A Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices

摘要

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecid-able in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning.