Cédric Dégremont

Agreement Theorems in Dynamic-Epistemic Logic

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements.

Finite identification from the viewpoint of epistemic update

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.

Exploring the tractability border in epistemic tasks

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.

Modal Logics for Preferences and Cooperation: Expressivity and Complexity

This paper studies expressivity and complexity of normal modal logics for reasoning about cooperation and preferences. We identify a class of local and global notions relevant for reasoning about cooperation of agents that have preferences. Many of these notions correspond to game- and social choice-theoretical concepts. We specify the expressive power required to express these notions by determining whether they are invariant under certain relevant operations on different classes of Kripke models and frames. A large class of known extended modal languages is specified and we show how the chosen notions can be expressed in fragments of this class. To determine how demanding reasoning about cooperation is in terms of computational complexity, we use known complexity results for extended modal logics and obtain for each local notion an upper bound on the complexity of modal logics expressing it.

Bridges between dynamic doxastic and doxastic temporal logics

In this paper, we compare two modal frameworks for multi-agent belief revision: dynamic doxastic logics computing stepwise updates and temporal doxastic logics describing global system evolutions, both based on plausibility pre-orders. We prove representation theorems showing under which conditions a doxastic temporal model can be represented as the stepwise evolution of a doxastic model under successive ’priority updates’. We define these properties in a suitable doxastic-temporal language, discuss their meaning, and raise some related definability issues. Analyzing the behavior of agents in a dynamic environment requires describing the evolution of their knowledge as they receive new information. Moreover agents entertain beliefs that need to be revised after learning new facts. I might be confident that I will find the shop open, but once I found it closed, I should not crash but rather make a decision on the basis of new consistent beliefs. Such beliefs and information may concern ground-level facts, but also beliefs about other agents. I might be a priori confident that the price of my shares will rise, but if I learn that the market is rather pessimistic (say because the shares fell by 10%), this information should change my higher-order beliefs about what other agents believe. Tools from modal logic have been successfully applied to analyze knowledge dynamics in multi-agent contexts. Among these, Temporal Epistemic Logic [23], [19]’s Interpreted Systems, and Dynamic Epistemic Logic [2] have been particularly fruitful. A recent line of research [11, 10, 9] compares these alternative frameworks, and [10] presents a representation theorem that shows under which conditions a temporal model can be represented as a dynamic one. Thanks to this link, the two languages also become comparable, and one can merge ideas: for example, a new line The second author was supported by a GLoRiClass fellowship of the European Commission (Research Training Fellowship MEST-CT-2005020841). of research explores the introduction of protocols into the logic of public announcements PAL, as a way of modeling informational processes (see [9]). To the best of our knowledge, there are no similar results yet for multi-agent belief revision. One reason is that dynamic logics of belief revision have only been wellunderstood recently. But right now, there is work on both dynamic doxastic logics [5, 3] and on temporal frameworks for belief revision, with [14] as a recent example. The exact connection between these two frameworks is not quite like the case of epistemic update. In this paper we make things clear, by viewing belief revision as priority update over plausibility pre-orders. This correspondence allows for similar language links as in the knowledge case, with similar precise benefits. We start in the next section with background about earlier results and basic terminology. In section 2 we give the main new definitions needed in the paper. Section 3 presents the key temporal doxastic properties that we will work with. In section 4 we state and prove our main result linking the temporal and the dynamic frameworks, first for the special case of total pre-orders and then in general. We also discuss some variations and extensions. In section 5 we introduce formal languages, providing an axiomatization for our crucial properties, and discussing some related definability issues. We state our conclusions and mention some further applications and open problems in the last section.

Getting together: a unified perspective on modal logics for coalitional interaction

Cooperation of agents is a major issue in fields such as computer science, economics and philosophy. The conditions under which coalitions are formed occur in various situations involving multiple agents.

Dynamics we can believe in: a view from the Amsterdam School on the centenary of Evert Willem Beth

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.