Giorgos Stoilos

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.

HermiT: An OWL 2 Reasoner

This system description paper introduces the OWL 2 reasoner HermiT. The reasoner is fully compliant with the OWL 2 Direct Semantics as standardised by the World Wide Web Consortium (W3C). HermiT is based on the hypertableau calculus, and it supports a wide range of standard and novel optimisations that improve the performance of reasoning on real-world ontologies. Apart from the standard OWL 2 reasoning task of entailment checking, HermiT supports several specialised reasoning services such as class and property classification, as well as a range of features outside the OWL 2 standard such as DL-safe rules, SPARQL queries, and description graphs. We discuss the system’s architecture, and we present an overview of the techniques used to support the mentioned reasoning tasks. We further compare the performance of reasoning in HermiT with that of FaCT++ and Pellet—two other popular and widely used OWL 2 reasoners.

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.

A novel approach to ontology classification

Ontology classification-the computation of the subsumption hierarchies for classes and properties-is a core reasoning service provided by all OWL reasoners known to us. A popular algorithm for computing the class hierarchy is the so-called Enhanced Traversal (ET) algorithm. In this paper, we present a new classification algorithm that attempts to address certain shortcomings of ET and improve its performance. Apart from classification of classes, we also consider object and data property classification. Using several simple examples, we show that the algorithms commonly used to implement these tasks are incomplete even for relatively weak ontology languages. Furthermore, we show that property classification can be reduced to class classification, which allows us to classify properties using our optimised algorithm. We implemented all our algorithms in the OWL reasoner HermiT. The results of our performance evaluation show significant performance improvements on several well-known ontologies.

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.

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.

Image indexing and retrieval using expressive fuzzy description logics

The effective management and exploitation of multimedia documents requires the extraction of the underlying semantics. Multimedia analysis algorithms can produce fairly rich, though imprecise information about a multimedia document which most of the times remains unexploited. In this paper we propose a methodology for semantic indexing and retrieval of images, based on techniques of image segmentation and classification combined with fuzzy reasoning. In the proposed knowledge-assisted analysis architecture a segmentation algorithm firstly generates a set of over-segmented regions. After that, a region classification process is employed to assign semantic labels using a confidence degree and simultaneously merge regions based on their semantic similarity. This information comprises the assertional component of a fuzzy knowledge base which is used for the refinement of mistakenly classified regions and also for the extraction of rich implicit knowledge used for global image classification. This knowledge about images is stored in a semantic repository permitting image retrieval and ranking.

Completeness guarantees for incomplete ontology reasoners: theory and practice

To achieve scalability of query answering, the developers of Semantic Web applications are often forced to use incomplete OWL 2 reasoners, which fail to derive all answers for at least one query, ontology, and data set. The lack of completeness guarantees, however, may be unacceptable for applications in areas such as health care and defence, where missing answers can adversely affect the applications functionality. Furthermore, even if an application can tolerate some level of incompleteness, it is often advantageous to estimate how many and what kind of answers are being lost. In this paper, we present a novel logic-based framework that allows one to check whether a reasoner is complete for a given query Q and ontology T -- that is, whether the reasoner is guaranteed to compute all answers to Q w.r.t. T and an arbitrary data set A. Since ontologies and typical queries are often fixed at application design time, our approach allows application developers to check whether a reasoner known to be incomplete in general is actually complete for the kinds of input relevant for the application. We also present a technique that, given a query Q, an ontology T, and reasoners R1 and R2 that satisfy certain assumptions, can be used to determine whether, for each data set A, reasoner R1 computes more answers to Q w.r.t. T and A than reasoner R2. This allows application developers to select the reasoner that provides the highest degree of completeness for Q and T that is compatible with the applications scalability requirements. Our results thus provide a theoretical and practical foundation for the design of future ontology-based information systems that maximise scalability while minimising or even eliminating incompleteness of query answers.

Optimising ontology classification

Ontology classification--the computation of subsumption hierarchies for classes and properties--is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification procedure that addresses several open issues of the original algorithm, and that uses several novel optimisations in order to achieve superior performance. We also consider the classification of (object and data) properties. We show that algorithms commonly used to implement that task are incomplete even for relatively weak ontology languages. Furthermore, we show how to reduce the property classification problem into a standard (class) classification problem, which allows reasoners to classify properties using our optimised procedure. We have implemented our algorithms in the OWL HermiT reasoner, and we present the results of a performance evaluation.