Simple example of weak modal logic based on intuitionistic core

2018/06/25 by Witczak, Tomasz
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.1806.09443

Abstract

In this paper we present simple example of propositional logic which has one modal operator and is based on intuitionistic core. This system is very weak in modal sense - e.g. rules of regularity or monotonicity do not hold. It has complete semantics composed of possible worlds equipped with neighborhoods and pre-order relation. We discuss certain restrictions imposed on those structures. Also, we present characterization of axiom 4 known from logic S4.

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