculated from three components: pleasure, activation, and determination.

Applications of Emotion Models

Concerning applications, teaching systems have been developed to deal with emotions and thus increase the degree of perseverance and commitment of the students. In parallel, simulators, video games, and ambient-intelligence systems have been developed (see e.g., [START_REF] Adam | Logical modeling of emotions for Ambient Intelligence[END_REF] for an overview of the literature and applications of emotions in that domain). Among the very large variety of existing ACA, EM11 is a typical system that simulates the decline of emotions with time for a specific set of emotions corresponding to the goals that generated them. Another example is the system Affective Reasoner of Gratch & Marsella where agents use representations of themselves and others. Finally, GRETA [START_REF] De Rosis | From greta's mind to her face: modelling the dynamics of affective states in a conversational embodied agent[END_REF]] is an ACA 3D that can be animated in real time and is capable of expressing emotional states.

Conclusion

In the present chapter, we have first tackled the formalization of cognitiveagent systems. Such an agent is capable of behaving in an autonomous way, according to its goals. In addition, it is characterized, a minima, by mental attitudes (beliefs, desires, norms, etc.), time, and action. After a brief overview of the great research avenue in this domain, we have presented the fundamental concept of BDI systems, as well as the tools to deal with the well-known AI problem of knowledge evolution. Finally, we used the aforementioned material in order to formalize two concepts used in those systems: trust and emotion. We also showed that those two concepts can also be formalized in a more numerical fashion, which is less fine from the point of view of the definitions of the concepts of interest, but easier to be applied in concrete frameworks.

Of course, there are many other branches in AI about the formalization of cognitive-agent systems. But, some of them are not based on mental states, other are limited to a certain formal language. The peculiarity of the systems presented in this chapter is that they correspond to logic (with both a semantics and an axiomatization) whose properties (in terms of complexity, decidability, and completeness) are also studied. More precisely, those logics are modal logics particularly convenient to represent mental states, as well as relations between those states (beliefs about beliefs, goals, etc. of other agents. The objective is to represent in a fine grain the concepts used by the agents with a logic having "good" logical properties. So, the issues are both computational and mathematical. In addition, they are strongly related to SHS via philosophy and psychology, in particular. It is worth noting that there are studies about the influence of trust on emotions, and vice versa (see e.g., [START_REF] Bonnefon | A Logical Framework for Trust-Related Emotions[END_REF]).

Naturally, trust and emotion are not the only concepts investigated in the literature. In particular, we have not presented non-reductionist social concepts, for example, notions of group belief or acceptance that are reducible to the sum, over all agents of the group, of their beliefs or acceptance. Consequently, it is necessary to capture a group as a unique entity constituting an institution ruled by specific social rules.

The study of formal properties of intelligent agents is thus a first step in the study of multi-agent systems. The latter need to capture the nature of the group constituted by the agents (What unites them? What is the structure of the group represented by them? Is it just a set of agents or a more complex relational structure including e.g. friendship, hierarchy, commerce, etc.?). van Benthem J (1991)

Fig. 1

 1 Fig. 1 Kripke semantics of the operator Bel i

Fig. 3

 3 Fig.3Transition from the world w 0 to the world w 0 via the execution of the action i:α

Figure 4 :

 4 Figure 4: Exemple des cartes

  Figure 4 le modèle à gauche de la flèche représente les croyances de Marie, de Paul et d'Alice dans la situation initiale venant d'être décrite. Il y a six mondes possibles et celui en gris est le monde réel. Les flèches qui partent de chaque monde représentent les relations d'accessibilité B aux mondes épistémiques pour chaque joueur. Par exemple, dans le monde réel Marie envisage comme possible le monde dans lequel Marie a la carte 1, Paul a la carte 2 et Alice a la carte 3 et le monde dans lequel Marie a la carte 1, Paul a la carte 3 et Alice a la carte 2. Donc, dans le monde réel Marie est incertaine de la distribution des cartes.

