Giorgos B. Stamou

Reasoning with very expressive fuzzy description logics

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.

Optimized query rewriting for OWL 2 QL

The OWL 2 QL profile has been designed to facilitate query answering via query rewriting. This paper presents an optimized query rewriting algorithm which takes advantage of the special characteristics of the query rewriting problem via first-order resolution in OWL 2 QL and computes efficiently the rewriting set of a user query, by avoiding blind and unnecessary inferences, as well as by reducing the need for extended subsumption checks. The evaluation shows that in several cases the algorithm achieves a significant improvement and better practical scalability if compared to other similar approaches.

Fuzzy extensions of OWL: Logical properties and reduction to fuzzy description logics

The Semantic Web is an extension of the current web, where information would have precisely defined meaning, based on knowledge representation languages. The current W3C standard for representing knowledge is the Web Ontology Language (OWL). OWL is based on Description Logics which is a popular knowledge representation formalism. Although, DLs are quire expressive they feature limitations with respect to what can be said about vague knowledge, which appears in several applications. Consequently, fuzzy extensions to OWL and DLs have gained considerable attention. In the current paper we study fuzzy extensions of the Semantic Web language OWL. First, we present the (abstract) syntax and semantics of a rather elementary fuzzy extension of OWL creating fuzzy OWL (f-OWL). More importantly we use this extension to provide an investigation on the semantics of several f-OWL axioms and more precisely for those which, in classical DLs, can be expressed in different but equivalent ways. Moreover, we present a translation method which reduces inference problems of f-OWL into inference problems of expressive fuzzy Description Logics, in order to provide reasoning support through fuzzy DLs. Finally, we present two further fuzzy extensions of OWL based on fuzzy subsumption and fuzzy nominals.

Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max–min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm that is not Archimedean is the “minimum”.

Context-sensitive semantic query expansion

Modern information retrieval systems match the terms included in a users query with available documents, through the use of an index. A fuzzy thesaurus is used to enrich the query with associated terms. In this work, we use semantic entities, rather than terms; this allows us to use knowledge stored in a semantic encyclopedia, specifically the ordering relations, in order to perform a semantic expansion of the query. The process of query expansion takes into account the query context, which is defined as a fuzzy set of semantic entities. Furthermore, we integrate our approach with the users profile.

Scalable querying services over fuzzy ontologies

Fuzzy ontologies are envisioned to be useful in the Semantic Web. Existing fuzzy ontology reasoners are not scalable enough to handle the scale of data that the Web provides. In this paper, we propose a framework of fuzzy query languages for fuzzy ontologies, and present query answering algorithms for these query languages over fuzzy DL-Lite ontologies. Moreover, this paper reports on implementation of our approach in the fuzzy DL-Lite query engine in the ONTOSEARCH2 system and preliminary, but encouraging, benchmarking results. To the best of our knowledge, this is the first ever scalable query engine for fuzzy ontologies.

Query Extensions and Incremental Query Rewriting for OWL 2 QL Ontologies

Query rewriting over lightweight ontologies, like DL-Lite ontologies, is a prominent approach for ontology-based data access. It is often the case in realistic scenarios that users ask an initial query which they later refine, e.g., by extending it with new constraints making their initial request more precise. So far, all DL-Lite systems would need to process the new query from scratch. In this paper, we study the problem of computing the rewriting of an extended query by ‘extending’ a previously computed rewriting of the initial query and avoiding recomputation. Interestingly, our approach also implies a novel algorithm for computing the rewriting of a fixed query. More precisely, the query can be ‘decomposed’ into its atoms and then each atom can be processed incrementally. We present detailed algorithms, several optimisations for improving the performance of our query rewriting algorithm, and finally, an experimental evaluation.

Semantic association of multimedia document descriptions through fuzzy relational algebra and fuzzy reasoning

According to the emerging MPEG-7 standard, the semantic description of multimedia documents is expressed in terms of semantic entities such as objects, events, concepts, and relations among them. The semantic entities can be used as index terms, in order to support the semantic search process. In this paper, we propose a method that a) applies fuzzy relational operations (closure, composition) and fuzzy rules to expand a semantic encyclopedia and b) uses the encyclopedia to associate the semantic entities with the aid of a fuzzy thesaurus. This method is shown to reduce the need for human intervention in creating semantic descriptions of multimedia documents, as well as correct for incompleteness and inconsistency.

Optimising resolution-based rewriting algorithms for OWL ontologies

An important approach to query answering over OWL ontologies is via rewriting the input ontology (and query) into a new set of axioms that are expressed in logics for which scalable query answering algorithms exist. This approach has been studied for many important fragments of OWL like SHIQ SHIQ , Horn- SHIQ SHIQ , OWL 2 QL, and OWL 2 EL. An important family of rewriting algorithms is the family of resolution-based algorithms, mostly because of their ability to adapt to any ontology language (such algorithms have been proposed for all aforementioned logics) and the long years of research in resolution theorem-proving. However, this generality comes with performance prices and many approaches that implement algorithms that are tailor-made to a specific language are more efficient than the (usually) general-purposed resolution-based ones. In the current paper we revisit and refine the resolution approaches in order to design efficient rewriting algorithms for many important fragments of OWL. First, we present an algorithm for the language DL-Lite R,⊓ R,⊓ which is strongly related to OWL 2 QL. Our calculus is optimised in such a way that it avoids performing many unnecessary inferences, one of the main problems of typical resolution algorithms. Subsequently, we extend the algorithm to the language ELHI ELHI which is strongly related to OWL 2 EL. This is a difficult task as ELHI ELHI is a relatively expressive language, however, we show that the calculus for DL-Lite R,⊓ R,⊓ requires small extensions. Finally, we have implemented all algorithms and have conducted an extensive experimental evaluation using many well-known large and complex OWL ontologies. On the one hand, this is the first evaluation of rewriting algorithms of this magnitude, while, on the other hand, our results show that our system is in many cases several orders of magnitude faster than the existing systems even though it uses an additional backwards subsumption checking step.

Fuzzy relation equations and fuzzy inference systems: an inside approach

This paper investigates and extends the use of fuzzy relation equations for the representation and study of fuzzy inference systems. Using the generalized sup-t (t is a triangular norm) composition of fuzzy relations and the study of sup-t fuzzy relation equations, interesting results are provided concerning the completeness and the theoretical soundness of the representation, as well as the ability to mathematically formulate and satisfy application-oriented design demands. Furthermore, giving a formal study of fuzzy partitions and some useful aspects of fuzzy associations and fuzzy systems, the paper can be used as a theoretical background for designing consistent fuzzy inference systems.