A minimal logic for interactive epistemology

Emiliano Lorini

pp. 725-755

in: Thomas Ågotnes, Giacomo Bonanno, Wiebe van der Hoek (eds), Logic and the foundations of game and decision theory, Synthese 193 (3), 2016.

Abstract

We propose a minimal logic for interactive epistemology based on a qualitative representation of epistemic individual and group attitudes including knowledge, belief, strong belief, common knowledge and common belief. We show that our logic is sufficiently expressive to provide an epistemic foundation for various game-theoretic solution concepts including “1-round of deletion of weakly dominated strategies, followed by iterated deletion of strongly dominated strategies” ((hbox {DWDS}^1hbox {-IDSDS})) and “2-rounds of deletion of weakly dominated strategies, followed by iterated deletion of strongly dominated strategies” ((hbox {DWDS}^2hbox {-IDSDS})). Axiomatization and complexity results for the logic are given in the paper.