Fuzzy Description Logics and t-norm based fuzzy logics
Fuzzy Description Logics and t-norm based fuzzy logics
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DOI：
10.1016/j.ijar.2010.01.001
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
Àngel García-Cerdaña;Eva Armengol;F. Esteva
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文献类型：
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作者：
Àngel García-Cerdaña;Eva Armengol;F. Esteva
描述逻辑是建立在经典逻辑基础上的知识表示语言。DL允许创建知识库，并提供对这些库的内容进行推理的方法。模糊描述逻辑是描述逻辑的自然扩展，用于处理真实的应用中常见的模糊概念。哈耶克提出以基于t-范数的模糊逻辑为基础来处理FDL，目的是丰富FDL的表达能力，并利用数学模糊逻辑领域的最新发展。从这个角度来看，我们定义了一个家庭的描述语言，表示为ALC（S），其中包括真值常数表示真度。在语言中有真值常量允许我们以与经典DL中大致相同的方式将知识库的公理定义为谓词语言的句子。另一方面，利用这些真值常数提供的表达能力，我们定义了一个分级的概念，可满足性，有效性和包容的DL概念的可满足性，有效性和包容的评估公式。在最后一节中，我们总结了与这些新的描述语言相关的模糊逻辑的一些结果，我们分析了与一般和规范语义相关的方面，并且我们证明了本文中考虑的一些FDL的规范标准完备性相关的一些结果。
Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications. Hájek proposed to deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the expressive possibilities in FDLs and to capitalize on recent developments in the field of Mathematical Fuzzy Logic. From this perspective we define a family of description languages, denoted by ALC∗(S), which includes truth constants for representing truth degrees. Having truth constants in the language allows us to define the axioms of the knowledge bases as sentences of a predicate language in much the same way as in classical DLs. On the other hand, taking advantage of the expressive power provided by these truth constants, we define a graded notion of satisfiability, validity and subsumption of DL concepts as the satisfiability, validity and subsumption of evaluated formulas. In the last section we summarize some results concerning fuzzy logics associated with these new description languages, we analyze aspects relative to general and canonical semantics, and we prove some results relative to canonical standard completeness for some FDLs considered in the paper.