DR-Prolog:A System for Reasoning with Rules and Ontologies on the Semantic Web Grigoris Antoniou and Antonis Bikakis Computer Science Department, University of Crete, Greece Institute of Computer Science, FORTH, Greece {antoniou,bikakis}@ics.forth.gr Abstract Efficient reasoning support exists to support rule lan- Defeasible reasoning is a rule-based approach for guages. efficient reasoning with incomplete and inconsis- Rules are well known in practice, and are reasonably tent information. Such reasoning is, among others, well integrated in mainstream information technology. useful for ontology integration, where conflicting information arises naturally; and for the modeling Possible interactions between description logics and monotonic rule systems were studied in [Grosof et al., of business rules and policies, where rules with ex- 2003]. Based on that work and on previous work on hybrid ceptions are often used. This paper describes these scenarios in more detail, and reports on the imple- reasoning [Levy and Rousset, 1998] it appears that the best one can do at present is to take the intersection of the ex- mentation of a system for defeasible reasoning on pressive power of Horn logic and description logics; one the Web. The system (a) is syntactically compati- ble with RuleML; (b) features strict and defeasible way to view this intersection is the Horn-definable subset of OWL. rules, priorities and two kinds of negation; (c) is This paper is devoted to a different problem, namely con- based on a translation to logic programming with flicts among rules declarative semantics; (d) is flexible and adaptable . Here we just mention the main sources of such conflicts, which are further expanded in section 2. to different intuitions within defeasible reasoning; At the ontology layer: and (e) can reason with rules, RDF, RDF Schema and (parts of) OWL ontologies. Default inheritance within ontologies Ontology merging 1 Introduction And at the logic and reasoning layers: The development of the Semantic Web [Berners Lee et al., Rules with exceptions as a natural representation of 2001] proceeds in layers, each layer being on top of other business rules layers. At present, the highest layer that has reached suffi- Reasoning with incomplete information cient maturity is the ontology layer in the form of the de- scription logic based languages of DAML+OIL [Connolly Defeasible reasoning is a simple rule-based approach to et al., 2001] and OWL [Dean and Schreiber, 2004]. reasoning with incomplete and inconsistent information. It The next step in the development of the Semantic Web can represent facts, rules, and priorities among rules. This will be the logic and proof layers that will offer enhanced reasoning family comprises defeasible logics [Nute, 1994; representation and reasoning capabilities. Rule systems ap- Antoniou et al., 2001] and Courteous Logic Programs [Gro- pear to lie in the mainstream of such activities. Moreover, sof 1999]. The main advantage of this approach is the com- rule systems can also be utilized in ontology languages. So, bination of two desirable features: enhanced representa- in general rule systems can play a twofold role in the Se- tional capabilities allowing one to reason with incomplete mantic Web initiative: (a) they can serve as extensions of, or and contradictory information, coupled with low computa- alternatives to, description logic based ontology languages; tional complexity compared to mainstream nonmonotonic and (b) they can be used to develop declarative systems on reasoning. top (using) ontologies. Reasons why rule systems are ex- In this paper we report on the implementation of a defea- pected to play a key role in the further development of the sible reasoning system for reasoning on the Web. Its main Semantic Web include the following: characteristics are the following: Seen as subsets of predicate logic, monotonic rule sys- Its user interface is compatible with RuleML tems (Horn logic) and description logics are orthogo- [RuleML], the main standardization effort for rules on nal; thus they provide additional expressive power to the Semantic Web. ontology languages. It is based on Prolog. The core of the system consists senting its technical details, we motivate the use of non- of a well-studied translation [Antoniou et. al., 2001] of monotonic rules in more detail. defeasible knowledge into logic programs under Well- Reasoning with Incomplete Information: Antoniou and Founded Semantics [van Gelder et al., 1991]. This de- Arief [2002] describe a scenario where business rules have clarative translation distinguishes our work from other to deal with incomplete information: in the absence of cer- tain information some assumptions have to be made which implementations [Grosof et