Name
Abstract | ||
|---|---|---|
Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic, the proposed reasoning algorithms are neither correct nor complete and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. In this work, we show that knowledge base satisfiability is also an undecidable problem for Lukasiewicz Logic. We additionally provide a decision algorithm for acyclic ALC knowledge bases under Lukasiewicz Logic via a Mixed Integer Linear Programming (MILP) based procedure (note, however, that the decidability of this problem is already known). While similar MILP based algorithms have been proposed in the literature for acyclic ALC knowledge bases under Lukasiewicz Logic, none of them exhibit formal proofs of their correctness and completeness, which is the additional contribution here. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.ins.2012.11.019 | Inf. Sci. |
Keywords | Field | DocType |
fuzzy description logics,similar milp,acyclic alc knowledge base,fuzzy description logic,undecidable problem,general concept inclusions,dl alc,lukasiewicz logic,proposed reasoning algorithm,knowledge base satisfiability,product logic,ukasiewicz t-norm,fuzzy logic | T-norm fuzzy logics,Discrete mathematics,Łukasiewicz logic,Autoepistemic logic,Substructural logic,Many-valued logic,Predicate logic,Intermediate logic,Higher-order logic,Mathematics | Journal |
Volume | ISSN | Citations |
227, | 0020-0255 | 39 |
PageRank | References | Authors |
1.04 | 34 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marco Cerami | 1 | 110 | 7.98 |
| Umberto Straccia | 2 | 2731 | 251.15 |