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European Conference on Logics in Artificial Intelligence

JELIA 2016: Logics in Artificial Intelligence pp 447–462Cite as

Extensional Semantics for Higher-Order Logic Programs with Negation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10021))

Abstract

We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [2, 3] for positive higher-order programs. In this way we provide an alternative extensional semantics for higher-order logic programs with negation to the one proposed in [6]. As an immediate useful consequence of our developments, we define for the language we consider the notions of stratification and local stratification, which generalize the familiar such notions from classical logic programming. We demonstrate that for stratified and locally stratified higher-order logic programs, the proposed semantics never assigns the unknown truth value.

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References

  1. Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann (1988)

    Google Scholar 

  2. Bezem, M.: Extensionality of simply typed logic programs. In: Schreye, D.D. (ed.) Logic Programming: The 1999 International Conference, Las Cruces, 29 November–4 December 1999, pp. 395–410. MIT Press (1999)

    Google Scholar 

  3. Bezem, M.: An improved extensionality criterion for higher-order logic programs. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 203–216. Springer, Heidelberg (2001). doi:10.1007/3-540-44802-0_15

    Chapter  Google Scholar 

  4. Bloom, S.L., Ésik, Z.: Iteration Theories - The Equational Logic of Iterative Processes. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  5. Carayol, A., Ésik, Z.: An analysis of the equational properties of the well-founded fixed point. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, 25–29 April 2016, pp. 533–536. AAAI Press (2016)

    Google Scholar 

  6. Charalambidis, A., Ésik, Z., Rondogiannis, P.: Minimum model semantics for extensional higher-order logic programming with negation. TPLP 14(4–5), 725–737 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Charalambidis, A., Handjopoulos, K., Rondogiannis, P., Wadge, W.W.: Extensional higher-order logic programming. ACM Trans. Comput. Log. 14(3), 21 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Charalambidis, A., Rondogiannis, P., Symeonidou, I.: Equivalence of two fixed-point semantics for definitional higher-order logic programs. In: Matthes, R., Mio, M. (eds.) Proceedings Tenth International Workshop on Fixed Points in Computer Science, FICS 2015, Berlin, 11–12 September 2015. EPTCS, vol. 191, pp. 18–32 (2015)

    Google Scholar 

  9. Chen, W., Kifer, M., Warren, D.S.: HILOG: a foundation for higher-order logic programming. J. Log. Program. 15(3), 187–230 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cholak, P., Blair, H.A.: The complexity of local stratification. Fundam. Inform. 21(4), 333–344 (1994)

    MathSciNet  MATH  Google Scholar 

  11. Ésik, Z.: Equational properties of stratified least fixed points (extended abstract). In: de Paiva, V., de Queiroz, R., Moss, L.S., Leivant, D., de Oliveira, A. (eds.) WoLLIC 2015. LNCS, vol. 9160, pp. 174–188. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47709-0_13

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  13. Kountouriotis, V., Rondogiannis, P., Wadge, W.W.: Extensional higher-order datalog. In: Short Paper Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), pp. 1–5, December 2005

    Google Scholar 

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

    Book  MATH  Google Scholar 

  15. Miller, D., Nadathur, G.: Programming with Higher-Order Logic, 1st edn. Cambridge University Press, New York (2012)

    Book  MATH  Google Scholar 

  16. Rondogiannis, P., Wadge, W.W.: Minimum model semantics for logic programs with negation-as-failure. ACM Trans. Comput. Log. 6(2), 441–467 (2005)

    Article  MathSciNet  Google Scholar 

  17. Wadge, W.W.: Higher-order horn logic programming. In: Saraswat, V.A., Ueda, K. (eds.) Proceedings of the 1991 International Symposium on Logic Programming, San Diego, 28 October–1 November 1991, pp. 289–303. MIT Press (1991)

    Google Scholar 

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Authors and Affiliations

  1. Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece

    Panos Rondogiannis & Ioanna Symeonidou

Authors
  1. Panos Rondogiannis
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  2. Ioanna Symeonidou
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Correspondence to Panos Rondogiannis .

Editor information

Editors and Affiliations

  1. Open University of Cyprus, Nicosia, Cyprus

    Loizos Michael

  2. University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

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Rondogiannis, P., Symeonidou, I. (2016). Extensional Semantics for Higher-Order Logic Programs with Negation. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_29

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  • DOI: https://doi.org/10.1007/978-3-319-48758-8_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48757-1

  • Online ISBN: 978-3-319-48758-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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