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Default Negation in Normal Logic Programs Considered as Minimal Abduction of Positive Hypotheses

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Handbook of Abductive Cognition

Abstract

Logic programs (LPs) are a practical tool for declarative knowledge representation and consist of normal rules and integrity constraints (ICs). Reasoning with LPs is parameterized by the particular semantics chosen. However, the declaratively of the knowledge represented by an LP is restricted if the semantics chosen for the normal rules allows them to play the role ICs already can have. Namely because odd loops over negation, such as in rule {p ← not p}, entail the absence of two-valued semantics models and complex odd loops over negation are often deliberately used as ICs. Here the authors propose a more flexible reading of default negation, such that NLPs always have a two-valued model before ICs are evaluated. To wit, the authors do so by allowing for minimally assuming (or abducing) positive hypotheses and hence still maximizing the assumption of negative hypotheses that preserve consistency. The authors show how that translates into a semantics for normal logic programs (NLPs) – the minimal hypotheses (MH) semantics – which safeguards declarativity in this sense and moreover enjoys useful semantic properties such as cumulativity and relevancy, besides existence. Moreover, the authors introduce a program transformation which allows to compute the MH models of a program as a selection of the stable models of the transform.

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References

  • Alferes, J., Brogi, A., Leite, J. A., & Pereira, L. M. (2002). Evolving logic programs. In S. Flesca et al. (Eds.), Proceedings of JELIA’02 (LNCS, Vol. 2424, pp. 50–61). Springer.

    Google Scholar 

  • Alferes, J. J., Pereira, L. M., & Swift, T. (2004). Abduction in well-founded semantics and generalized stable models via tabled dual programs. Theory and Practice of Logic Programming, 4(4), 383–428.

    Article  MathSciNet  MATH  Google Scholar 

  • Brass, S., Dix, J., Freitag, B., & Zukowski, U. (2001). Transformation-based bottom-up computation of the well-founded model. TPLP, 1(5), 497–538.

    MathSciNet  MATH  Google Scholar 

  • Brewka, G. (2002). Logic programming with ordered disjunction. In AAAI-02 (pp. 100–105). AAAI Press.

    Google Scholar 

  • Dix, J. (1995a). A classification theory of semantics of normal logic programs: I. Strong properties. Fundamenta Informaticae, 22(3), 227–255.

    Article  MathSciNet  MATH  Google Scholar 

  • Dix, J. (1995b). A classification theory of semantics of normal logic programs: II. Weak properties. Fundamenta Informaticae, 22(3), 257–288.

    Article  MathSciNet  MATH  Google Scholar 

  • Dix, J., Gottlob, G., Marek, W., & Rauszer, C. (1996). Reducing disjunctive to non-disjunctive semantics by shift-operations. Fundamenta Informaticae, 28, 87–100.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Eiter, T., Fink, M., & Moura, J. (2010). Paracoherent answer set programming. In Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2010) (pp. 486–496).

    Google Scholar 

  • Eiter, T., & Gottlob, G. (1993). Complexity results for disjunctive logic programming and application to nonmonotonic logics. In International Logic Programming Symposium (pp. 266–278). MIT Press.

    Google Scholar 

  • Eshghi, K., & Kowalski, R. A. (1989). Abduction compared with negation by failure. In 6th International Conference on Logic Programming (ICLP 1989) (pp. 234–255). MIT Press.

    Google Scholar 

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

    Google Scholar 

  • Gelder, A. V., Ross, K. A., & Schlipf, J. S. (1991). The well-founded semantics for general logic programs. The Journal of the ACM, 38(3), 620–650.

    MathSciNet  MATH  Google Scholar 

  • Gelfond, M., & Lifschitz, V. (1988). The stable model semantics for logic programming. In ICLP’88 (pp. 1070–1080).

    Google Scholar 

  • Gelfond, M., & Lifschitz, V. (1990). Logic programs with classical negation. In D. Warren et al. (Eds.), ICLP (pp. 579–597). MIT Press.

    Google Scholar 

  • Gomes, A. S., Alferes, J. J., & Swift, T. (2010). Implementing query answering for hybrid MKNF knowledge bases. In M. Carro et al. (Eds.), PADL’10 (LNCS, Vol. 5937, pp. 25–39). Springer.

    Google Scholar 

  • Kakas, A. C., Kowalski, R. A., & Toni, F. (1992). Abductive logic programming. The Journal of Logic and Computation, 2(6), 719–770.

    Article  MathSciNet  MATH  Google Scholar 

  • Moore, R. C. (1985). Semantical considerations on nonmonotonic logic. AI, 25(1), 75–94.

    MathSciNet  MATH  Google Scholar 

  • Osorio, M., & Nieves, J. C. (2007). Pstable semantics for possibilistic logic programs. In MICAI’07 (LNCS, Vol. 4827, pp. 294–304). Springer.

    Google Scholar 

  • Pereira, L. M., & Pinto, A. M. (2005). Revised stable models – a semantics for logic programs. In C. Bento et al. (Eds.), EPIA’05 (LNAI, Vol. 3808, pp. 29–42). Springer.

    Google Scholar 

  • Pereira, L. M., & Pinto, A. M. (2007a). Approved models for normal logic programs. In N. Dershowitz & A. Voronkov (Eds.), LPAR’07 (LNAI, Vol. 4790). Springer.

    Google Scholar 

  • Pereira, L. M., & Pinto, A. M. (2007b). Reductio ad absurdum argumentation in normal logic programs. In Hamid R. Tizhoosh and Mario Ventresca (Eds.), ArgNMR’07-LPNMR’07 (pp. 96–113), Springer.

    Google Scholar 

  • Pereira, L. M., & Pinto, A. M. (2008). Collaborative vs. Conflicting Learning, Evolution and Argumentation, in: Oppositional Concepts in Computational Intelligence (Studies in Computational Intelligence, Vol. 155). Springer.

    Google Scholar 

  • Sakama, C., & Inoue, K. (1995). Paraconsistent stable semantics for extended disjunctive programs. Journal of Logic and Computation, 5(3), 265–285.

    Article  MathSciNet  MATH  Google Scholar 

  • Tarjan, R. (1972). Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2), 146–160.

    Article  MathSciNet  MATH  Google Scholar 

  • Witteveen, C. (1995). Every normal program has a nearly stable model. In J. Dix, L. Pereira, & T. Przymusinski, (Eds.), Non-monotonic Extensions of Logic Programming (Lecture Notes in Artificial Intelligence, Vol. 927, pp. 68–84). Berlin: Springer.

    Google Scholar 

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Acknowledgements

L.M.P. is supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT- Fundação para a Ciência e a Tecnologia, Portugal, through national funds.

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Authors and Affiliations

  1. Outra Limited, London, UK

    Alexandre Miguel Pinto

  2. NOVA-LINCS – Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisbon, Portugal

    Luís Moniz Pereira

Authors
  1. Alexandre Miguel Pinto
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  2. Luís Moniz Pereira
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Correspondence to Luís Moniz Pereira .

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Editors and Affiliations

  1. Department of Humanities, University of Pavia, Pavia, Italy

    Lorenzo Magnani

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Pinto, A.M., Pereira, L.M. (2022). Default Negation in Normal Logic Programs Considered as Minimal Abduction of Positive Hypotheses. In: Magnani, L. (eds) Handbook of Abductive Cognition. Springer, Cham. https://doi.org/10.1007/978-3-030-68436-5_22-1

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  • DOI: https://doi.org/10.1007/978-3-030-68436-5_22-1

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  • Print ISBN: 978-3-030-68436-5

  • Online ISBN: 978-3-030-68436-5

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