Fuzzy Lattice-based Description Logic

• URL: http://arxiv.org/abs/2506.05833v1
• Date: Fri, 06 Jun 2025 07:57:54 GMT
• Title: Fuzzy Lattice-based Description Logic
• Abstract summary: We introduce a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic.<n>This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts.<n>We provide a tableaux algorithm that provides a complete and sound-time decision procedure to check the consistency of LE-FALC ABoxes.
• Score: 1.509090088899154
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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