Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes
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 dox...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1105 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849730323014746112 |
|---|---|
| author | Jinjin Zhang Xiaoxia Zhou Yan Zhang Lixing Tan |
| author_facet | Jinjin Zhang Xiaoxia Zhou Yan Zhang Lixing Tan |
| author_sort | Jinjin Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-638c2b389ebb4762af41292d6b9de3d6 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-638c2b389ebb4762af41292d6b9de3d62025-08-20T03:08:55ZengMDPI AGMathematics2227-73902025-03-01137110510.3390/math13071105Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic AttitudesJinjin Zhang0Xiaoxia Zhou1Yan Zhang2Lixing Tan3Department of Computer Science, Nanjing Audit University, Nanjing 211815, ChinaDepartment of Computer Science, Nanjing Audit University, Nanjing 211815, ChinaCollege of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, ChinaCollege of Information Engineering, Taizhou University, Taizhou 225300, ChinaIn 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.https://www.mdpi.com/2227-7390/13/7/1105epistemic logiclogic of doxastic attitudesfuzzy logicsoundnesscompleteness |
| spellingShingle | Jinjin Zhang Xiaoxia Zhou Yan Zhang Lixing Tan Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes Mathematics epistemic logic logic of doxastic attitudes fuzzy logic soundness completeness |
| title | Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes |
| title_full | Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes |
| title_fullStr | Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes |
| title_full_unstemmed | Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes |
| title_short | Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes |
| title_sort | fuzzy epistemic logic fuzzy logic of doxastic attitudes |
| topic | epistemic logic logic of doxastic attitudes fuzzy logic soundness completeness |
| url | https://www.mdpi.com/2227-7390/13/7/1105 |
| work_keys_str_mv | AT jinjinzhang fuzzyepistemiclogicfuzzylogicofdoxasticattitudes AT xiaoxiazhou fuzzyepistemiclogicfuzzylogicofdoxasticattitudes AT yanzhang fuzzyepistemiclogicfuzzylogicofdoxasticattitudes AT lixingtan fuzzyepistemiclogicfuzzylogicofdoxasticattitudes |