2025/10/06 by Marta Bílková, T. Ferguson, Bílková, Marta +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2510.04642
openalex publication_date 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28
We propose a multi-agent epistemic logic capturing reasoning with degrees of plausibility that agents can assign to a given statement, with 1 interpreted as "entirely plausible for the agent" and 0 as "completely implausible" (i.e., the agent knows that the statement is false). We formalise such reasoning in an expansion of Gödel fuzzy logic with an involutive negation and multiple S5-like modalities. As already Gödel single-modal logics are known to lack the finite model property w.r.t. their standard [0,1]-valued Kripke semantics, we provide an alternative semantics that allows for the finite model property. For this semantics, we construct a strongly terminating tableaux calculus that allows us to produce finite counter-models of non-valid formulas. We then use the tableaux to show that the validity problem in our logic is PSpace-complete when there are two or more agents, and coNP-complete for the single-agent case.