  The Logic of Time. D. Reidel Publishing Company Wooldridge M (2000) Reasoning about Rational Agents. MIT Press Zeelenberg M, van Dijk WW, Manstead ASR (1998) Reconsidering the relation between regret and responsibility. Organizational Behavior and Human Decision Processes 74:254-272

Note that the word agent comes from Latin language agere and means to act, to do.

These logics are often called BDI logics (for belief, desire, intention). By analogy, we speak also of BDI agents (systems).

Their paper in Artificial Intelligence has received the AAMAS most influential paper award in 2008.

This explains by the way the success of the theory of linguistic actions[START_REF] Austin | How To Do Things With Words[END_REF][START_REF] Searle | Speech acts: An essay in the philosophy of language[END_REF] in the agent community: in those theories, the language is seen as the accomplishment of actions, facilitating de facto the formal union of physical and linguistic actions.

http://www.fipa.org/repository/aclspecs.html

that is, a concept constructed from lower-level concepts.

Besides BDI logics, the operator After α is often denoted by[α].

it is a system based on the Tok architecture of the project Oz. See http://www.cs.cmu.edu/ afs/cs.cmu.edu/project/oz/web/.


SOLICITING HYDROTHERMAL SYSTEMS: THE CASE OF LA SOUFRIÈRE OF GUADELOUPE (FWI) UNREST

Introduction

The Grande Découverte -Soufrière complex is made up of three stratovolcanoes, Grande Découverte, Carmichael and Soufrière which were built during the last 445 000 years. Soufrière is the most recent building and its eruptive history began about 9150 years ago. It is an active volcano, explosive type, which has experienced many magmatic and non-magmatic eruptions, the latter called "phreatic", in the past. The most recent major magmatic eruption dates from 1530 AD. The historical activity of La Soufrière since 1635 is characterized by non-magmatic eruptions, which were minor in 1690, 1812, and 1956, and major in 1797-1798, 1836-1837, and 1976-1977 [START_REF] Komorowski | Guadeloupe. In Volcanic Atlas of the Lesser Antilles[END_REF]. The phreatic eruption of 1956 lasted ten days with two explosions. That of 1976-77 was particularly violent with 26 major explosions between July 1976 and March 1977. It was a phreatic or hydrothermal eruption, which can also be considered as a failed (aborted) magmatic eruption, in which the magma did not rise to the surface. The state-of-the-art knowledge on phreatic eruptions reveals that i) they are typically frequent and sudden, ii) precursory signals are frequently absent or few and equivocal, iii) they are characterized by a variable duration and intensity, and iv) the associated phenomena are varied and can be particularly dangerous up-close. The great majority of phreatic eruptions are not systematically followed by a magmatic eruption.

Methods and results

Since late 2017 we have improved the fumarole sampling involving "Giggenbach" type soda bottles [START_REF] Giggenbach | Collection and analysis of geothermal and volcanic water and gas discharges[END_REF]. The temporal evolution of the chemical composition of fumarolic emissions can be qualitatively interpreted by interpreting ratios or chemical species. The variation in the gas/water vapor ratio essentially measures the variation of the relative proportion of magmatic gas to the meteoric component (rainwater) in the hydrothermal system; this ratio may increase due to the arrival of magmatic gases and / or the condensation of steam. The C/S ratio can increase during the rise of deep magmatic gases or by loss of sulfur, especially H2S (gas scrubbing) in the hydrothermal system, often associated with a decrease in temperature. An increase in the CO2/CH4 ratio is considered as a clear signal of the arrival of oxidized hot magmatic gases enriched in CO2, whose arrival oxidizes and potentially warms the base of the hydrothermal system, limiting the conversion of CO2 in CH4. Finally, the CO/CO2 ratio, for an oxidation state set within the system, is normally associated with the heating of the hydrothermal system. It is also recalled that in hydrothermal systems characterized by the coexistence of water vapour and liquid (pure water or brines), the heating and overpressure phenomena are associated, so that temperature and pressure increase together. On the dome of the volcano, the fumarole CSC is the most representative for the monitoring and study of the La Soufrière hydrothermal system. The Figure 1 shows the variation of these molar ratios at this fumarole CSC.

It should be noted that the ratio gas/steam, stable since 11/2017, rose considerably on 2 nd June (up to 0.1), before falling on 21 st June 2018 and vary between 0.03 and 0.06. The C/S ratio, after reaching a minimum (3) at the end of March, rises to a peak of 6 in September 2018, then goes back to 4 in February 2019 and after shows values between 4 and 6. The CO2/CH4 ratio shows a general upward trend, with values rising sharply at the end of April and beginning of May (200 000 to 250 000). This ratio reaches a peak of the same value as late April at the beginning of June and in September. Same as in early June 2018, this ratio has an average value of around 150,000 since October 2018, ranging between 120,000 (February and April and 170,000 (November 2018 and January 2019). In June the ratio had values around 100,000, in line with those of November 2017, but since July 2019 it decreased to around 80,000.

Overall, the behavior of these indicators is related to the increase of the deep magmatic gas component in the hydrothermal system, which seems to be recurrent when comparing the C/S and CO2/CH4 values recorded in September and early June 2018.

The progressive infiltration of magmatic deep gas was responsible for the rise in the CO/CO2 ratio, which peaked at the end of April -beginning of May, typically in response to a process of deep heating of the hydrothermal system. As of June, this indicator has returned to a baseline value that has been identified since November 2017, which fluctuates between 0.000005 and 0.00001 with a minimum (0.000003) in September 2018. Since then, the CO/CO2 ratio fluctuates around a value of 0.0000050.

Discussion and conclusions

The infiltration of deep magmatic gases caused an increase in temperature and pressure inside the hydrothermal system, at depths of 2-3 km, compatible with the hypocenters of the seismic swarms recorded between February and April 2018 [START_REF] Moretti | The 2018 unrest phase at La Soufrière of Guadeloupe (French West Indies) andesitic volcano: scrutiny of a failed but prodromal phreatic eruption[END_REF]. The latest data show that the Soufrière volcanic system is governed by the cyclically dynamics of energy recharge and discharge due to the infiltration of deep magmatic gases into the hydrothermal system. This generates a recurring process of overheating and overpressuring of the boiling hydrothermal fluids whose pressure and temperature conditions approach those of the critical point of water. Also the accumulation and energy released has, for the moment, reached its peak with the strong seismic and fumarolic activity of March-April 2018. Given the clear infiltration of magmatic gases into the hydrothermal system, as well as the high temperatures and pressures inside the hydrothermal system, we estimate that the volcanic system is currently recharging energy.

