A Game-Theoretical Notion of Consequence

B.P. Harrenstein

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Abstract

In this paper we introduce a distributed kind of logical evaluation game for propostional languages. The set of propositional variables is partitioned and each block is assigned to a player who has control over the semantical values of the variables in his block. The preferences of each player are laid down in a theory; each player aims at satisfying as strong a subtheory of his theory as possible. We also introduce a solution concept of a maximum equilibrium, which is a generalization of Nash equilibrium that also applies to partial preorders. On this basis we define a consequence relation between families of theories and formulae. We say that, given a partition of the propositional variables, a formula follows from a family of theories (indexed by the blocks of the partition) if and only if that formula holds in all maximum equilibria of the corresponding evaluation game. We give an independent characterization of this consequence relation using rough sets and investigate its formal properties especially in relation to classical propositional consequence. In particular, we show our game-theoretical notion of consequence to be decidable.
Original languageUndefined/Unknown
Title of host publicationProceedings of the Fifth Conference on Logic the Foundations of Game and Decision Theory LOFT5
EditorsG. Bonanno, E. Colombatto, W. van der Hoek
Place of PublicationTorino
PublisherInternational Center for Economic Research (ICER)
Pages1-21
Number of pages21
Publication statusPublished - 2002

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