Fuzzy Lattice-based Description Logic
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910991915155456 |
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| author | Ding, Yiwen Manoorkar, Krishna |
| author_facet | Ding, Yiwen Manoorkar, Krishna |
| contents | Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fuzzy Lattice-based Description Logic Ding, Yiwen Manoorkar, Krishna Logic in Computer Science Artificial Intelligence Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling. |
| title | Fuzzy Lattice-based Description Logic |
| topic | Logic in Computer Science Artificial Intelligence |
| url | https://arxiv.org/abs/2506.05833 |