Modal Logic for Reasoning About Uncertainty and Confusion

2025/05/05 by Marta Bílková, T. Ferguson, Bílková, Marta +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2505.02548

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand Gödel modal logic KG with the involutive negation ~ defined as v(~A,w)=1-v(A,w). We provide semantics with the finite model property for our new logic that we call KG_inv and show its equivalence to the standard semantics over [0,1]-valued Kripke models. Namely, we show that a formula is valid in the standard semantics of KG_inv iff it is valid in the new semantics. Using this new semantics, we construct a constraint tableaux calculus for KG_inv that allows for an explicit extraction of countermodels from complete open branches and then employ the tableaux calculus to obtain the PSPACE-completeness of the validity in KG_inv.

Citations

• Simplified Kripke semantics for K45-like Godel modal logics and its axiomatic extensions
• Bi-modal Gödel logic over [0,1]-valued Kripke frames

Cited by

• Tableaux for epistemic Gödel logic

Related

• Simple tableaux for two expansions of Gödel modal logic
• Modal Semantics for Reasoning with Probability and Uncertainty
• Provability Models
• Simplified Kripke semantics for K45-like Godel modal logics and its axiomatic extensions
• Paraconsistent Constructive Modal Logic