research-article

Well-founded semantics for description logic programs in the semantic web

Authors:

Giovambattista Ianni,

Thomas Lukasiewicz,

Roman SchindlauerAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 12, Issue 2

Article No.: 11, Pages 1 - 41

https://doi.org/10.1145/1877714.1877717

Published: 27 January 2011 Publication History

Abstract

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic knowledge base is polynomial; under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.

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Cited By

Alviano MGiordano LTheseider Dupré D(2024)Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicalityJournal of Logic and Computation10.1093/logcom/exae03834:8(1469-1499)Online publication date: 5-Aug-2024
https://doi.org/10.1093/logcom/exae038
Casini GStraccia U(2023)Defeasible RDFS via rational closureInformation Sciences10.1016/j.ins.2022.11.165643(118409)Online publication date: Sep-2023
https://doi.org/10.1016/j.ins.2022.11.165
Knorr M(2021)On Combining Ontologies and RulesReasoning Web. Declarative Artificial Intelligence 10.1007/978-3-030-95481-9_2(22-58)Online publication date: 8-Sep-2021
https://dl.acm.org/doi/10.1007/978-3-030-95481-9_2
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Index Terms

Well-founded semantics for description logic programs in the semantic web
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Logic programming and answer set programming
      2. Nonmonotonic, default reasoning and belief revision
2. Theory of computation
  1. Logic
    1. Constraint and logic programming
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Inductive inference

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 12, Issue 2

January 2011

317 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1877714

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Copyright © 2011 ACM.

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Publication History

Published: 27 January 2011

Accepted: 01 April 2010

Revised: 01 January 2010

Received: 01 March 2009

Published in TOCL Volume 12, Issue 2

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Cited By

Alviano MGiordano LTheseider Dupré D(2024)Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicalityJournal of Logic and Computation10.1093/logcom/exae03834:8(1469-1499)Online publication date: 5-Aug-2024
https://doi.org/10.1093/logcom/exae038
Casini GStraccia U(2023)Defeasible RDFS via rational closureInformation Sciences10.1016/j.ins.2022.11.165643(118409)Online publication date: Sep-2023
https://doi.org/10.1016/j.ins.2022.11.165
Knorr M(2021)On Combining Ontologies and RulesReasoning Web. Declarative Artificial Intelligence 10.1007/978-3-030-95481-9_2(22-58)Online publication date: 8-Sep-2021
https://dl.acm.org/doi/10.1007/978-3-030-95481-9_2
Giordano LGliozzi V(2019)Reasoning About Exceptions in Ontologies: An Approximation of the Multipreference SemanticsSymbolic and Quantitative Approaches to Reasoning with Uncertainty10.1007/978-3-030-29765-7_18(212-225)Online publication date: 18-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29765-7_18
Cao SNguyen L(2017)Query–subquery nets for Horn knowledge bases in first-order logicJournal of Information and Telecommunication10.1080/24751839.2017.12956641:1(79-99)Online publication date: 7-Mar-2017
https://doi.org/10.1080/24751839.2017.1295664
Cruz-Filipe LGaspar GNunes I(2017)From description-logic programs to multi-context systemsJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2017.01.00588(26-44)Online publication date: Apr-2017
https://doi.org/10.1016/j.jlamp.2017.01.005
Eiter TFink MStepanova D(2016)Data repair of inconsistent nonmonotonic description logic programsArtificial Intelligence10.1016/j.artint.2016.06.003239:C(7-53)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.1016/j.artint.2016.06.003
Liu FBi YChowdhury MYou JFeng Z(2016)Flexible Approximators for Approximating Fixpoint TheoryProceedings of the 29th Canadian Conference on Artificial Intelligence on Advances in Artificial Intelligence - Volume 967310.1007/978-3-319-34111-8_28(224-236)Online publication date: 31-May-2016
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Nguyen LNguyen TSzałas A(2015)Towards richer rule languages with polynomial data complexity for the Semantic WebData & Knowledge Engineering10.1016/j.datak.2015.04.00596:C(57-77)Online publication date: 1-Mar-2015
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Cruz-Filipe LGaspar GNunes I(2015)Design Patterns for Description-Logic ProgramsKnowledge Discovery, Knowledge Engineering and Knowledge Management10.1007/978-3-662-46549-3_13(199-214)Online publication date: 25-Apr-2015
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