描述逻辑中的统一 $\mathcal{FL}_\bot$

arXiv - CS - Symbolic Computation Pub Date : 2024-05-01 DOI:arxiv-2405.00912

Barbara Morawska

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引用次数: 0

摘要

描述逻辑学是一种用于知识表示的形式主义，在这种形式主义中，知识以概念的形式被捕获，这些概念是以受控的方式从一个受限的词汇表中构建出来的。概念的统一同样可以成为分析概念之间关系的有用工具。统一问题已经在描述逻辑$\mathcal{FL}_0$和$\mathcal{EL}$中得到了解决。这些小逻辑没有提供任何表达否定的方法。在这里，我们展示了一种在 $\mathcal{FL}_\bot$ 中求解统一的算法，这种逻辑用底部概念扩展了 $\mathcal{FL}_0$ 。底层概念允许我们表达两个概念是不相交的。我们的算法运行时间与问题的大小成指数关系。

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Unification in the description logic $\mathcal{FL}_\bot$

Description Logics are a formalism used in the knowledge representation, where the knowledge is captured in the form of concepts constructed in a controlled way from a restricted vocabulary. This allows one to test effectively for consistency of and the subsumption between the concepts. Unification of concepts may likewise become a useful tool in analysing the relations between concepts. The unification problem has been solved for the description logics $\mathcal{FL}_0$ and $\mathcal{EL}$. These small logics do not provide any means to express negation. Here we show an algorithm solving unification in $\mathcal{FL}_\bot$, the logic that extends $\mathcal{FL}_0$ with the bottom concept. Bottom allows one to express that two concepts are disjoint. Our algorithm runs in exponential time, with respect to the size of the problem.

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arXiv - CS - Symbolic Computation

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