带传递关系和存在量词的描述逻辑MSC推理

Computing Most Specific Concept in Description Logic with Transitive Roles and Existential Restrictions

分析了描述逻辑非标准推理的重要性,特别分析了描述逻辑MSC推理的研究现状和存在的问题.针对目前描述逻辑MSC推理不能同时处理传递关系和存在量词的不足,研究了带传递关系和存在量词的描述逻辑εL+的MSC推理问题.提出了一种新的εL+-描述图,利用描述树和描述图给出了描述逻辑εL+的MSC近似推理算法,并利用εL+-描述树同态和εL+-描述树描述图同态证明了MSC近似推理算法的正确性.作为一个附带的结果,利用εL+-描述树描述图同态给出了εL+的实例推理算法,也证明了实例推理算法的正确性.

Description logic is a logical reconstruction of the flame-based knowledge representation languages, with the aim of providing simple well-established declarative semantics to capture the meaning of structured representation of knowledge. The fundamentality of non-standard inferences in description logic, especially the current research progress and existing problems of the MSC （most specific concept） inference in description logic, are analyzed in this paper. Aiming at the insufficiency of the MSC inference in description logics which can not deal with transitive roles and existential restrictions, the MSC inference for description logic with transitive roles and existential restrictions εL＋ is studied. A kind of new εL＋-description graph is presented. The inference algorithm of approximating MSC in description logic with transitive roles and existential restrictions εL^＋ is presented using description tree and description graph, and its correctness is proved using εL＋ description trees homomorphism and description graph homomorphism. As a by-product, the instance reasoning algorithm in description logic with transitive roles and existential restrictions εL＋ is presented using εL＋ -description tree and description graph homomorphism, and its correctness is also proved. Theoretical foundation for the MSC inference for more expressive description logics such as ALe is provided through the MSC inference algorithm of εL＋.