On Computational Complexity of the Extended Fuzzy Description Logic with Numerical Restriction

Abstract

Extended fuzzy description logic EFALCN (extended fuzzy attributive concept description language with complements and unqualified number restriction) is the fuzzy extension of the description logic with numerical restriction ALCN (attributive concept description language with complements and unqualified number restriction), but it lacks of reasoning algorithms and complexity analysis for reasoning tasks. In this paper, a constraint-propagation based tableau algorithm is proposed, and it is proved that this algorithm can be executed in PSPACE (polynomial space). For there is a polynomial time reduction that can reduce ALCN reasoning tasks into EFALCN reasoning tasks and ALCN reasoning tasks are PSPACE-complete, EFALCN reasoning tasks are