The Semantic Web is well recognized as an effective infrastructure to enhance visibility of knowledge on the Web. The core of the Semantic Web is ontology, which is used to explicitly represent our conceptualizations. Ontology engineering in the Semantic Web is primarily supported by languages such as RDF, RDFS and OWL. This chapter discusses the requirements of ontologies in the context of the Web, compares the above three languages with existing knowledge representation formalisms, and surveys tools for managing and applying ontologies. Advantages of using ontologies in both knowledge-base-style and database-style applications are demonstrated using three real world applications.

It is always essential but difficult to capture incomplete, partial or uncertain knowledge when using ontologies to conceptualize an application domain or to achieve semantic interoperability among heterogeneous systems. This chapter presents an on-going research on developing a framework which augments and supplements the semantic web ontology language OWL 5 for representing and reasoning with uncertainty based on Bayesian networks (BN) [26], and its application in ontology mapping. This framework, named BayesOWL, has gone through several iterations since its conception in 2003 [8,9]. BayesOWL provides a set of rules and procedures for direct translation of an OWL ontology into a BN directed acyclic graph (DAG), it also provides a method based on iterative proportional fitting procedure (IPFP) [19,7,6,34,2,4] that incorporates available probability constraints when constructing the conditional probability tables (CPTs) of the BN. The translated BN, which preserves the semantics of the original ontology and is consistent with all the given probability constraints, can support ontology reasoning, both within and across ontologies as Bayesian inferences. At the present time, BayesOWL is restricted to translating only OWL-DL concept taxonomies into BNs, we are actively working on extending the framework to OWL ontologies with property restrictions.If ontologies are translated to BNs, then concept mapping between ontologies can be accomplished by evidential reasoning across the translated BNs. This approach to ontology mapping is seen to be advantageous to many existing methods in handling uncertainty in the mapping. Our preliminary work on this issue is presented at the end of this chapter.This chapter is organized as follows: Sect. 1 provides a brief introduction to semantic web 6 and discusses uncertainty in semantic web ontologies; Sect. 2 5

Abstract. This paper presents our ongoing effort on developing a principled methodology for automatic ontology mapping based on BayesOWL, a probabilistic framework we developed for modeling uncertainty in semantic web. In this approach, the source and target ontologies are first translated into Bayesian networks (BN); the concept mapping between the two ontologies are treated as evidential reasoning between the two translated BNs. Probabilities needed for constructing conditional probability tables (CPT) during translation and for measuring semantic similarity during mapping are learned using text classification techniques where each concept in an ontology is associated with a set of semantically relevant text documents, which are obtained by ontology guided web mining. The basic ideas of this approach are validated by positive results from computer experiments on two small real-world ontologies.

Abstract

This paper deals with an important probabilistic knowledge integration problem: revising a Bayesian network (BN) to satisfy a set of probability constraints representing new or more specific knowledge. We propose to solve this problem by adopting IPFP (iterative proportional fitting procedure) to BN. The resulting algorithm E-IPFP integrates the constraints by only changing the conditional probability tables (CPT) of the given BN while preserving the network structure; and the probability distribution of the revised BN is as close as possible to that of the original BN. Two variations of E-IPFP are also proposed: 1) E-IPFP-SMOOTH which deals with the situation where the probabilistic constraints are inconsistent with each other or with the network structure of the given BN; and 2) D-IPFP which reduces the computational cost by decomposing a global E-IPFP into a set of smaller local E-IPFP problems.