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

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.

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.

Enabling applications that exploit heterogeneous data in the Semantic Web will require us to harness a broad variety of semantics. Considering the role of semantics in a number of research areas in computer science, we organize semantics in three forms: implicit, formal and powerful, and explore their roles in enabling some of the key capabilities related to the Semantic Web. The central message of this paper is that building the Semantic Web purely on description logics will artificially limit it potential, and that we will need to both exploit well known techniques that support implicit semantics, and

Fuzzy Description Logics are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by uncertainty and vagueness. They were born to overcome the limitations of classical Description Logics when dealing with such kind of knowledge, but they bring out some new challenges, requiring an appropriate fuzzy language to be agreed and needing practical and highly optimized implementations of the reasoning algorithms. In the current paper we face these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of SHOIN, which makes possible to reuse a crisp representation language as well as currently available reasoners, which have demonstrated a very good performance in practice. As an additional contribution, we define the syntax and semantics of a novel fuzzy version of the nominal construct and allow to reason within fuzzy general concept inclusions.

Vagueness and imprecision abound in multimedia information processing and retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to fuzzy description logic programs under the answer set semantics. We generalize normal description logic programs (dl-programs) under the answer set semantics by fuzzy vagueness and imprecision. We define a canonical semantics of positive and stratified fuzzy dl-programs in terms of a unique least model and iterative least models, respectively. We then define the answer set semantics of general fuzzy dlprograms, and show in particular that all answer sets of a fuzzy dl-program are minimal models, and that the answer set semantics of positive and stratified fuzzy dl-programs coincides with their canonical least model and iterative least model semantics, respectively. Furthermore, we also provide a characterization of the canonical semantics of positive and stratified fuzzy dl-programs in terms of a fixpoint and an iterative fixpoint semantics, respectively. 1.

. Knowledge representation, in particular logic, combined together with database and information retrieval techniques may play an important role in the development of so-called intelligent multimedia retrieval systems. In this paper we will present a logic-based framework in which multimedia objects' medium dependent properties (objects' low level features) and multimedia objects' medium independent properties (abstract objects' features, or objects' semantics) are addressed in a principled way. The framework is logic-based as it relies on the use of a four-valued fuzzy Description Logics for (i) representing the semantics of multimedia objects and (ii) for defining the retrieval process in terms of logical entailment. Low level features are not represented explicitly within the logic, but may be addressed by means of procedural attachments over a concrete domain. Description Logics are object-oriented representation formalisms capturing the most popular features of structured represen...

. Digital libraries offer a vast source of very different information. To enable users to fruitfully browse through a collection of documents without necessarily having to state a complex query, advanced retrieval techniques have to be developed. Those methods have to be able to structure information in a semantic manner. This work presents some first steps in semantically organizing thematically pre-selected documents of a digital library. The semantic structure of the document collection will be expressively visualized by the proposed system. We illustrate our ideas using a database of medical abstracts from the field of oncology as a walking example. 1