Work

Modal Logic for Reasoning About Uncertainty and Confusion

Year: 2025

Type: article

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(∼φ , w) = 1v(φ , 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 φ 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 .

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.437.20

Authors: Marta Bílková, Thomas M. Ferguson, Daniil Kozhemiachenko

Institutions: Czech Academy of Sciences, Rensselaer Polytechnic Institute, Centre National de la Recherche Scientifique, Aix-Marseille Université, Laboratoire d’Informatique et Systèmes

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Grantová Agentura České Republiky

Award: Logical Structure of Information Channels