Fuzzy Description Logic With Qualifying Number Restrictions

Fuzzy description logics is a family of knowledge representation formalisms, dealingwith structured fuzzy knowledge.There are close relathionships between expressiveness and the num-her of constructor. In this paper, we extend fuzzy description logics -FALC by adding constructor-qualifying number restriction,which strengthens the ability to represent fuzzy information.We presentthe syntax and sematics of fuzzy ALCQ. (≥pR.C)^I(d)=sup_{e1,…,ep}∈△^Imin_i=1^p{min(R^I(d, e_i),C^I(e_i))} (≤pR.C)^I(d)=inf₍e₁,…,e_p+1∈△^Imax_i=1^p+1{max(1-R^I(d,e_i),(1-C^I(e_i))}We also investigate the reasoning algorithm, give the reasoning rules of F ALCQ-Abox,We will prove the correctness of tableaux reasoning algorithm,including the proof of termina-tion, soundness and completeness.Theorem 3.2 [Termination] For each fuzzy ACCQ KB A, Tableaux-algorithm terminates.Theorem 3.3 [Soundness] If the expansion rules can be applied to an fuzzy ACCQ purelyassertional knowledge base A such that they yield a complete and clash-free completion-forest,thenA has a fuzzy tableau. Theorem 3.4 [completeness] If A has a fuzzy tableau,then the expansion rules can be appliedpurely assertional knowledge base A in such a appropriate way that the tableaux-algorithm yields acomplete and clash-free completion-forest for A.We have seen that the inference problems in fuzzy Description Logics can be reduced to theconsistency checking problem for A, therefore, The fuzzy tableaux algorithm we present here can alsobe used to solve the problem of fuzzy entailment, fuzzy subsumption and the best truth value bound...