On infinitary proof theory of logics of information and common belief

Abstrakt

Recently there has been a growing interest in applying nonclassically based modal logics in the context of logics for agency and social behaviour. In particular, substructural or other information-based modal logics of knowledge and belief, or similar versions of PDL, have been designed. While basic modal extensions of substructural logics on one side, and classically based logics of common belief and other fixed point modalities, are relatively well understood when it comes to completeness and proof theory, with logics we have in mind it is not so.