Work

Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes

Year: 2025

Type: article

Abstract: In traditional epistemic logic—particularly modal logic—agents are often assumed to have complete and certain knowledge, which is unrealistic in real-world scenarios where uncertainty, imprecision, and the incompleteness of information are common. This study proposes an extension of the logic of doxastic attitudes to a fuzzy setting, representing beliefs or knowledge as continuous values in the interval [0, 1] rather than binary Boolean values. This approach offers a more nuanced and realistic modeling of belief states, capturing the inherent uncertainty and vagueness in human reasoning. We introduce a set of axioms for the fuzzy logic of doxastic attitudes, formalizing how agents reason with regard to uncertain beliefs. The theoretical foundations of this logic are established through proofs of soundness and completeness. To demonstrate practical utility, we present a concrete example, illustrating how the fuzzy logic of doxastic attitudes can model uncertain preferences and beliefs.

Source: Mathematics

DOI: 10.3390/math13071105

Authors: Jinjin Zhang, Xiaoxia Zhou, Yan Zhang, Lixing Tan

Institutions: Nanjing Audit University, Nanjing Forestry University, Taizhou University, Taizhou University

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China