Extending Logic Programs with Description Logic Expressions for the Semantic Web

Shen, Yi-Dong; Wang, Kewen

doi:10.1007/978-3-642-25073-6_40

Cited by 9 publications

(10 citation statements)

References 11 publications

(27 reference statements)

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“…We show that the semantics generalizes the wellfounded semantics for normal logic programs. Also, we prove that the well-founded semantics defined here approximates the well-supported answer set semantics for the language of (Shen and Wang 2011); namely, all well-founded atoms (resp. unfounded atoms) of a program remain to be true (resp.…”

Section: Introductionmentioning

confidence: 79%

“…The well-supported answer set semantics is defined for what are called normal DL logic programs (Shen and Wang 2011), which applies to FOL-programs. There is however a subtle difference: in the definition of the entailment relation, the W KB operator uses 3-valued evaluation while the well-supported semantics is based on the notion of 2-valued up to satisfaction.…”

Section: Proofmentioning

confidence: 99%

“…Recent literature has shown extensive interests in combining ASP with fragments of classical logic, such as description logics (DLs) (see, e.g., (de Bruijn et al 2008;de Bruijn et al 2007;Eiter et al 2008;Lukasiewicz 2010;Motik and Rosati 2010;Rosati 2005;Rosati 2006;Shen and Wang 2011;Yang et al 2011)). A program in this context is a combined knowledge base KB = (L, Π), where L is a knowledge base of a decidable fragment of first-order logic and Π a set of rules possibly containing first-order formulas or interface facilities.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Well-Founded Semantics for FOL-Programs

Bi¹,

You²,

Feng³

2014

Preprint

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An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with description logics. In this paper, we define a well-founded semantics for FOL-programs based on a new notion of unfounded sets on consistent as well as inconsistent sets of literals, and study some of its properties. The semantics is defined for all FOL-programs, including those where it is necessary to represent inconsistencies explicitly. The semantics supports a form of combined reasoning by rules under closed world as well as open world assumptions, and it is a generalization of the standard well-founded semantics for normal logic programs. We also show that the well-founded semantics defined here approximates the well-supported answer set semantics for normal DL programs.To appear in Theory and Practice of Logic Programming (TPLP).

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Section: Introductionmentioning

confidence: 79%

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Well-Founded Semantics for FOL-Programs

Bi¹,

You²,

Feng³

2014

Preprint

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“…This method of defining answer sets has further been applied to description logic programs and hex-programs [25,24], tightly coupled dl-programs [46], modular logic programs [12], etc. Since FLP reducts are treated as classical implications instead of rules, such FLP answer sets suffer from possible circular justifications (see Examples 1 and 15; Shen and Wang [55,56] illustrated the circular justification problem with the FLP answer set semantics of Lukasiewicz [46]). …”

Section: Related Workmentioning

confidence: 99%

FLP answer set semantics without circular justifications for general logic programs

Shen

Wang

Eiter

et al. 2014

Artificial Intelligence

Self Cite

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The answer set semantics presented by Faber et al. [27] has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by selfsupporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden-Kowalski operator for the FLP reduct f Π I ). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden-Kowalski one-step provability operator for the Gelfond-Lifschitz reduct Π I , which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, hex-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice.

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“…we just mention that other semantics of HEX-programs may not involve such a step which is intractable in general (as follows from Leone et al, 2006, already for ground Horn programs with nonmonotonic external atoms that are decidable in polynomial time). For instance, Shen (2011) and Shen and Wang (2011) present a well-justified semantics where unfounded set checking is essentially replaced by a fixpoint iteration which, intuitively, tests if a model candidate reproduces itself but excludes circular justifications. However, the complexity of answer set computation does not decrease by this approach in general, and in particular deciding well-justified answer set existence for ground Horn programs with nonmonotonic external atoms that are decidable in polynomial time is Σ p 2 -complete, and thus as hard as deciding the existence of answer sets as in Definition 3.…”

Section: Related Workmentioning

confidence: 99%

Efficient HEX-Program Evaluation Based on Unfounded Sets

Eiter

Fink

Krennwallner

et al. 2014

jair

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HEX-programs extend logic programs under the answer set semantics with external computations through external atoms. As reasoning from ground Horn programs with nonmonotonic external atoms of polynomial complexity is already on the second level of the polynomial hierarchy, minimality checking of answer set candidates needs special attention. To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs. The unfounded set detection is expressed as a propositional SAT problem, for which we provide two different encodings and optimizations to them. We then integrate our approach into a previously developed evaluation framework for HEX-programs, which is enriched by additional learning techniques that aim at avoiding the reconstruction of the same or related unfounded sets. Furthermore, we provide a syntactic criterion that allows one to skip the minimality check in many cases. An experimental evaluation shows that the new approach significantly decreases runtime.

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Extending Logic Programs with Description Logic Expressions for the Semantic Web

Cited by 9 publications

References 11 publications

A Well-Founded Semantics for FOL-Programs

A Well-Founded Semantics for FOL-Programs

FLP answer set semantics without circular justifications for general logic programs

Efficient HEX-Program Evaluation Based on Unfounded Sets

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