The Complexity of Fuzzy Description Logics over Finite Lattices with Nominals
نویسنده
چکیده
The complexity of reasoning in fuzzy description logics (DLs) over finite lattices usually does not exceed that of the underlying classical DLs. This has recently been shown for the logics between L-IALC and L-ISCHI using a combination of automataand tableau-based techniques. In this report, this approach is modified to deal with nominals and constants in L-ISCHOI. Reasoning w.r.t. general TBoxes is ExpTime-complete, and PSpace-completeness is shown under the restriction to acyclic terminologies in two sublogics. The latter implies two previously unknown complexity results for the classical DLs ALCHO and SO.
منابع مشابه
Fuzzy DLs over Finite Lattices with Nominals
The complexity of reasoning in fuzzy description logics (DLs) over a finite lattice L usually does not exceed that of the underlying classical DLs. This has recently been shown for the logics between L-IALC and L-ISCHI using a combination of automataand tableau-based techniques. In this paper, this approach is modified to deal with nominals and constants in L-ISCHOI. Reasoning w.r.t. general TB...
متن کاملConsistency in Fuzzy Description Logics over Residuated De Morgan Lattices
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 undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI...
متن کاملConsistency 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. T...
متن کاملA Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices
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 undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI...
متن کاملEQ-logics with delta connective
In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...
متن کامل