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Approved Models for Normal Logic Programs

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4790))

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Abstract

We introduce an original 2-valued semantics for Normal Logic Programs (NLPs) extending the well-known Argumentation work of Phan Minh Dung on Admissible Arguments and Preferred Extensions. In the 2-valued Approved Models Semantics set forth, an Approved Model (AM) correspond to the minimal positive strict consistent 2-valued completion of a Dung Preferred Extension. The AMs Semantics enjoys several non-trivial useful properties such as (1) Existence of a 2-valued Model for every NLP; (2) Relevancy, and (3) Cumulativity. Crucially, we show that the AMs Semantics is a conservative extension to the Stable Models (SMs) Semantics in the sense that every SM of a NLP is also an AM, thus providing every NLP with a model: a property not enjoyed by SMs. Integrity constraints, written in a simpler way, are introduced to identify undesired semantic scenarios, whilst permitting these to be produced nevertheless. We end the paper with some conclusions and mention of future work.

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References

  1. Alferes, J.J., Brogi, A., Leite, J.A., Pereira, L.M.: Evolving logic programs. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 50–61. Springer, Heidelberg (2002)

    Google Scholar 

  2. Alferes, J.J., Pereira, L.M.: An argumentation theoretic semantics based on non-refutable falsity. In: Dix, J., et al. (eds.) NMELP, pp. 3–22. Springer, Heidelberg (1994)

    Google Scholar 

  3. Baral, C., Subrahmanian, V.S.: Dualities between alternative semantics for logic programming and nonmonotonic reasoning. J. Autom. Reasoning 10(3), 399–420 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93, 63–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dix, J.: A Classification-Theory of Semantics of Normal Logic Programs: I, II. Fundamenta Informaticae XXII(3), 227–255, 257–288 (1995)

    MathSciNet  Google Scholar 

  6. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–358 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dung, P.M., Kowalski, R.A., Toni, F.: Dialectic proof procedures for assumption-based, admissible argumentation. Artif. Intell. 170(2), 114–159 (2006)

    Article  MathSciNet  Google Scholar 

  8. Fages, F.: Consistency of Clark’s completion and existence of stable models. Methods of Logic in Computer Science 1, 51–60 (1994)

    Google Scholar 

  9. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: ICLP/SLP, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  10. Kakas, A.C., Mancarella, P.: Negation as stable hypotheses. In: LPNMR, pp. 275–288. MIT Press, Cambridge (1991)

    Google Scholar 

  11. Malý, M.: Complexity of revised stable models. Master’s thesis, Comenius University Bratislava (2006)

    Google Scholar 

  12. Pereira, L.M., Pinto, A.M.: Revised stable models - a semantics for logic programs. In: Bento, C., Cardoso, A., Dias, G. (eds.) EPIA 2005. LNCS (LNAI), vol. 3808, pp. 29–42. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Pereira, L.M., Pinto, A.M.: Reductio ad absurdum argumentation in normal logic programs. In: Argumentation and Non-monotonic Reasoning (ArgNMR 2007) workshop at LPNMR 2007, pp. 96–113 (2007)

    Google Scholar 

  14. Pinto, A.M.: Explorations in revised stable models — a new semantics for logic programs. Master’s thesis, Universidade Nova de Lisboa (February 2005)

    Google Scholar 

  15. Soares, L.: Revising undefinedness in the well-founded semantics of logic programs. Master’s thesis, Universidade Nova de Lisboa (2006)

    Google Scholar 

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Authors and Affiliations

  1. Centro de Inteligência Artificial (CENTRIA), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

    Luís Moniz Pereira & Alexandre Miguel Pinto

Authors
  1. Luís Moniz Pereira
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  2. Alexandre Miguel Pinto
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Nachum Dershowitz Andrei Voronkov

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© 2007 Springer-Verlag Berlin Heidelberg

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Pereira, L.M., Pinto, A.M. (2007). Approved Models for Normal Logic Programs. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_33

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  • DOI: https://doi.org/10.1007/978-3-540-75560-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75558-6

  • Online ISBN: 978-3-540-75560-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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