A Description Logic for Vague Knowledge

This work introduces the concept language ALCFM which is an extension of ALC to many-valued logics. ALCFM allows to express vague concepts, e.g. more or less enlarged or very small. To realize this extension to many-valued logics, the classical notions of satisfiability and subsumption had to be modied appropriately. For example, ALCFM-concepts are no longer either satisfiable or unsatisfiable, but they are satisfiable to a certain degree. The main contribution of this paper is a sound and complete method for computing the degree of subsumption between two ALCFM-concepts.An abridged version of this paper has been published in the Proceedings of the 13th biennial European Conference on Artificial Intelligence (ECAI'98)

Consistency 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, we provide upper complexity bounds that match the complexity of crisp reasoning

Ranking Services Using Fuzzy HEX Programs

Abstract. The need to reason with knowledge expressed in both Logic Program-ming (LP) and Description Logics (DLs) paradigms on the Semantic Web lead to several integrating formalisms, e.g., Description Logic programs (dl-programs) allow a logic program to retrieve results from and feed results to a DL knowledge base. Two functional extensions of dl-programs are HEX programs and fuzzy dl-programs. The former abstract away from DLs, allowing for general exter-nal queries, the latter deal with the uncertain, vague, and inconsistent nature of knowledge on the Web by means of fuzzy logic mechanisms. In this paper, we generalize both HEX programs and fuzzy dl-programs to fuzzy HEX programs: a LP-based paradigm, supporting both fuzziness as well as reasoning with exter-nal sources. We define basic syntax and semantics and analyze the framework semantically, e.g., by investigating the complexity. Additionally, we provide a translation from fuzzy HEX programs to HEX programs, enabling an implementa-tion via the dlvhex reasoner. Finally, we illustrate the use of fuzzy HEX programs for ranking services by using them to model non-functional properties of services and user preferences.

Towards integrating fuzzy logic capabilities into an ontology-based Inductive Logic Programming framework

Abstract—Ontologies based on Description Logics (DLs) have proved to be useful in formally sharing knowledge across applications. Recently, several tools have extended ontologies with fuzzy logic capabilities in order to apply ontology-based reasoning to vague and imprecise domains. This paper first analyses the state of the art in tools for fuzzy ontologies man-agement and then describes how some of the most significant ones have been integrated in order to extend an ontology-based Inductive Logic Programming (ILP) system with fuzzy logic capabilities. A fuzzy version of a well-known ILP test case has been developed in order to validate the approach. This research represents a first step towards fuzzy inductive reasoning for OWL ontologies. Keywords-ontologies; fuzzy logic; inductive learning pro-gramming I