Uncertainty and Rule Extensions to Description Logics and Semantic Web Ontologies


The The Semantic Web is an evolving extension of the World Wide Web in which the semantics of the information and resources available on the Web are formally described, making it more machine-interpretable. In the layered architecture of the Semantic Web, the Web ontology language (OWL), built upon the logic-based knowledge formalism Description Logics (DLs), is a W3C recommendation for the ontology layer; the Rule Interchange Format (RIF), built upon the formalism Logic Programs (LP), is a W3C recommendation for the rule layer. Uncertainty is an intrinsic feature of real-world knowledge and refers to a form of de_ciency or imperfection in the information: the truth of such information is not crisply established, yet can be rigorously formalized. In the last decade, one of the key research directions in the Semantic Web community has been to handle uncertainty, as evidenced by W3Cs Uncertainty Reasoning for the World Wide Web Incubator Group. At the same time, in order to enrich the knowledge representation capabilities of ontologies based on traditional DLs, considerable research e_orts have also been directed towards the integration of ontologies and rules. In this chapter, we _rst give a comprehensive overview of existing approaches in uncertainty extensions to DLs and OWL based on various uncertainty treatments, mainly including Fuzzy Logic and Probability Theory. We summarize and classify previous work based on (a) the generalized classical description logics, (b) the supported forms and allowed constructors of uncertain knowledge, (c) the underlying fuzzy logics or probabilistic semantics, and (d) their inference problems and reasoning algorithms. Second, we summarize the differences between the two subsets of _rst-order logic formalism, Description Logics and Horn Logic. On top of this, we then review a number of theoretical proposals for integrating ontologies with rules, as well as some practical implementations. By and large, existing approaches for rule extensions to DLs and ontologies can be classi_ed into two categories: the so-called homogeneous approach and the so-called hybrid approach. We explain several existing work as representatives of the homogenous approach, as well as some work following the hybrid approach. 1 DESCRIPTION LOGICS WITH UNCERTAINTY The famous British author, mathematician, and philosopher, Bertrand Russell, once said, “Everything is vague to a degree you do not realize till you have tried to make it precise.” Uncertainty, which refers to a form of deficiency or imperfection in the information for which the truth is not established definitely [Lakshmanan and Shiri, 2001)], is an intrinsic feature of real-world knowledge. Faculty of Computer Science, University of New Brunswick, Fredericton, Canada E-mail: Judy.Zhao AT unb.ca 2 Advances in Semantic Computing As shown in (Bacchus, 1990; Lakshmanan and Shiri, 2001; Motro and Smets, 1997; Parsons, 1996), many real-world applications need the capability to handle uncertainty and the modeling of uncertainty and reasoning with it have been challenging issues for over two decades in databases, operations research, and artificial intelligence. Handling uncertain knowledge is inevitably also a challenge for the Semantic Web and Description Logic community. The need to model and reason with uncertainty has been found in many different Semantic Web contexts, such as matchmaking in Web services (Martin-Recuerda and Robertson, 2005), classification of genes in bioinformatics (Stevens et al., 2007), multimedia annotation (Stamou et al., 2006), and ontology learning (Haase and Völker, 2005). Triggered by such necessities in numerous Web-based applications, W3C founded the Uncertainty Reasoning for the World Wide Web (URW3) Incubator Group (Laskey et al., 2008), which addressed challenges and defined methodologies of reasoning with, and representing uncertain information available through, the World Wide Web and the Semantic Web. According to the latest URW3 draft report, uncertainty is a term intended to include different forms of incomplete knowledge, such as inconclusiveness, vagueness, ambiguity, and others (Laskey et al., 2008). An OWL ontology is actually a knowledge base composed of a finite set of axioms in Description Logics (DLs). Such a knowledge base can be divided into two components, namely the TBox and the ABox (Baader et al., 2003). The TBox consists of concept inclusions (C v D), concept definitions (C ≡ D), role inclusions (R v P ), and role definitions (R ≡ P ), while the ABox consists of concept assertions (C(a)) and role assertions (R(a, b)), where C,D are concepts, R,P are roles, and a, b are individuals. Intuitively, the TBox refers to the schema of the ontology, whereas the ABox to the instances. DLs (Baader et al., 2003) are a family of logic-based knowledge representation formalisms designed to represent and reason about the conceptual knowledge of arbitrary domains. Elementary descriptions of a DL are atomic concepts (also called classes) and atomic roles (also called properties or relations). Complex concept descriptions and role descriptions can be built from the elementary constructors according to construction rules. The basic propositionally closed DL is ALC in which the letters AL stand for attributive language and the letter C for complement (negation of arbitrary concepts). Concepts in ALC are constructed using boolean operators (conjunction, disjunction, negation) plus restricted quantifiers and atomic roles, as shown in table 1. For example, a complex concept description for “the set of persons all of whose children are doctor or have a child who is a doctor” in ALC can be written as: Person u ∀hasChild.(Doctor t ∃hasChild.Doctor) Table 1: A set of concept constructors for a simple description logic Constructor Name Syntax

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@inproceedings{Zhao2009UncertaintyAR, title={Uncertainty and Rule Extensions to Description Logics and Semantic Web Ontologies}, author={Jidi Zhao}, year={2009} }