Consistency reasoning in lattice-based fuzzy Description Logics

Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning withvague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whetheran ontology representing a knowledge domain is consistent. Surprisingly, not much is known about thecomplexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in thispaper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail.The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm fordeciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed forclassical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logicsover infinite lattices. For all the decidable classes, we also provide tight complexity bounds.