Intrinsic and relative characterization results for logics with negative modalities

TL;DR

This paper develops simulation-based methods for modal logics with non-classical negations, providing characterization results that clarify their expressive power and relationship to first-order logic.

Contribution

It introduces simulations for modal logics with subclassical negations, establishing intrinsic and relative characterization theorems for these logics.

Findings

Simulations for modal logics with negative modalities are introduced.

Intrinsic and relative characterization theorems are proved.

The expressive profile of these logics is delineated.

Abstract

We introduce simulations for modal logics with subclassical negations and restoration modalities, establish an adequacy theorem, and prove intrinsic (Hennessy-Milner-type) and relative (Van Benthem-type) characterization results. These results identify each restorative language with the fragment of first-order logic invariant under its simulations and delineate the expressive profile of modal logics with non-classical negations.