Steam-dominated summit fumaroles result from the boiling of the hydrothermal deep aquifer, solicited by the arrival of magmatic gases [START_REF] Moretti | The 2018 unrest phase at La Soufrière of Guadeloupe (French West Indies) andesitic volcano: scrutiny of a failed but prodromal phreatic eruption[END_REF][START_REF] Villemant | Evidence for a new shallow magma intrusion at La Soufrière of Guadeloupe (Lesser Antilles): insights from long-term geochemical monitoring of halogen-rich hydrothermal fluids[END_REF]. They also show chemical variations related to anomalous (and deeper than usual [START_REF] Moretti | The 2018 unrest phase at La Soufrière of Guadeloupe (French West Indies) andesitic volcano: scrutiny of a failed but prodromal phreatic eruption[END_REF]) magmatic gas inputs. This, in turn, provoked thermoelastic solicitation of the hydrothermal system, leading to hydrofracturing and/or hydroshearing. Depending on the thermochemical data treatment, important P-T variations can be calculated. Here we follow the approach by Cardellini et al. [START_REF] Cardellini | Monitoring diffuse volcanic degassing during volcanic unrests: the case of Campi Flegrei (Italy)[END_REF]), which is based on a set of thermometers and barometers derived by reaction equilibrium chemistry restricted to the system CO2-CO-H2, under the obvious hypothesis of two-phase vapor-liquid coexistence to fix the partial pressure of the steam. Although H2O is the dominant component, its abundance may be biased by secondary phenomena (e.g., late steam condensation). In the literature many authors prefer then to assume PH2O from steam tables at the temperature of interest. This latter is computed from the measured CO/CO2 ratio coupled to a typical oxybarometer fixing oxygen fugacity, fO2, with temperature (see [START_REF] Cardellini | Monitoring diffuse volcanic degassing during volcanic unrests: the case of Campi Flegrei (Italy)[END_REF][START_REF] Moretti | Hydrothermal versus magmatic: geochemcial views and clues into the unrest dilemma at Campi Flegrei[END_REF] for details) Despite much has to be said yet about the transient behavior of the overpressure source (« pulsatory degassing ») versus the structural modulation of the volcanic system, the recent 2018 unrest producing the M 4.1 earthquake on 27 April 2018 (Figures 1 and2) was related to an « extra » supply of deep and hot magmatic gases which added up to the usual magmatic basal flux. This batch was discharged after the 27 April 2018 earthquake, as shown by the increase in CO2/CH4 (Figure 1). These gas batches may trigger phreatic eruptions, like the 1976-77, but represent a magmatic forcing related to magma dynamics at depth. Is this magma a residual of the past (e.g., 1530) or is it a new emplacing magma? The relatively few data that we have do not allow answering definitely to such a question. However, it can be clearly said that in 20 years the system evolved toward hotter conditions, which can lead to the drying of the hydrothermal system. This longterm process is however accompanied by short-term thermal and baric transients, such as the one embracing the M 4.1 earthquake occurred on 27 April 2018 and related to an increase of several degrees and bars in fluid temperature and pressure (Figure 2). The sudden overpressure of around 20 bar computed in this study can further increase under the undrained conditions occurring on the fault plane (off-volcanic axis) that slipped on 27 April 2018, due to pore pressure build-up which escalated up to rock failure. Under tha approximation adopted in this study an anomaly of around 20°C and 20 bar occurred in correspondence with the M 4.1 earthquake on 27 April 2018. This is in line with the CO/CO2 peak observed the day in fumarolic chemistry (Figure 2)

Figure 1 :

 1 Figure 1: Chronograms of variations of molar ratios at the South Crater CSC fumarole. Peaks in the left panels mark the discharge of magmatic gas. Peaks in the right panels mark the heating and overpressurization of the hydrothermal system. Note the correspondences with the 4.1 EQ on 27 April 2018

Figure 2 :

 2 Figure 2: P-T computed for the hydrothermal reservoir feeding the summit fumaroles (drained conditions).Under tha approximation adopted in this study an anomaly of around 20°C and 20 bar occurred in correspondence with the M 4.1 earthquake on 27 April 2018. This is in line with the CO/CO2 peak observed the day in fumarolic chemistry (Figure2)


Rory J Gamble
email: rgamble@physics.otago.ac.nz

Craig J Rodger
email: crodger@physics.otago.ac.nz

Mark A Clilverd
email: m.clilverd@bas.ac.uk

Neil R Thomson
email: thomson@physics.otago.ac.nz

Thomas Ulich

Michel Parrot
email: mparrot@cnrs--orleans.fr

Jean-André Sauvaud
email: sauvaud@cesr.fr

Jean-Jacques Berthelier
email: jean-jacques.berthelier@cetp.ipsl.fr

Jean- André Sauvaud

Satellite and ground-based observations of a large-scale electron precipitation event

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

Background

In order to describe how geomagnetic storms couple to the upper atmosphere, and hence to atmospheric chemistry and dynamics, measurements of energetic electron precipitation into the atmosphere are required. The process of energetic electron precipitation into the atmosphere produces nitric and hydrogen oxides (NO x & HO x ), which are catalysts for the destruction of atmospheric ozone; energetic electron precipitation triggered by geomagnetic storms therefore alters the radiation balance and is a factor in natural climate variability.

