Reflexive insensitive modal logics

TL;DR

This paper investigates a class of modal logics that are insensitive to reflexivity, providing semantic characterizations, completeness theorems, and conditions for soundness, thus advancing understanding of modal logic variants.

Contribution

It introduces reflexive-insensitive modal logics, establishes their semantic properties, and proves a general completeness theorem via translation from normal modal logics.

Findings

Semantic characterization of reflexive-insensitive modal logics

A general completeness theorem based on translation methods

Conditions for soundness of these logics

Abstract

We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general completeness theorem on the basis of a translation between normal modal logics and their reflexive-insensitive counterparts. Lastly, we provide a sufficient semantic condition describing when a similarly general soundness result is also available.