Guarded hybrid knowledge bases

Heymans, Stijn; Bruijn, Jos de; Predoiu, Livia; Feier, Cristina; niewenborgh, Davy Van

doi:10.1017/s1471068407003201

Cited by 20 publications

(41 citation statements)

References 20 publications

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“…Moreover, other interesting approaches have been presented. Some of the most recent ones study the combination of DLs and rules under a different semantic approach [21] or under different restrictions on variables in rules [17].…”

Section: Discussionmentioning

confidence: 99%

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

Rosati

2008

Web Reasoning and Rule Systems

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Abstract. Reasoning in systems integrating Description Logics (DL) ontologies and Datalog rules is a very hard task, and previous studies have shown undecidability of reasoning in systems integrating (even very simple) DL ontologies with recursive Datalog. However, the results obtained so far constitute a very partial picture of the computational properties of systems combining DL ontologies and Datalog rules. The aim of this paper is to contribute to complete this picture, extending the computational analysis of reasoning in systems integrating ontologies and Datalog rules. More precisely, we first provide a set of decidability and complexity results for reasoning in systems combining ontologies specified in DLs and rules specified in nonrecursive Datalog (and its extensions with inequality and negation): such results identify, from the viewpoint of the expressive abilities of the two formalisms, minimal combinations of Description Logics and Datalog in which reasoning is undecidable. Then, we present new results on the decidability and complexity of the so-called restricted (or safe) integration of DL ontologies and Datalog rules. Our results show that: (1) the unrestricted interaction between DLs and Datalog is computationally very hard even in the absence of recursion in rules; (2) surprisingly, the various "safeness" restrictions, which have been defined to regain decidability of reasoning in the interaction between DLs and recursive Datalog, appear as necessary restrictions even when rules are not recursive.

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Section: Discussionmentioning

confidence: 99%

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

Rosati

2008

Web Reasoning and Rule Systems

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“…[1]. Two variations of this semantics, the open [8] and generalised open answer set [9] semantics, consider non-ground programs and open domains, thereby relaxing the PNA. For the present version of QEL the correspondence to answer sets can be summarised as follows (see [17,18,3]).…”

Section: Relation To Answer Setsmentioning

confidence: 99%

“…It follows that if Π is a logic program (of any form), a total QHT model U, T, T of Π is an equilibrium model of Π iff it is a generalised open answer set of Π in the sense of [9]. If we assume all models are UNA-models, we obtain the version of QEL found in [17].…”

Section: Relation To Answer Setsmentioning

confidence: 99%

A Revised Concept of Safety for General Answer Set Programs

Cabalar

Pearce

Valverde

2009

Logic Programming and Nonmonotonic Reasoning

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Abstract.Some answer set solvers deal with programs with variables by requiring a safety condition on program rules. This ensures that there is a close relation between the answer sets of the program and those of its ground version. If we move beyond the syntax of disjunctive programs, for instance by allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, new definitions of safety are required. In this paper we consider a new concept of safety for formulas in quantified equilibrium logic where answer sets can be defined for arbitrary first-order formulas. The new concept captures and generalises two recently proposed safety definitions: that of Lee, Lifschitz and Palla (2008) as well as that of Bria, Leone and Faber (2008). We study the main metalogical properties of safe formulas.

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“…Hybrid approaches (e.g. [18][19][20]9]) fall between these extremes. Common to hybrid approaches is the definition of a modular semantics based on classical first-order models, on the one hand, and stable models, on the other hand.…”

Section: Introductionmentioning

confidence: 99%

“…First, we survey and compare different (extensions of the) answer set semantics, as well as the existing approaches to hybrid knowledge bases. Second, we propose to use Quantified Equilibrium Logic (QEL) as a unified logical foundation for hybrid knowledge bases: As it turns out, the equilibrium models of the combined knowledge base coincide exactly with the modular nonmonotonic models for all approaches we are aware of [18][19][20]9].…”

Section: Introductionmentioning

confidence: 99%

Quantified Equilibrium Logic and Hybrid Rules

Bruijn¹,

Pearce

Polleres

et al. 2007

Web Reasoning and Rule Systems

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Abstract. In the ongoing discussion about combining rules and Ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way.

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Guarded hybrid knowledge bases

Cited by 20 publications

References 20 publications

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

A Revised Concept of Safety for General Answer Set Programs

Quantified Equilibrium Logic and Hybrid Rules

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