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PSPACE-completeness of bimodal transitive weak-density logic

Year: 2025

Type: article

Abstract: Windows have been introduced in [1] as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the “folklore” case of bimodal ${\textbf{K}}4$ already treated in [8], but which is worth a fresh review, we show that windows allow to polynomially solve the satisfiability problem when adding transitivity to weak-density, by mixing algorithms for bimodal ${\textbf{K}}4$ together with windows-approach. The conclusion is that both satisfiability and validity are $\textbf{PSPACE}$-complete for these logics.

Source: Logic Journal of IGPL

DOI: 10.1093/jigpal/jzaf097

Author: Olivier Gasquet

Institutions: Centre National de la Recherche Scientifique, Institut de Recherche en Informatique de Toulouse, Université de Toulouse

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7129329139

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Cites: 8

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