Modal Logic of Hearsay between Beliefs with Inconsistent Individual Ideas

Abstract

In analysing logic of hearsay, the inconsistency of individual notions makes difficulty. Modal logic is suitable for analysing logic of hearsay. The most previous semantics of modal logic such as using possible worlds makes the formula x = y ⊃ □x = y valid. However, in logic of hearsay, it can happen that the quoting person recognises x = y although the quoted person recognises x ≠ y. As such, the formula x = y∧¬□x = y is satisfiable in logic of hearsay. In order to deal with this, this study propose a new semantics with belief structure.