描述逻辑μALCQO 的语义及推理

蒋运承; 王驹; 汤庸; 邓培民

引用本文:	蒋运承,王驹,汤庸,邓培民.描述逻辑μALCQO 的语义及推理.软件学报,2009,20(3):491-504

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描述逻辑μALCQO 的语义及推理
蒋运承^1,2, 王驹¹, 汤庸², 邓培民¹
1.广西师范大学计算机科学与信息工程学院,广西桂林 541004;2.中山大学计算机科学系,广东广州 510275

摘要:

循环术语集是描述逻辑长期以来的研究难点,其最基本的问题即语义及推理问题没有得到合理的解决.基于混合分级μ-演算将不动点构造算子引入到含有枚举构造算子的描述逻辑ALCQO 中,提出了一种允许包含循环术语集的描述逻辑μALCQO.给出了μALCQO 的语法、语义和不动点构造算子的性质,证明了μALCQO 的可满足性推理等价于混合分级μ-演算的可满足性推理.基于混合分级μ-演算可满足性推理算法,并利用完全强化自动机给出了μALCQO的可满足性推理算法,以及给出了推理算法正确性证明和复杂性定理.μALCQO为进一步给出同时含有不动点构造算子和枚举构造算子的表达能力强的描述逻辑推理算法提供了理论基础.

关键词: 描述逻辑 μALCQO 混合分级μ-演算完全强化自动机不动点构造算子

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基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60663001, 60573010, 60673135, 60373081 (国家自然科学基金); the Postdoctoral Science Foundation of China under Grant No.20060400226 (中国博士后科学基金); the NaturalScience Key Foundation of Guangdong Province of China under Grant No.04105503 (广东省自然科学重点基金); the Natural ScienceFoundation of Guangxi Province of China under Grant Nos.0640030, 0832103 (广西自然科学基金)

Semantics and Reasoning of Description Logic μALCQO

JIANG Yun-Cheng,WANG Ju,TANG Yong,DENG Pei-Min

Abstract:

Terminological cycles have been a very hard problem in description logics for a long time, and their essential problems, i.e. semantics and reasoning problem, have not been solved reasonably. Based on hybrid graded μ-calculus, the description logic μALCQO which may include terminological cycles is presented, and the μALCQO is derived form the description logic ALCQO which includes the nominal constructor by adding the least and greatest fixpoint constructors. The syntax, semantics and properties of the fixpoint constructors of description logic μALCQO are given. The equality between satisfiability of description logic μALCQO and that of hybrid graded μ-calculus is proved. Based on the satisfiability reasoning algorithm of hybrid graded μ-calculus, the satisfiability reasoning algorithm of description logic μALCQO is presented using fully enriched automata. The correctness of the satisfiability reasoning algorithm is proved, and the complexity property of the reasoning algorithm is given.The theoretical foundation for reasoning algorithms of more expressive description logics including fixpoint constructors and nominal constructor is provided through μALCQO.

Key words: description logic μALCQO hybrid graded μ-calculus fully enriched automata fixpoint constructor