nd (universal child.Human 7 . is given in terms of an the domain (a non-empty set) an interpretation function that maps: (class) a (property) a an element of Interpretation extended to concept expressions: = = = = = \ = {x = {x 8 and . mapping to FOL: introduce unary an atomic binary a . Translate follows x) = x) = false t(A, x) ## A(x) x) = x) x) ## x) t(C, x) = t(#R.C, x) = y) t(#R.C, x) = 9 Knowledge . DL Knowledge Base is a A#, a TBox containing general inclusion axioms of the ("concept C"), i# definitions are of the (equiv A) concept definitions are of the Sometimes, a TBox can contain primitive and concept definitions only, where no atom can be defined more than once and no recursion is allowed complexity changes dramatically a ABox containing assertions of the

Ontologies play a central role in the development of the semantic web, as they provide precise definitions of shared terms in web resources. One important web ontology language is DAML+OIL; it has a formal semantics and a reasoning support through a mapping to the expressive description logic SHOQ(D) with the addition of inverse roles. In this paper, we present a probabilistic extension of SHOQ(D), called P-SHOQ(D), to allow for dealing with probabilistic ontologies in the semantic web. The description logic P-SHOQ(D) is based on the notion of probabilistic lexicographic entailment from probabilistic default reasoning. It allows to express rich probabilistic knowledge about concepts and instances, as well as default knowledge about concepts. We also present sound and complete reasoning techniques for P-SHOQ(D), which are based on reductions to classical reasoning in SHOQ(D) and to linear programming, and which show in particular that reasoning in P-SHOQ(D) is decidable.

Abstract. Research on multimedia information retrieval (MIR) has recently witnessed a booming interest. A prominent feature of this research trend is its simultaneous but independent materialization within several fields of computer science. The resulting richness of paradigms, methods and systems may, on the long run, result in a fragmentation of efforts and slow down progress. The primary goal of this study is to promote an integration of methods and techniques for MIR by contributing a conceptual model that encompasses in a unified and coherent perspective the many efforts that are being produced under the label of MIR. The model offers a retrieval capability that spans two media, text and images, but also several dimensions: form, content and structure. In this way, it reconciles similarity-based methods with semantics-based ones, providing the guidelines for the design of systems that are able to provide a generalized multimedia retrieval service, in which the existing forms of retrieval not only coexist, but can be combined in any desired manner. The model is formulated in terms of a fuzzy description logic, which plays a twofold role: (1) it directly models semantics-based retrieval, and (2) it offers an ideal framework for the integration of the multimedia and multidimensional aspects of retrieval mentioned above. The model also accounts for relevance feedback in both text and image retrieval, integrating known techniques for taking into account user judgments. The implementation of

Abstract. In this paper we consider Description Logics (DLs), which are logics for managing structured knowledge, with a well-known fuzzy extension to deal with vague information. While for fuzzy DLs ad-hoc, tableaux-like reasoning procedures have been given in the literature, the topic of this paper is to present a reasoning preserving transformation of fuzzy DLs into classical DLs. This has the considerable practical consequence that reasoning in fuzzy DLs is feasible using already existing DL systems. 1

We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a mixture of completion rules and bounded mixed integer programming.

In the Semantic Web context information would be retrieved, processed, shared, reused and aligned in the maximum automatic way possible. Our experience with such applications in the Semantic Web has shown that these are rarely a matter of true or false but rather procedures that require degrees of relatedness, similarity, or ranking. Apart from the wealth of applications that are inherently imprecise, information itself is many times imprecise or vague. For example, the concepts of a “hot” place, an “expensive” item, a “fast” car, a “near” city, are examples of such concepts. Dealing with such type of information would yield more realistic, intelligent and effective applications. In the current paper we extend the OWL web ontology language, with fuzzy set theory, in order to be able to capture, represent and reason with such type of information.

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. 1.

Abstract. In the Semantic Web information would be retrieved, processed, combined, shared and reused in the maximum automatic way possible. Obviously, such procedures involve a high degree of uncertainty and imprecision. For example ontology alignment or information retrieval are rarely true or false procedures but usually involve confidence degrees or provide rankings. Furthermore, it is often the case that information itself is imprecise and vague like the concept of a “tall ” person, a “hot” place and many more. In order to be able to represent and reason with such type of information in the Semantic Web (SW), as well as, enhance SW applications we present an extension of the Description Logic SHIN with fuzzy set theory. We present the semantics as well as detailed reasoning algorithms for the extended language. 1

Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.

Summary. In this paper we introduce ALCQ + F, a fuzzy description logic with extended qualified quantification. The proposed language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on N and Q ∩ [0, 1] respectively. These quantifiers extends the usual (qualified) ∃, ∀ and number restriction. The semantics of quantified expressions is defined by using method GD [4], that is based on recently developed measures of the cardinality of fuzzy sets. 1