Discrete tableau algorithms for FSHI

A variety of fuzzy description logics are proposed to extend classical description logics with fuzzy capability. However, reasoning with general TBoxes is still an open problem in fuzzy description logics. In this paper, we present a novel discrete tableau algorithm for a given fuzzy description logic FSHI with general TBoxes, which tries to construct discrete tableaus of FSHI knowledge bases. We prove the equivalence of existence between discrete tableaus and models of FSHI knowledge bases, hence getting that the discrete tableau algorithm is a sound and complete decision procedure for FSHI reasoning problems with general TBoxes.