Informational semantics for superintuitionistic modal logics

Abstrakt

In this paper we present a non-standard semantic framework that generalizes Kripke semantics in two directions: (i) it allows for weakening of some laws for “normal” modalities and (ii) it allows to weaken the background non-modal propositional logic to intuitionistic logic. In other words, the framework can be seen as a novel semantics for superintuitionistic non-normal modal logics. A peculiar feature of the framework is that not only diamond but also box is captured as an existential modality. We will show how this framework incorporates standard neighborhood semantics and indicate that it incorporates in a similar sense Boˇzi´c and Doˇsen’s semantics for normal intuitionistic modal logics.