Epistemic Logic of Shallow Depths and Game Theoretical Applications

摘要

This paper presents a multi-modal epistemic logic GL_(EF) of shallow depths. Logic GL_(EF) is a fragment of multi-modal KD", and enables us to consider interpersonal inferential epistemic complexities. The subscripts E and F are called epistemic structures, which restrict interpersonal epistemic depths involved in formulae and proofs. We give its Gentzen-type sequent formulation as well as its semantics. Also, we provide some meta-theorems in order to evaluate interpersonal inferential epistemic complexities of the provability of a given sequent. These meta-theorems are applied to some game theoretical problems.