描述逻辑μALCQO的语义及推理

Semantics and Reasoning of Description Logic μALCQO

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.

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.