Chinese Journal of Computers   Full Text
Title	Condition of Cyclic ALCN-Tbox Exists Model
Authors	CAO Fa-Sheng1),3) YU Quan2),3) WANG Ju4) JIANG Yun-Cheng4)
Address	1)(Institute of Logic and Applied Logic, Bijie College, Bijie, Guizhou 551700) 2)(Department of Mathematics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000) 3)(College of Mathematics Science, Guangxi Normal University, Guilin, Guangxi 541004) 4)(College of Computer Science and Information Engineering, Guangxi Normal University, Guilin, Guangxi 541004)
Year	2008
Issue	No.1(16—23)
Abstract &   Background	Abstract The current research progresses and the existing problems of description logic system ALCN with terminological cycles are analyzed in this paper. The condition of cyclic ALCN-Tbox exists model is studied. The mistake of proposition 2.9 in the paper published by Baadr in 2003 (Let T be a terminology such that each cycle in GT contains an even number of negative arcs. Then T is monotone) is pointed out, also some modification of proposition 2.9 is given. The condition of cyclic ALCN-Tbox exists fixpoint models (lfp-model and gfp-model) is given. keywords cyclic ALCN-Tbox; name symbol; lfp-model; gfp-model; Tbox monotone background Description logics are a logical reconstruction of the frame-based knowledge representation languages, with the aim of providing a simple well-established declarative semantics to capture the meaning of structured representation of knowledge. Terminological cycles (or cyclic definitions) have been a very hard problem in description logics for a long time, and their essential problems, i.e. semantics and reasoning problems, have not been solved reasonably. But terminological cycles may extend expressiveness capability of description logics, and in some applications (such as medical field) terminological cycles are inevitable. Also, envisioning a system that views a description logic knowledge base as an abstract entity that can be changed incrementally, terminological cycles can be easily created and either have to be detected and rejected by the system, which makes the system specification overly complex and hard to understand by a user, or the system has to accept them as legal constructions. For these reasons it seems worthwhile to analyze the semantic and algorithmic nature of terminological cycles. The current research progresses and the existing problems of description logic system ALCN with terminological cycles are analyzed. The condition of cyclic ALCN-Tbox exists model is studied. The mistake of proposition 2.9 in the paper published by Baadr in 2003 (Let T be a terminology such that each cycle in GT contains an even number of negative arcs. Then T is monotone) is pointed out, also some modification of proposition 2.9 is given. The condition of cyclic ALCN-Tbox exists fixpoint models (lfp-model and gfp-model) is given. Theoretical foundation for the application of terminological cycles in description logics is provided through the work in this paper. The work is supported by the National Natural Science Foundation of China under Nos.60573010, 60663001, the Natural Science Foundation of Guangxi Province of China under grant No.0447032, and the Youth Science Foundation of Guangxi Province of China under grant No.0640030.