Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes

Jinjin Zhang (), Xiaoxia Zhou, Yan Zhang and Lixing Tan
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Jinjin Zhang: Department of Computer Science, Nanjing Audit University, Nanjing 211815, China
Xiaoxia Zhou: Department of Computer Science, Nanjing Audit University, Nanjing 211815, China
Yan Zhang: College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China
Lixing Tan: College of Information Engineering, Taizhou University, Taizhou 225300, China

Mathematics, 2025, vol. 13, issue 7, 1-14

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.

Keywords: epistemic logic; logic of doxastic attitudes; fuzzy logic; soundness; completeness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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