al., 2002; Maher et al., lead to conclusions not supported by classical predicate 2001]. logic. In many applications on the Web such assumptions The main focus is on flexibility. Strict and defeasible must be made because other players may not be able (e.g. rules and priorities are part of the interface and the im- due to communication problems) or willing (e.g. because of plementation. Also, a number of variants were imple- privacy or security concerns) to provide information. This is mented (ambiguity blocking, ambiguity propagating, the classical case for the use of nonmonotonic knowledge conflicting literals; see below for further details). representation and reasoning [Marek and Truszczynski, 1993]. The system can reason with rules and ontological Rules with Exceptions: Rules with exceptions are a natu- knowledge written in RDF Schema (RDFS) or OWL. ral representation for policies and business rules [Antoniou The latter happens through the transformation of the et. al, 1999]. And priority information is often implicitly or RDFS constructs and many OWL constructs into rules. explicitly available to resolve conflicts among rules. Poten- Note, however, that a number of OWL constructs can- tial applications include security policies [Ashri et al., 2004; not be captured by the expressive power of rule lan- Li et al., 2003], business rules [Antoniou and Arief 2002], guages. personalization, brokering, bargaining, and automated agent negotiations [Governatori et al., 2001]. As a result of the above, DR-Prolog is a powerful de- Default Inheritance in Ontologies: Default inheritance is clarative system supporting a well-known feature of certain knowledge representation rules, facts and ontologies formalisms. Thus it may play a role in ontology languages, all major Semantic Web standards: RDF, RDFS, which currently do not support this feature. Grosof and OWL, RuleML Poon [2003] present some ideas for possible uses of default inheritance in ontologies. A natural way of representing monotonic and nonmonotonic rules, open and closed default inheritance is rules with exceptions, plus priority world assumption, reasoning with inconsistencies. information. Thus, nonmonotonic rule systems can be util- The paper is organized as follows. Section 2 describes the ized in ontology languages. main motivations for conflicting rules on the Semantic Web. Ontology Merging: When ontologies from different au- Section 3 describes the basic ideas of defeasible reasoning. thors and/or sources are merged, contradictions arise natu- Sections 4 describes the translation of defeasible logic, and rally. Predicate logic based formalisms, including all current of RDF, RDFS and (parts of) OWL into logic programs. Semantic Web languages, cannot cope with inconsistencies. Section 5 reports on the implemented system. Section 6 dis- If rule-based ontology languages are used and if rules are cusses related work, and section 7 concludes with a sum- interpreted as defeasible (that is, they may be prevented mary and some ideas for future work. from being applied even if they can fire) then we arrive at nonmonotonic rule systems. A skeptical approach, as adopted by defeasible reasoning, is sensible because it does 2 Motivation for Nonmonotonic Rules on the not allow for contradictory conclusions to be drawn. More- Semantic Web over, priorities may be used to resolve some conflicts We believe that we have to distinguish between two types of among rules, based on knowledge about the reliability of knowledge on the Semantic Web. One is static knowledge, sources or on user input. Thus, nonmonotonic rule systems such as factual and ontological knowledge which contains can support ontology integration. general truths that do not change often. And the other is dynamic knowledge, such as business rules, security poli- 3 Defeasible Logics cies etc. that change often according to business and strate- gic needs. The first type of knowledge requires monotonic 3.1 Basic Characteristics reasoning based on an open world assumption to guarantee correct propagation of truths. But for dynamic knowledge The root of defeasible logics lies on research in knowledge flexible, context-dependent and inconsistency tolerant non- representation, and in particular on inheritance networks. monotonic reasoning is more appropriate for drawing prac- Defeasible logics can be seen as inheritance networks ex- tical conclusions. pressed in a logical rules language. In fact, they are the first Obviously, a combination of both types of knowledge is nonmonotonic reasoning approach designed from its begin- required for practical systems. Defeasible logic, as described ning to be implementable. in section 3, supports both kinds of knowledge. Before pre- Being nonmonotonic, defeasible logics