We provide a new characterization of both belief update and belief revision in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of states, a Kripke belief relation and a Lewis selection function. Adding a valuation to a frame yields a model. Given a model and a state, we identify the initial belief set K with the set of formulas that are believed at that state and we identify either the updated belief set K⋄ϕ or the revised belief set K⁎ϕ (prompted by the input represented by formula ϕ) as the set of formulas that are the consequent of conditionals that (1) are believed at that state and (2) have ϕ as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the Alchourrón, Gärdenfors and Makinson (AGM) belief revision functions, in the following sense: (1) each model gives rise to a partial belief function that can be completed into a full KM/AGM update/revision function, and (2) for every KM/AGM update/revision function there is a model whose associated belief function coincides with it. The difference between update and revision can be reduced to two semantic properties that appear in a stronger form in revision relative to update, thus confirming the finding by Peppas et al. (1996) [30] that, “for a fixed theory K, revising K is much the same as updating K”. It is argued that the proposed semantic characterization brings into question the common interpretation of belief revision and update as change in beliefs in response to new information.

This special issue of the Journal of Logic and Computation contains a selection of papers presented at the 11th Conference on Logic and the Foundations of the Theory of Games and Decisions (LOFT11), which took place in Bergen (Norway), July 27–30, 2014. 1 LOFT11 marked 20 years of LOFT conferences: the first conference took place in 1994 in Marseille (France) and, since then, LOFT has become a regular bi-annual event. 2 The LOFT conferences are interdisciplinary events that bring together researchers from a variety of fields: cognitive psychology, computer science and artificial intelligence, economics, game theory, linguistics, logic, mind sciences, philosophy and social choice. In its original conception, LOFT had as its central theme the application of logic, in particular modal epistemic logic, to foundational issues in the theory of games and individual decision-making. Epistemic considerations have been central to game theory for a long time. The expression ‘interactive epistemology’ has been used in the game-theory literature to refer to the analysis of strategic interaction based on an explicit modelling of the players' beliefs about each other's beliefs and rationality. The LOFT conferences arose from the realization that the tools and methodology that were used in game theory were closely related to those used in other fields, notably computer science, logic and philosophy. Modal logic turned out to be the common language that made it possible to bring together different professional communities.

Within the context of extensive-form (or dynamic) games, we use choice frames to represent the initial beliefs of a player as well as her disposition to change those beliefs when she learns that an information set of hers has been reached. As shown in [5], in order for the revision operation to be consistent with the AGM postulates [1], the player's choice frame must be rationalizable in terms of a total pre-order on the set of histories. We consider four properties of choice frames and show that, together with the hypothesis of a common prior, are necessary and sufficient for the existence of a plausibility order that rationalizes the epistemic state (that is, initial beliefs and disposition to revise those beliefs) of all the players. The plausibility order satisfies the properties introduced in [6] as part of a new definition of perfect Bayesian equilibrium for dynamic games. Thus the present paper provides epistemic foundations for that solution concept.