Generalizing AGM to a multi-agent setting

International audienceWe generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single-agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting. Finally, we give an example of revision operator that fulfills one of these new postulates and give an example of revision on a concrete example

A logical formalism for the subjective approach in a multi-agent setting

Representing an epistemic situation involving several agents depends very much on the modeling point of view one takes. In fact, the interpretation of a formalism relies quite a lot on the nature of this modeling point of view. Classically, in epistemic logic, the models built are supposed to represent the situation from an external and objective point of view. We call this modeling approach the objective approach. In this paper, we study the modeling point of view of a particular agent involved in the situation with other agents. We propose a logical formalism based on epistemic logic that this agent can use to represent `for herself\u27 the surrounding world. We call this modeling approach the subjective approach. We then set some formal connections between the subjective approach and the objective approach. Finally we axiomatize our logical formalism and show that the resulting logic is decidable

Internal models and private multi-agent belief revision

International audienceWe generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single- agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting

Consistency preservation and crazy formulas in BMS

International audienceWe provide conditions under which seriality is preserved during an update in the BMS framework. We consider not only whether the entire updated model is serial but also whether its generated submodels are serial. We also introduce the notion of crazy formulas which are formulas such that after being publicly announced at least one of the agents' beliefs become inconsistent

De DEL à EDL ou comment illustrer la puissance des événements inverses

La logique épistémique dynamique (DEL) introduite par Baltag et col. et la logique propositionnelle dynamique (PDL) proposent différentes sémantiques aux événements. La seconde se prête facilement à l'introduction d'événements inverses et de relations d'accessibilité épistémiques. Nous appelons EDL le formalisme résultant. Nous montrons alors que DEL peut être traduit dans EDL grâce à cet emploi d'événements inverses. Il s'ensuit que EDL est plus expressive et générale que DEL . Dynamic epistemic logic (DEL) as viewed by Baltag et col. and propositional dynamic logic (PDL) offer different semantics of events. It turns out that converse events and epistemic accessibility relations can be easily introduced in PDL . We call EDL the resulting formalism. We then show that DEL can be translated into EDL thanks to this use of converse events. It follows that EDL is more expressive and general than DEL

Exploring the power of converse events

Dynamic epistemic logic as viewed by Baltag, Moss and Solecki (DEL) and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DEL adds dynamics to epistemic logic by introducing so-called event models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. In this paper we add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DEL can be translated into EDL thanks to this use of the converse operator: it enables us to translate the structure of the event model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic event model in the language (as done in DEL). It follows that EDL is more expressive and general than DEL and we characterize semantically and syntactically in EDL this embedding of DEL

Undecidability in Epistemic Planning

Dynamic epistemic logic (DEL) provides a very expressive framework for multi-agent planning that can deal with nondeterminism, partial observability, sensing actions, and arbitrary nesting of beliefs about other agents’ beliefs. However, as we show in this paper, this expressiveness comes at a price. The planning framework is undecidable, even if we allow only purely epistemic actions (actions that change only beliefs, not ontic facts). Undecidability holds already in the S5 setting with at least 2 agents, and even with 1 agent in S4. It shows that multi-agent planning is robustly undecidable if we assume that agents can reason with an arbitrary nesting of beliefs about beliefs. We also prove a corollary showing undecidability of the DEL model checking problem with the star operator on actions (iteration)

Correspondence Theory for Atomic Logics

We develop the correspondence theory for the framework of atomic and molecular logics on the basis of the work of Goranko & Vakarelov. First, we show that atomic logics and modal polyadic logics can be embedded into each other. Using this embedding, we reformulate the notion of inductive formulas introduced by Goranko & Vakarelov into our framework. This allows us to prove correspondence theorems for atomic logics by adapting their results

Supervisory Control Theory in Epistemic Temporal Logic

International audienceSupervisory control theory deals with problems related to the existence and the synthesis of supervisors. The role of a supervisor in a system is to control and restrict the behavior of this system in order to realize a specific behavior. When there are multiple supervisors, such systems are in fact multi-agent systems. The results of supervisory control theory are usually expressed in terms of operations like intersection and inclusion between formal languages. We reformulate them in terms of model checking problems in an epistemic temporal logic. Our reformulations are very close to natural language expressions and highlight their under-lying intuitions. From an applied perspective, they pave the way for applying model checking techniques developed for epistemic temporal logics to the problems of supervisory control theory

Logic and Commonsense Reasoning: Lecture Notes

MasterThese are the lecture notes of a course on logic and commonsense reasoning given to master students in philosophy of the University of Rennes 1. N.B.: Some parts of these lectures notes are sometimes largely based on or copied verbatim from publications of other authors. When this is the case, these parts are mentioned at the end of each chapter in the section “Further reading”