Bringing existential variables in answer set programming and bringing non-monotony in existential rules: two sides of the same coin
This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP)...
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| Published in | Annals of mathematics and artificial intelligence Vol. 82; no. 1-3; pp. 3 - 41 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
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Springer International Publishing
01.03.2018
Springer Springer Nature B.V Springer Verlag |
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| ISSN | 1012-2443 1573-7470 1573-7470 |
| DOI | 10.1007/s10472-017-9563-9 |
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| Abstract | This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP) is an appropriate formalism to represent various problems issued from Artificial Intelligence and arising when available information is incomplete. The combination of the two formalisms requires to extend existential rules with nonmonotonic negation and to extend ASP with existential variables. In this article, we present the syntax and semantics of Existential Non Monotonic Rules (ENM-rules) using skolemization which join together the two frameworks. We formalize its links with standard ASP. Moreover, since entailment with existential rules is undecidable, we present conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase and we discuss extension of these results in the nonmonotonic case. |
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| AbstractList | This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP) is an appropriate formalism to represent various problems issued from Artificial Intelligence and arising when available information is incomplete. The combination of the two formalisms requires to extend existential rules with nonmonotonic negation and to extend ASP with existential variables. In this article, we present the syntax and semantics of Existential Non Monotonic Rules (ENM-rules) using skolemization which join together the two frameworks. We formalize its links with standard ASP. Moreover, since entailment with existential rules is undecidable, we present conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase and we discuss extension of these results in the nonmonotonic case. This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP) is an appropriate formalism to represent various problems issued from Artificial Intelligence and arising when available information is incomplete. The combination of the two formalisms requires to extend existential rules with nonmonotonic negation and to extend ASP with existential variables. In this article, we present the syntax and semantics of Existential Non Monotonic Rules (ENMrules) using skolemization which join together the two frameworks. We formalize its links with standard ASP. Moreover, since entailment with existential rules is undecidable, we present conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase and we discuss extension of these results in the nonmonotonic case. Keywords Answer set programming * Existential rules * Ontologies * Decidability Mathematics Subject Classification (2010) 68T27 * 68T30 * 68N17 * 68Q17 * 68P15 |
| Audience | Academic |
| Author | Lefèvre, Claire Stéphan, Igor Rocher, Swan Garcia, Laurent Garreau, Fabien Baget, Jean-François |
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| Keywords | Existential rules 68N17 68P15 Decidability 68T27 Answer set programming 68Q17 Ontologies 68T30 |
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| SubjectTerms | Algorithms Artificial Intelligence Complex Systems Computer Science Computers Declarative programming Formalism Knowledge Knowledge representation Logic programming Mathematical programming Mathematics Monotony Ontology Semantics Services |
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| Title | Bringing existential variables in answer set programming and bringing non-monotony in existential rules: two sides of the same coin |
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