Cédric Dégremont’s research while affiliated with Université Toulouse III - Paul Sabatier and other places

We study labeled transition systems where at each state an agent is aware of and hence reasons about only a part of the entire system (called the ‘sight’). We develop a logic for such systems: the ‘logic of sights’. We explore its model theory, give an axiomatization and prove its completeness. We show that the logic is a fragment of the loosely guarded fragment of first-order logic. We show that the satisfiability problem of the logic is PSPACE-complete and the combined complexity of its model-checking problem is in PTIME. Finally we discuss its relation to other logics as well as extensions.

Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem’s work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages, in particular modal languages, and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics, and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the chapter.

We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we investigate the impact of assuming information structures to be partition-based (rather than arbitrary relational structures) on the complexity of various problems. We focus on the tractability of concrete epistemic tasks and not on epistemic logics describing them.

This paper investigates measures of semantic similarity between conversations from an axiomatic perspective. We abstract away from real conversations, representing them as sequences of formulas, equipped with a notion of semantic interpretation that maps them into a different space. An example we use to illustrate our approach is the language of propositional logic with its classical semantics. We introduce and study a range of different candidate properties for metrics on such conversations, for the structure of the semantic space, and for the behavior of the interpretation function, and their interactions. We define four different metrics and explore their properties in this setting.

We describe a dialogue model and an implemented annotation scheme for a pilot corpus of annotated online chats concerning bargaining negotiations in the game The Settlers of Catan. We will use this model and data to analyze how conversations proceed in the absence of strong forms of cooperativity, where agents have diverging motives. Here we concentrate on the description of our annotation scheme for negotiation dialogues, illustrated with our pilot data, and some perspectives for future research on the issue.

We study a model where a group of self-interested agents negotiate over a set of resources. The agents believe that at the end of the negotiation phase a certain randomisation will take place: either the bundles of resources the agents have accumulated will get reassigned to other agents, or the valuation functions the agents use to assess the values of these bundles will get reassigned, or both. The uncertainty as to which combination of valuation function and bundle an agent will end up with will influence her negotiation strategy. For certain types of uncertainty of this kind and for certain assumptions on the attitude towards risk of the agents involved, it is possible to show that negotiation is guaranteed to converge to an allocation with certain desirable properties, such as maximising egalitarian or utilitarian social welfare. This model of distributed negotiation under uncertainty thus provides a new perspective on theories of social welfare.

Van Benthem, Gerbrandy, Hoshi and Pacuit gave a natural translation of dynamic epistemic logic (DEL) into epistemic temporal logic (ETL) and proved a representation theorem, characterizing those ETL models that are translations of some DEL protocol; among the characterizing properties we also find synchronicity. In this paper, we argue that synchronicity is not an inherent property of DEL, but rather of the translation that van Benthem et al.\ used. We provide a different translation that produces asynchronous ETL models and discuss a minimal temporal extension of DEL that removes the ambiguities between the possible translations. This allows us a first attempt of an assessment which of the epistemic-temporal properties are intrinsic to DEL and which are properties of the translation.

Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of learning in the context of dynamic and temporal logics of epistemic change. We first introduce the basic formal notions of learning theory and basic epistemic logic. We provide a translation of the components of learning scenarios into the domain of epistemic logic. Then, we propose a characterization of finite identifiability in an epistemic temporal language. In the end we discuss consequences and possible extensions of our work.

Logic is breaking out of the confines of the single-agent static paradigm that has been implicit in all formal systems until recent times. We sketch some recent developments that take logic as an account of information-driven interaction. These two features, the dynamic and the social, throw fresh light on many issues within logic and its connections with other areas, such as epistemology and game theory.