Semantics for intuitionistic epistemic logics of shallow depths for game theory

Epistemic logic of shallow depths has been developed by Kaneko–Suzuki using classical logic. In this paper, we adopt intuitionistic logic as the base logic to limit each player’s reasoning to constructive one. The resulting logical system is denoted by IG<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$_{EF}$$</EquationSource> </InlineEquation>, and we introduce epistemic possible world semantics for IG<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$_{EF}$$</EquationSource> </InlineEquation>. We show the soundness and completeness of IG<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$_{EF}$$</EquationSource> </InlineEquation> with respect to this semantics for it. We also show some applications to game theoretical decision making. Copyright Springer-Verlag 2013