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A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases

A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases,10.3233/978-1-58603-891-5-99,Matthias Knorr,José Júlio Alferes,Pascal Hitzler

A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases   (Citations: 21)
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With the advent of the Semantic Web, the question be- comes important how to best combine open-world based ontology languages, like OWL, with closed-world rules paradigms. One of the most mature proposals for this combination is known as Hybrid MKNF knowledge bases (11), which is based on an adaptation of the stable model semantics to knowledge bases consisting of ontology axioms and rules. In this paper, we propose a well-founded semantics for such knowledge bases which promises to provide better efficiency of reasoning, which is compatible both with the OWL-based seman- tics and the traditional well-founded semantics for logic programs, and which surpasses previous proposals for such a well-founded se- mantics by avoiding some issues related to inconsistency handling.
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    • ...6A short version of this paper appeared in [29]...
    • ...9In comparison to [29] the denition has been slightly altered to simplify proofs and computation: in case of a total interpretation pair (M;M) it is sucient to check that no other total interpretation pair (M0;M0) actually yields a true evaluation for all I0 2 M0. This simplica-...

    Matthias Knorret al. Local closed world reasoning with description logics under the well-fo...

    • ...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 Caoet al. WORL: A Web Ontology Rule Language

    • ...Knorr et al. [2008] have recently proposed an extension of MKNF knowledge bases to the well-founded semantics [van Gelder et al. 1991]...

    Boris Motiket al. Reconciling description logics and rules

    • ...edge bases (MKNFWFS), introduced in [7] and overviewed in Section 2 below, is the only one which allows knowledge about instances to be fully inter-definable between rules and an ontology that is taken as a parameter of the formalism...
    • ...The well-founded MKNF semantics as presented in [7] is based on a complete threevalued extension of the original MKNF semantics...
    • ...However, here, as we are only interested in querying for literals and conjunctions of literals, we limit ourselves to the computation of what is called the well-founded partition in [7]: basically the atoms which are true and false...
    • ...At first, we recall some notions from [7] which will be useful in the definition of the operators for obtaining that wellfounded model...
    • ...We continue now by recalling the definition in [7] of an operator TK which allows conclusions to be drawn from positive hybrid MKNF knowledge bases...
    • ...The operator TK is shown to be monotonic in [7] so, by the Knaster-Tarski theorem, it has a unique least fixpoint, denoted lfp(TK), which is reached after a finite number of iteration steps...
    • ...Both operators are shown to be antitonic [7], hence their composition is monotonic and form the basis for defining the well-founded MKNF model...
    • ...Note that by finiteness of the ground knowledge base the iteration stops before reaching ω. It was shown in [7] that the sequences are monotonically increasing, decreasing respectively, and that Tω and TUω form the well-founded model:...
    • ...As shown in [7], the well founded model is sound with respect to the original semantics of [10], i.e...
    • ...In fact, the relation between the semantics of [7] and [10], is tantamount to that of the well founded semantics and the answer-sets semantics of logic programs...
    • ...The algorithm shown in Figure 1 creates two different sets corresponding to the application of the operator Γ of the MKNFWFS [7]...
    • ...The system answers queries according to MKNFWFS [7] and, as such, is also sound w.r.t...
    • ...The definition of MKNFWFS is parametric on a decidable description logic (in which the ontology is written), and it is worth noting that, as shown in [7], the complexity of reasoning in MKNFWFS is in the same class as that in the decidable description logic; a complexity result that is extended to a query-driven approach in [1]...
    • ...For a survey on these proposals, see [6], and [10,7] for comparisons to MKNF...

    Ana Sofia Gomeset al. Implementing Query Answering for Hybrid MKNF Knowledge Bases

    • ...Recently, also hybrid rule combinations based on the well-founded semantics have been proposed by Drabent et al. [7 ]o r Knorr et al. [18], defining an analogous, modular...

    Jos de Bruijnet al. A semantical framework for hybrid knowledge bases

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