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ABSTRACT: Open answer set programming (OASP) solves the lack of modularity in closed world answer set programming by allowing for the grounding of logic programs with an arbitrary non-empty countable superset of the program’s constants. However, OASP is, in general, undecidable: the undecidable domino problem can be reduced to it. In order to regain decidability, we restrict the shape of logic programs, yielding conceptual logic programs (CoLPs). CoLPs are logic programs with unary and binary predicates (possibly inverted) where rules have a tree shape. Decidability of satisfiability checking of predicates w.r.t. CoLPs is shown by a reduction to non-emptiness checking of two-way alternating tree automata. We illustrate the expressiveness of CoLPs by simulating the description logic SHIQ\mathcal{SHIQ}. CoLPs thus integrate, in one unifying framework, the best of both the logic programming paradigm (a flexible rule-based representation and nonmonotonicity by means of negation as failure) and the description logics paradigm (decidable open domain reasoning).
Annals of Mathematics and Artificial Intelligence 04/2012; 47(1):103-137. · 0.36 Impact Factor
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ABSTRACT: Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules.
10/2011;
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ABSTRACT: Open Answer Set Programming (OASP) is an attractive framework for integrating ontologies and rules. In general OASP is undecidable. In previous work we provided a tableau-based algorithm for satisfiability checking w.r.t. forest logic programs, a decidable fragment of OASP, which has the forest model property. In this paper we introduce an optimized version of that algorithm achieved by means of a knowledge compilation technique. So-called unit completion structures, which are possible building blocks of a forest model, in the form of trees of depth 1, are computed in an initial step of the algorithm. Repeated computations are avoided by using these structures in a pattern-matching style when constructing a model. Furthermore we identify and discard redundant unit completion structures: a structure is redundant if there is another structure which can always replace the original structure in a forest model. Comment: ASPOCP 2010
11/2010;
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J. Artif. Intell. Res. (JAIR). 01/2010; 38:535-568.
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[show abstract]
[hide abstract]
ABSTRACT: Open Answer Set Programming (OASP) is an attractive framework for integrating ontologies and rules. Although several decidable
fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating
algorithm for satisfiability checking w.r.t. forest logic programs, a fragment where rules have a tree shape and allow for
inequality atoms and constants. We further introduce f-hybrid knowledge bases, a hybrid framework where SHOQ\mathcal SHOQ knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to
reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety
of the rule component, providing thus a genuine alternative approach to hybrid reasoning.
05/2009: pages 338-352;
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The Semantic Web: Research and Applications, 6th European Semantic Web Conference, ESWC 2009, Heraklion, Crete, Greece, May 31-June 4, 2009, Proceedings; 01/2009
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Logical Foundations of Computer Science, International Symposium, LFCS 2009, Deerfield Beach, FL, USA, January 3-6, 2009. Proceedings; 01/2009
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Logic Programming and Nonmonotonic Reasoning, 10th International Conference, LPNMR 2009, Potsdam, Germany, September 14-18, 2009. Proceedings; 01/2009
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Web Reasoning and Rule Systems, Third International Conference, RR 2009, Chantilly, VA, USA, October 25-26, 2009, Proceedings; 01/2009
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Proceedings of the Fourth International Workshop on Uncertainty Reasoning for the Semantic Web, Karlsruhe, Germany, October 26, 2008; 01/2008
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Proceedings of the 21st International Workshop on Description Logics (DL2008), Dresden, Germany, May 13-16, 2008; 01/2008
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Fundam. Inform. 01/2008; 82:213-236.
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Logic Programming, 24th International Conference, ICLP 2008, Udine, Italy, December 9-13 2008, Proceedings; 01/2008
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ABSTRACT: Recently, there has been a lot of interest in the integration of Description Logics and rules on the Semantic Web.We define guarded hybrid knowledge bases (or g-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and a guarded logic program, similar to the DL+log knowledge bases from (Rosati 2006). G-hybrid knowledge bases enable an integration of Description Logics and Logic Programming where, unlike in other approaches, variables in the rules of a guarded program do not need to appear in positive non-DL atoms of the body, i.e. DL atoms can act as guards as well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL DLRO, which is close to OWL DL, by a reduction to guarded programs under the open answer set semantics. Moreover, we show 2-EXPTIME-completeness for satisfiability checking of such g-hybrid knowledge bases. Finally, we discuss advantages and disadvantages of our approach compared with DL+log knowledge bases.
12/2007;
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Web Reasoning and Rule Systems, First International Conference, RR 2007, Innsbruck , Austria, June 7-8, 2007, Proceedings; 01/2007
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The Semantic Web, 6th International Semantic Web Conference, 2nd Asian Semantic Web Conference, ISWC 2007 + ASWC 2007, Busan, Korea, November 11-15, 2007.; 01/2007
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The Semantic Web: Research and Applications, 4th European Semantic Web Conference, ESWC 2007, Innsbruck, Austria, June 3-7, 2007, Proceedings; 01/2007
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ABSTRACT: Many popular ontology languages are based on (subsets of) first-order predicate logic, where classes are modeled as unary predicates and properties as binary predicates. Specifically, the ontology language OWL DL is based on the Description Logic SHOIQ. F-Logic is an ontology language which is also based on first-order logic, but classes and properties are modeled as terms, rather than predicates. In this paper we define a translation from predicate-based ontologies to F-Logic ontologies and show that this translation preserves entailments for large classes of ontologies, including most of OWL DL. We define the class of equality-safe (epsiv-safe) formulas, show that the Description Logic SHIQ is epsiv-safe, and show that the translation preserves validity of epsiv-safe formulas. Finally, we use these results to close the open problems of layering F-Logic programming on top of Description Logic Programs and language layering in WSML
Rules and Rule Markup Languages for the Semantic Web, Second International Conference on; 12/2006
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ABSTRACT: Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (mu(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling for the first time, a characterization of an answer set semantics by muLGF formulas. We further extend the open answer set semantics for programs with generalized literals. Such generalized programs (gPs) have interesting properties, e.g., the ability to express infinity axioms. We restrict the syntax of gPs such that both rules and generalized literals are guarded. Via a translation to guarded fixed point logic, we deduce 2-exptime-completeness of satisfiability checking in such guarded gPs (GgPs). Bound GgPs are restricted GgPs with exptime-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog lite programs to GgPs, establishing equivalence of GgPs under an open answer set semantics, alternation-free muGF, and Datalog lite.
04/2006;
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Foundations of Information and Knowledge Systems, 4th International Symposium, FoIKS 2006, Budapest, Hungary, February 14-17, 2006, Proceedings; 01/2006
