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Well-founded semantics for description logic programs in the semantic web

Well-founded semantics for description logic programs in the semantic web,10.1145/1877714.1877717,ACM Transactions on Computational Logic,Thomas Eiter

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Well-founded semantics for description logic programs in the semantic web   (Citations: 4)
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The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic knowledge base is polynomial; under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.
Journal: ACM Transactions on Computational Logic - TOCL , vol. 12, no. 2, pp. 1-41, 2011
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    • ...Interaction between O and P is either one-way (O affects P) or two-way (where P may also affect O). The approach of defining a knowledge base as a pair �O , P� is adopted in a considerable number of works: [7] (on AL-log), [17] (on CARIN), [19] (on DL-safe rules), [28] (on DL+log), [18], [16] (on hybrid MKNF), [8] (on hybrid programs), [11] (on dl-programs)...
    • ...This differs from all the above mentioned works [7], [17], [19], [28], [18], [16], [8], [11]...

    Son Thanh Cao, et al. WORL: A Web Ontology Rule Language

    • ...There also exists a variant of dl-programs for (non-disjunctive) rules with WFS [28]...

    Wlodzimierz Drabent. Hybrid Reasoning with Non-monotonic Rules

    • ...Another such formalism is dlprograms [14,16,17,18,21], which again combines description logic ontologies with extended logic programs (i.e., programs using both ¬ and not, the latter being default negation)...
    • ...In [16], well-founded semantics for dl-programs are defined...

    Adila Krisnadhi, et al. OWL and Rules

    • ...For dl-programs over LDL + ontologies, it computes the well-founded model [3]...

    Guohui Xiao, et al. Inline Evaluation of Hybrid Knowledge Bases

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