Since the introduction of the Semantic Web vision (Berners- Lee, Hendler, & Lassila, 2001), attempts have been made for making Web resources more machine interpretable by giving them a well-defined meaning through semantic markups. One way to encode such semantic markups is to use ontologies. An ontology is “an explicit specification of a conceptualization” (Gruber, 1993, p. 199). Informally, an ontology consists of a set of terms in a domain, relationships between the terms, and a set of constraints on the way in which those terms can be combined. By explicitly defining the relationships and constraints among the terms, the semantics of the terms can be better defined and understood. Over the last few years, a number of ontology languages have been developed, most of which use Description Logics (DLs) (Baader, McGuinness, Nardi, & Schneider, 2003) as the foundation. The family of DLs is a subset of first-order logic (FOL) and is considered to be attractive as it keeps a good compromise between expressive power and computational tractability. Uncertainty is a form of deficiency or imperfection in the information/data, where the truth of information is not established definitely. Uncertainty modeling and reasoning have been challenging issues for over two decades in many disciplines, such as database and artificial intelligence. Most of the information in the real world is uncertain or imprecise, for example, classifications of genes in bioinformatics, schema matching in information integration, finding best matches in a Web search, and so forth. Therefore, uncertainty management is essential for the success of many such applications and in particular DLs and the Semantic Web. Despite its popularity, it has been realized that classical DLs are inadequate to model uncertainty. For example, in the medical domain, one might want to express that: “It is very likely that an obese person would have heart disease,” where “obese” is a vague concept that may vary across regions and “likely” shows the uncertain nature of this information. Such an expression cannot be expressed using classical DLs. The importance of incorporating uncertainty in DLs has been recognized by the knowledge representation community: “modeling primitives such as … fuzzy/probabilistic definitions” could be the next step for extension (Horrocks et al., 2000, p. 3). For this, a number of frameworks have been proposed to incorporate uncertainty in DLs. This paper provides a survey of these proposals. The rest of this paper is organized as follows. We first provide the background on the classical DL framework. We then study representative extensions of DLs with uncertainty. This follows by some possible research directions for incorporating uncertainty in the Semantic Web. We conclude with a summary and some remarks.
Unifying Class-Based Representation Formalisms
