Intrinsic and relative characterization results for logics with negative modalities

2025/12/17 by de Groot, Jim, Marcos, João, Stefanes, Rodrigo
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2512.15496

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.

Citations

• Hennessy-Milner Properties via Topological Compactness
• Logic-Induced Bisimulations
• Sequent systems for negative modalities
• It ain't necessarily so: Basic sequent systems for negative modalities
• Algebraic laws for nondeterminism and concurrency

Related

• It ain't necessarily so: Basic sequent systems for negative modalities
• Sequent systems for negative modalities
• Explicit non-normal modal logic
• Toward the van Benthem Characterization Theorem for Non-Distributive Modal Logic
• Non-normal logics: semantic analysis and proof theory (extended version)