Currently, satellite observations are poorly suited to providing measurements of energetic and relativistic electron precipitation. The AARDDVARK network (Antarctic-Arctic Radiation-belt (Dynamic) Deposition -VLF Atmospheric Research Konsortium) provides continuous long-range observations of ionisation levels from ~30-85 km altitude by monitoring of subionospheric VLF (very-low frequency) signals, with the goal of increasing the understanding of energy coupling between the Earth's atmosphere, Sun, and Space.

In this study we combine AARDDVARK subionospheric VLF measurements with DEMETER (detection of electromagnetic emissions transmitted from earthquake regions) electron spectra using modelling techniques to study >100 keV energetic and relativistic electron precipitation into the atmosphere for the 24-hour period beginning 0600UT 19 January, during the 17-21 January 2005 geomagnetic storms.

The DEMETER satellite provides detailed measurements of drift-loss cone electrons during this event, which are used to provide an indication of the precipitating (bounce-loss cone) electron energy spectra. Perturbations in subionospheric VLF amplitudes caused by the electron precipitation event are measured on two paths using the AARDDVARK network. Modelling of VLF propagation in response to the precipitation region reveals its L range and flux intensity.


Florence Leclercq

Clément Lonjon

Grégory Marin

Mariama Akodad

François Roubille

Jean-Christophe Macia

Luc Cornillet

Richard Gervasoni

Laurent Schmutz

Bertrand Ledermann

Post resuscitation electrocardiogram for coronary angiography indication after out-of-hospital cardiac arrest

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.


Arthur Casals
email: arthur.casals@lip6.fr

Assia Belbachir
email: assia.belbachir@ipsa.fr

Amal El Fallah-Seghrouchni

Adaptive and Collaborative Agent-based Traffic Regulation Using Behavior Trees

Keywords: Behavior trees, Traffic regulation, Smart Mobility

  L'archive ouverte pluridisciplinaire

INTRODUCTION

Traffic congestion is characterized by slower speeds, longer trip times, and increased vehicular queuing on road networks. Since congestion can have cumulative effects on neighboring roads, it is natural to conclude that alleviating traffic in a single intersection can also affect neighboring intersections. From a macro-level perspective, optimizing traffic through the use of dynamic traffic lights control is a problem that requires a network of traffic lights to be taken into account simultaneously.

In this sense, Vilarinho et al [START_REF] Vilarinho | A Conceptual MAS Model for Real-Time Traffic Control[END_REF] described various steps to analyze and design a multiagent system for real-time traffic control at isolated intersections. According to their description, each isolated intersection was modeled as an individual multiagent system. Another work conducted by Fleck et al [START_REF] Fleck | Adaptive quasidynamic traffic light control[END_REF] proposed a quasi-dynamic adaptive system for a single intersection, modeled as a stochastic hybrid system. In both works, the cumulative effects on neighboring road networks were not studied.

There are also other studies using techniques such as Petri nets [START_REF] Luo | Design of Variable Traffic Light Control Systems for Preventing Two-Way Grid Network Traffic Jams Using Timed Petri Nets[END_REF][START_REF] Kok Mun Ng | A review on the applications of Petri nets in modeling, analysis, and control of urban traffic[END_REF][START_REF] Zhang | A new traffic signal control method based on hybrid colored petri net in isolated intersections[END_REF] and Finite State Machines (FSM) [START_REF] Venkata Kishore | FPGA based traffic light controller[END_REF][START_REF] Lei | Decentralized hybrid intersection control[END_REF][START_REF] Nath | Design of an FPGA based intelligence traffic light controller with VHDL[END_REF]. Regardless of the approach, these techniques aim at providing an adaptive mechanism for traffic lights, considering (i) the dynamic conditions of traffic (such as the number of cars flowing through an intersection) and (ii) the effects of the changes resulting from the adaptation process. Adapting the traffic lights duration according to dynamic changes in traffic requires a process of decision making based on the observed traffic conditions. Nevertheless, neither FSMs nor Petri nets formalisms can easily capture the dynamics of the traffic conditions in complex scenarios.

Recently, BTs have been used as an alternative to FSMs due to their increased robustness and flexibility [START_REF] Colledanchise | How behavior trees modularize robustness and safety in hybrid systems[END_REF]. One of the main advantages of BTs over FSMs is their modularity: a single tree can be composed of different modular behaviors, which also means that it is easy to reuse a modular behavior across different trees. Another advantage of BTs over FSMs is related to concurrency. FSMs do not allow the execution of parallel states; BTs, on the other hand, offer this possibility, allowing the modeling of more complex behaviors.

In this paper, we propose an adaptive and collaborative architecture to regulate the traffic congestion for several intersections using multiagent paradigm. Our architecture combines agents and BTs concepts as follows: we model each intersection as an agent endowed with a BT that implements the dynamic reasoning and decision making of the agent. Due to the cumulative effects of traffic congestion on intersections, we introduce intersection agents that collaborate among themselves within the multiagent system in order to mitigate the cumulative effects of traffic congestion. We implemented a multiagent simulator to demonstrate how the architecture would fare when compared with another existing multiagent based traffic regulation system. We then proceed to implement a dynamically regulated scenario, where traffic regulation policies can be imposed dynamically in order to enforce specific control conditions in a controlled area. The chosen urban area for this simulation was Place Charles de Gaulle, modeled in SUMO.

SCENARIO

Let us consider an urban scenario where each intersection has its traffic lights controlled by intelligent agents. Each agent is capable of perceiving how many cars are queued in each lane of the intersection. This agent is also capable of informing the neighbor intersection about how many cars are queued in each lane and receiving similar information from its neighbors. With this information, the agent is capable of adjusting the traffic lights (red and green) duration according to the current traffic flow: depending on how many cars are queued, the red light duration can be shortened to increase the flow in a specific lane, for example.

For illustration, let us consider a free-form disposition of intersections, such a roundabout. Each lane can be either classified as inbound (the traffic flows towards the center of the roundabout) or outbound (the similar opposite). In a typical situation, we could make all the agents collaborate among themselves and optimize the traffic flow in the roundabout as a whole. However, during rush hour, for example, we only want to optimize the route between three of the roads connected to the roundabout. Optimizing traffic in a specific route, in this scenario, could lead to a degradation of the traffic flow in the other roads -which could be acceptable depending on the objective at hand. Ultimately, if specific routes can be optimized, the set of effective neighboring intersections can also be considered as dynamic.

CONCEPTUAL FRAMEWORK

In our multiagent system (MAS), we implemented a distributed mechanism that allows multiple Intersection agents to collaborate and to adapt the duration of the traffic light according to the observed environment changes (i.e traffic flow). The agents compute adjustments (𝛾) of their traffic lights and communicate them to their agents intersections neighbors. The agents are contextaware and can dynamically adapt to the continuous changes in the environment. The decision-making module processes the perceived information and decides which action to be performed to adapt the traffic light duration. To make decisions, the agents rely on BTs as the basis for the deliberation mechanism. A Communication module allows an Intersection agent to communicate with other Intersection agents by message passing while perception module manages the sensors and their inputs. Each intersection agent:

• Has a set of views V 𝑖 ⊂ V for an intersection 𝑖 ∈ I (all intersections in the model). The number of cars on each light is acquired as an individual perception. In the case of a perception fault, a previously stored value associated with conditions similar to the current context can be retrieved and used. • Computes the adequate duration of the traffic light (red and green) using an Adaptive Value Tracking (AVT) [START_REF] Yildirim | Efficient Time Synchronization in a Wireless Sensor Network by Adaptive Value Tracking[END_REF]. We model this computation as 𝑎𝑣𝑡 .𝑎𝑑 𝑗𝑢𝑠𝑡 (). The computed value is embedded in 𝛾 𝑖 , where 𝛾 𝑖 ← 𝑎𝑣𝑡 .𝑎𝑑 𝑗𝑢𝑠𝑡 (). The computation of 𝛾 𝑖 used the computed 𝛾 𝑗 from its intersection neighbor as follows:

𝛾 𝑖 ← 𝜂 𝑣 1 𝑖 -𝜂 𝑣 2 𝑖 +𝜂 𝑣 3 𝑖 -𝜂 𝑣 4 𝑖 +𝛾 𝑗 .
In the case where no value for 𝛾 𝑗 is received, the calculation is based on a locally stored historical value.

