Intuitionistic modal logic based on neighborhood semantics without superset axiom
Tomasz Witczak
Abstract:In this paper we investigate certain systems of propositional intuitionistic modal logic defined semantically in terms of neighborhood structures. We discuss various restrictions imposed on those frames but our constant approach is to discard superset axiom. Such assumption allows us to think about specific modalities ∆, ∇ and new functor depending on the notion of maximal neighborhood. We show how it is possible to treat our models as bi-relational ones.We prove soundness and completeness of proposed axiomati… Show more
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