Duquenne-Guigues Bases Of Lattice -valued Fuzzy Description Logic L-ALCN

Formal concept analysis (FCA) is a field of applied mathematics that is based on a lattice-theoretic formalization of the notion of a concept and of a hierarchy of concepts.It is supposed to facilitate the use of mathematical reasoning for conceptual data analysis and knowledge processing. In FCA, for a certain formal context, Duquenne and Guigues have proved there is a consistent, complete and non-redundant implication set if M is a finite attribution set,and called it Duquenne-Guigues base. They have found the so-called " attribute exploration algorithms" to compute the Duquenne-Guigues base. In this paper, we apply Formal Concept Analysis to Description Logics L-ALCN. In the international community, this direction of reasech is still in its infancy stage, but commomly kowledged its scientific significance:to deal with mass information of Semantics Web, it has a very good prospect. In accordance with the characteristics of L-ALCN, this article redefines the theory of intension, pseudo-intention and finite bases correctly and completely. We Present the definition of supporting set of L-ALCN and the theorem of existence of Duquenne-Guigues bases. We also give corresponding algorithms. The finite bases of L-ALCN which we have given in this paper is consistent, complete and non-redundant.The arrangement of the contents of this paper is as follows:Chaper 1:We present a brief survey of related works presented in this direction.Chaper 2:We introduce the description logic L-ALCN, including its syntax and semantics. L-ALCN is an extension of ALCN by a value set being extend to complete lattices.Chaper 3:Firstly we introduce two fundamental concepts in the theory of formal concept analysis.One is "formal contex", the other is "formal concept".After that we introduce the implication of attributes in formal context. Duquenne and Guigues have proved that in each context there always exist a valid,completed,non-redundant implication set by which we can logically deduce all other valid implications of this context,We call it Duquenne-Guigues bases or the main basis.Chaper 4:We set up the theoretical framwork of applying formal concept analysis into description logic.We give the definition of the description context , in accordance with the characteristics of L-ALCN we redefines the notions of intent, pseudo-intent and finite bases correctly and completely. We Present the definition of supporting set of L-ALCN and the existence theorem of Duquenne-Guigues bases in the framwork of description logic.Chaper 5:Consider the complete fuzzy description context, we will present an algorithm for finding Duquenne-Guigue base in two major steps:firstly, we present the algorithm to find a supporting set, noted as algorithm (â… ). Secondly,we find the preudo-intent in the supporting set, hence give Duquenne-Guigue base, noted as the algorithm (â…¡).Chaper 6:We give the summary and the comments on future work.