Propositional Mixed Logic: Its Syntax and Semantics

TL;DR

This paper introduces mixed logic, combining minimal, intuitionistic, and classical propositional logics, and provides a completeness theorem, semantic relations, and a sequent calculus for it.

Contribution

It presents a novel propositional logic integrating three different logical systems with formal semantics and proof calculus.

Findings

Completeness theorem established for mixed logic

Relations between mixed, minimal, intuitionistic, and classical logics shown

Sequent calculus version developed for the logic

Abstract

In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish some relations between mixed logic and minimal, intuitionistic and classical logics. We present at the end a sequent calculus version for this logic.