Symmetries in Modal Logics

TL;DR

This paper extends the concept of symmetries from propositional formulas to modal formulas using coinductive models, demonstrating that such symmetries preserve logical entailment across various modal logics.

Contribution

It introduces a generalized framework for symmetries in modal logics, applicable to hybrid logics and beyond, and proves that these symmetries preserve entailment.

Findings

Symmetries in modal formulas preserve entailment.

The framework applies to a wide class of modal logics.

Includes hybrid logics as a special case.

Abstract

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment.