The limits of decidability in fuzzy description logics with general concept inclusions
The limits of decidability in fuzzy description logics with general concept inclusions
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DOI：
10.1016/j.artint.2014.09.001
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发表时间：
2015-01-01
影响因子：
14.4
通讯作者：
Penaloza, Rafael
中科院分区：
文献类型：
--
作者：
Borgwardt, Stefan;Distel, Felix;Penaloza, Rafael
模糊描述逻辑可以用来表示和推理模糊知识。这个逻辑形式主义家族是非常多样的，每个成员的特征在于构造器、公理和三角规范的特定选择，这些构造器、公理和三角规范用于指定语义。不幸的是，它最近被证明，在许多模糊DL的一般概念包含公理的一致性问题是不可判定的。在本文中，我们提出了一个证明框架，使我们能够扩展这些结果，以涵盖大型类的模糊DL。另一方面，我们也提供了匹配的可判定性结果的其余大部分逻辑。因此，我们得到了一个接近普遍的分类模糊DL根据其一致性问题的可判定性。(C)2014爱思唯尔有限公司版权所有。
Fuzzy description logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclusion axioms is undecidable. In this paper, we present a proof framework that allows us to extend these results to cover large classes of fuzzy DLs. On the other hand, we also provide matching decidability results for most of the remaining logics. As a result, we obtain a near-universal classification of fuzzy DLs according to the decidability of their consistency problem. (C) 2014 Elsevier B.V. All rights reserved.