7,264 research outputs found
Weakly Aggregative Modal Logic: Characterization and Interpolation
Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic
logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation
BRANCHING TIME LOGIC, PERFECT INFORMATION GAMES AND BACKWARD INDUCTION
The logical foundations of game-theoretic solution concepts have so far been developed within the confines of epistemic logic. In this paper we turn to a different branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. We extend the branching time framework by adding agents and by defining the notion of prediction. We show that perfect information games are a special case of extended branching time frames and that the backward-induction solution is a prediction. We also provide a characterization of backward induction in terms of the property of internal consistency of prediction.
Relation-changing modal operators
We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Proof-theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets
In the context of strategic games, we provide an axiomatic proof of the
statement Common knowledge of rationality implies that the players will choose
only strategies that survive the iterated elimination of strictly dominated
strategies. Rationality here means playing only strategies one believes to be
best responses. This involves looking at two formal languages. One is
first-order, and is used to formalise optimality conditions, like avoiding
strictly dominated strategies, or playing a best response. The other is a modal
fixpoint language with expressions for optimality, rationality and belief.
Fixpoints are used to form expressions for common belief and for iterated
elimination of non-optimal strategies.Comment: 16 pages, Proc. 11th International Workshop on Computational Logic in
Multi-Agent Systems (CLIMA XI). To appea
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