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 Łukasiewicz 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 Łukasiewicz Logic. We additionally provide a decision algorithm for acyclic ALC knowledge bases under Łukasiewicz 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 Łukasiewicz Logic, none of them exhibit formal proofs of their correctness and completeness, which is the additional contribution here.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
