模糊描述逻辑L-ALCN

Fuzzy Description Logic L-ALCN

为了使描述逻辑能够处理更一般化的模糊信息,Straccia给出了基于完备格的L-ALC描述逻辑系统.在该方法的基础上,提出了带数量约束算子的L-ALCN系统,给出了L-ALCN的语法,并详细给出了概念(≥nR)和(≤nR)的语义.经典的描述逻辑系统中引入了数量约束算子后,角色R就出现了多个后继.当系统的真子集扩充到完备格时,角色R的后继和断言的真值同时出现了多个.为了保证推理算法的合理性且得到可行的计算复杂度,引入了一个特殊的集合DL(c),并且利用集合DL(c)扩展了完备格上的两条运算性质.在这些工作的基础上,深入研究了系统的推理算法,并证明了算法的终止性、可靠性与完全性.相对于L-ALC,系统L-ALCN具有更强的表达能力,并且L-ALCN的计算复杂度是Pspace完全的.

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 DL（c） is introduced. Two properties of certainty lattice are obtained by taking advantage of the set DL（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.