提出模糊格上描述逻辑，支持多值语义下的知识推理。
Fuzzy Lattice-based Description Logic
- 基于模糊格构建新型描述逻辑LE-FALC
- 提供多项式时间的合一算法验证知识库一致性
- 适用于模糊概念与多值逻辑推理场景
近期提出的描述逻辑LE-ALC用于增强形式上下文中的语义推理，并开发了多项式时间的表列算法来检查无环公理库的一致性。本文引入LE-ALC的模糊推广——LE-FALC，作为多值非分配逻辑（即多值LE逻辑）的描述逻辑对应物。该逻辑可用于表示和推理模糊形式上下文与模糊形式概念中的知识。我们提出了一个表列算法，提供了完整且正确的多项式时间决策程序，用于检查LE-FALC ABoxes的一致性。通过展开法，我们也获得了检查带有无环TBox的LE-FALC一致性的指数时间决策程序。
原文摘要 · Abstract (English)
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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