Fuzzy Description Logic L-ALCN

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. In order to make description logics deal with more general fuzzy information, U. Straccia has presented a fuzzy description logic L-ALC based on a certainty lattice. Based on the work of U. Straccia, a new description logic L-ALCN with the constructor of unqualified number restriction is proposed in this paper, and the syntax of L-ALCN and the semantics of the two concept (≥n R) and (≤n R) are defined. In classical description logics, when the constructor of unqualified number restriction is introduced, the role R has more than one successor. Because the description logic based on certainty lattice L-ALCN contains the constructor of unqualified number restriction, so the value of the assertion may have more than one. In order to ensure to gain the reasonable reasoning algorithm and its feasible complexity, a special set D\-L(c) is introduced. Two properties of certainty lattice are obtained by taking advantage of the set D\-L(c). After these preparations, the constraint propagation calculus for the system is studied, and soundness and completeness of the constraint propagation calculus are proved. Compared with L-ALC, the system L-ALCN is more expressive and it can be proved that reasoning tasks of the system L-ALCN are Pspace-complete.