• Compares the duration of 𝛾 𝑖 for each traffic light in the intersection with the current BT policies 𝑃 𝑖 . The traffic lights are then updated accordingly. In the case the computation fails, the BT can remain unchanged, or it can use previously stored parameters depending on the scenario in place. Thresholds can also be parameterized for each of the traffic lights.

• Sends the calculated adjustments to each of its neighbor intersections, modeled for a neighbor 𝑗 as 𝑠𝑒𝑛𝑑𝐴𝑑 𝑗𝑢𝑠𝑡𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐 ( 𝑗, 𝛾 𝑖 ).

IMPLEMENTATION AND DISCUSSION

In order to test the effectiveness of our developed model, we implemented a simulator for the proposed architecture and tested it using different scenarios. We also compared our approach to the one developed in [START_REF] Belbachir | Smart Mobility Using Multi-Agent System[END_REF]. We divided the experiments into three parts: (i) implementing a simulator using intersection agents capable of using BTs in their decision-making process; (ii) simulating scenarios using both the previous agent model [START_REF] Belbachir | Smart Mobility Using Multi-Agent System[END_REF] and the one currently being proposed, comparing the results from both simulations to verify the effectiveness of the new model; and (iii) simulating a scenario for Place Charles De Gaulle (a roundabout), located in Paris, with dynamic optimization rules to illustrate a more complex situation (as described in section 2). Our simulator was implemented using two different tools: SUMO [START_REF] Behrisch | SUMO -simulation of urban mobility (an overview)[END_REF] and JADE [START_REF] Bellifemine | Jade -A Java Agent Development Framework[END_REF]. We divided our experiments into three different parts. In all cases, the agents used a parametrized BT. The first one, using a single intersection, was aimed at verifying if the proposed model would work as expected. The second part of our experiment compared traffic flow convergence when using the two different models: the original one [START_REF] Belbachir | Smart Mobility Using Multi-Agent System[END_REF] and the proposed BT-based model. Our original work used different types of agents to process all the information and make the decision related to changing the duration of the traffic lights for a given intersection. The current model uses only one agent to do the same, relying on a more complex decisionmaking mechanism.

The third part of our experiment was intended to observe how the proposed architecture would behave in a scenario involving dynamic optimization conditions. We recreated Place Charles de Gaulle as a SUMO model and used it in two different situations: in the first one, similarly to the previous part of the experiment, each agent considered the information from its direct neighbors to optimize the traffic flow as a whole. In the second situation, we defined a group of three intersection agents in different parts of the roundabout (not physically consecutive) to optimize a specific route. This configuration was possible due to the insertion of a dynamic policy mechanism, capable of updating the stored policies in each of the agents.

In the first two parts of the experiment, we observed that the new model behaved as expected: there was a slight difference in the convergence pace of the traffic lights duration, but both models converged to the same duration under the same conditions. In the third part of the experiment, we observed that the overall behavior in the first situation (adjacent neighbors) was similar to the previous simulations. The difference between the initial traffic light duration and the duration on convergence was significantly smaller than in the previous experiments. The original optimization mechanism was still effective in policy-based scenarios, while proportionally less when compared with the previous experiments. Another relevant observation is that the obtained values for the policy-based situation are specific to a particular configuration. Considering that we did not stress the possible configurations and policy variations for the initial model, we understand that a more elaborate study regarding this aspect must take place in the future.

Proc. of the 19th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2020), B. An, N. Yorke-Smith, A. El Fallah Seghrouchni, G. Sukthankar (eds.), May 9-13, 2020, Auckland, New Zealand. © 2020 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.