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Theorems on Pre-fixed Points of Non-Monotonic Functions with Applications in Logic Programming and Formal Grammars

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Logic, Language, Information, and Computation (WoLLIC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8652))

Abstract

We derive two novel theorems regarding pre-fixed points of non-monotonic functions and demonstrate that they have immediate applications in logic programming and formal grammars. In particular, the results of the paper lead to a natural generalization of the model intersection theorem for definite logic programs, to the more general class of normal logic programs. Moreover, the obtained results also offer the first (to our knowledge) model intersection result for Boolean grammars.

This research is being supported by the Greek General Secretariat for Research and Technology, the National Development Agency of Hungary, and the European Commission (European Regional Development Fund) under a Greek-Hungarian intergovernmental programme of Scientific and Technological collaboration. Project title: “Extensions and Applications of Fixed Point Theory for Non-Monotonic Formalisms”. It is also supported by grant no. ANN 110883 from the National Foundation of Hungary for Scientific Research.

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References

  1. Krzysztof, R.: Apt. Logic programming. In: Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 493–574 (1990)

    Google Scholar 

  2. Charalambidis, A., Ésik, Z., Rondogiannis, P.: Minimum model semantics for extensional higher-order logic programming with negation. In: International Conference on Logic Programming (to appear, 2014)

    Google Scholar 

  3. Denecker, M., Marek, V.W., Truszczynski, M.: Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 127–144. Kluwer Academic Publishers (2000)

    Google Scholar 

  4. Denecker, M., Marek, V.W., Truszczynski, M.: Ultimate approximation and its application in nonmonotonic knowledge representation systems. Inf. Comput. 192(1), 84–121 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ésik, Z., Rondogiannis, P.: A fixed point theorem for non-monotonic functions. In: Proceedings of 13th Panhellenic Logic Symposium, Athens, Greece (2013)

    Google Scholar 

  6. Ésik, Z., Rondogiannis, P.: A fixed point theorem for non-monotonic functions. CoRR, abs/1402.0299 (2014)

    Google Scholar 

  7. Kountouriotis, V., Nomikos, C., Rondogiannis, P.: Well-founded semantics for boolean grammars. Information and Computation 207(9), 945–967 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lloyd, J.W.: Foundations of Logic Programming. Springer (1987)

    Google Scholar 

  9. Okhotin, A.: Boolean grammars. Information and Computation 194(1), 19–48 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rondogiannis, P., Wadge, W.W.: Minimum model semantics for logic programs with negation-as-failure. ACM Transactions on Computational Logic 6(2), 441–467 (2005)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Szeged, Hungary

    Zoltán Ésik

  2. Department of Informatics and Telecommunications, University of Athens, Greece

    Panos Rondogiannis

Authors
  1. Zoltán Ésik
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  2. Panos Rondogiannis
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 64289, Darmstadt, Germany

    Ulrich Kohlenbach

  2. Department of Computer Science, Universidad de Chile, Avenida Blanco Encalada 2120, Oficina 316, Tercer Piso, Santiago, Chile

    Pablo Barceló

  3. Centro de Informática, Universidade Federal de Pernambuco (UFPE), Av. Jornalista Anibal Fernandes, s/n, Cidade Universitária, 50., 740-560, Recife, PE, Brazil

    Ruy de Queiroz

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Ésik, Z., Rondogiannis, P. (2014). Theorems on Pre-fixed Points of Non-Monotonic Functions with Applications in Logic Programming and Formal Grammars. In: Kohlenbach, U., Barceló, P., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2014. Lecture Notes in Computer Science, vol 8652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44145-9_12

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  • DOI: https://doi.org/10.1007/978-3-662-44145-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44144-2

  • Online ISBN: 978-3-662-44145-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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