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Index Sets for Finite Normal Predicate Logic Programs with Function Symbols

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Logical Foundations of Computer Science (LFCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9537))

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Abstract

We study the recognition problem in the metaprogramming of finite normal predicate logic programs. That is, let \(\mathcal {L}\) be a computable first order predicate language with infinitely many constant symbols and infinitely many n-ary predicate symbols and n-ary function symbols for all \(n \ge 1\). Then we can effectively list all the finite normal predicate logic programs \(Q_0,Q_1,\ldots \) over \(\mathcal L\). Given some property \(\mathcal{P}\) of finite normal predicate logic programs over \(\mathcal L\), we define the index set \(I_\mathcal{P}\) to be the set of indices e such that \(Q_e\) has property \(\mathcal P\). Then we shall classify the complexity of the index set \(I_\mathcal{P}\) within the arithmetic hierarchy for various natural properties of finite predicate logic programs.

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References

  1. Andreka, H., Nemeti, I.: The generalized completeness of horn predicate logic as a programming language. Acta Cybernetica 4, 3–10 (1978)

    MathSciNet  MATH  Google Scholar 

  2. Apt, K.R., Blair, H.A.: Arithmetic classification of perfect models of stratified programs. Fund. Inf. 14, 339–343 (1991)

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  4. Bonatti, P.: Reasoning with infinite stable models. Art. Int. J. 156, 75–111 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Calautti, M., Greco, S., Spezzano, F., Trubitsyna, I.: Checking termination of bottom-up evaluation of logic programs with function symbols. Theor. Pract. Log. Program. 15, 854–859 (2015)

    Article  MathSciNet  Google Scholar 

  6. Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable functions in ASP: theory and implementation. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 407–424. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Cenzer, D., Marek, V.W., Remmel, J.B.: Index sets for finite predicate logic programs. In: Eiter, T., Gottlob, G. (eds.) FLOC 1999 Workshop on Complexity-theoretic and Recursion-theoretic Methods in Databases, Artificial Intelligence and Finite Model Theory, pp. 72–80 (1999)

    Google Scholar 

  8. Cenzer, D., Marek, V.W., Remmel, J.B.: Index sets for finite predicate logic programs (in preparation 2016)

    Google Scholar 

  9. Cenzer, D., Remmel, J.B.: Index Sets for \(\Pi ^0_1\) classes. Ann. Pure Appl. Logic 93, 3–61 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cenzer, D., Remmel, J.B.: A connection between Cantor-Bendixson derivatives and the well-founded semantics of finite logic programs. Ann. Math. Art. Int. 65, 1–24 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T. : Conflict-driven answer set solving. In: Veloso, M. (ed.) Proceedings of Joint International Conference on Artificial Intelligence, p. 386 (2007)

    Google Scholar 

  12. Gelfond, M., Lifschitz, V.: The stable semantics for logic programs. In: Proceedings of the 5th International Symposium on Logic Programming, pp. 1070–1080. MIT Press (1998)

    Google Scholar 

  13. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Log. 7, 499–562 (2006)

    Article  MathSciNet  Google Scholar 

  14. Lierler, Y., Lifschitz, V.: One more decidable class of finitely ground programs. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 489–493. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Lloyd, J.: Foundations of Logic Programming. Springer, New York (1989)

    MATH  Google Scholar 

  16. Marek, V.W., Nerode, A., Remmel, J.B.: How complicated is the set of stable models of a recursive logic program. Ann. Pure App. Logic 56, 119–136 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. Marek, V.W., Nerode, A., Remmel, J.B.: The stable models of predicate logic programs. J. Log. Program 21, 129–153 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  18. Niemelä, I., Simons, P.: Smodels — an implementation of the stable model and well-founded semantics for normal logic programs. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 420–429. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  19. Nerode, A., Shore, R.: Logic for Applications. Springer, New York (1993)

    Book  MATH  Google Scholar 

  20. Soare, R.: Recursively Enumerable Sets and Degrees. Springer, Heidelberg (1987)

    Book  MATH  Google Scholar 

  21. Syrjänen, T.: Omega-restricted logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 267–279. Springer, Heidelberg (2001)

    Google Scholar 

  22. Shepherdson, J.C.: Unsolvable problems for SLDNF-resolution. J. Log. Program. 10, 19–22 (1991)

    Article  MathSciNet  Google Scholar 

  23. Smullyan, R.M.: First-Order Logic. Springer, Heidelberg (1968)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Douglas Cenzer

  2. Department of Computer Science, University of Kentucky, Lexington, KY, 40506, USA

    Victor W. Marek

  3. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92903, USA

    Jeffrey B. Remmel

Authors
  1. Douglas Cenzer
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  2. Victor W. Marek
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  3. Jeffrey B. Remmel
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Corresponding author

Correspondence to Douglas Cenzer .

Editor information

Editors and Affiliations

  1. City University of New York , New York, New York, USA

    Sergei Artemov

  2. Cornell University , Ithaca, New York, USA

    Anil Nerode

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Cenzer, D., Marek, V.W., Remmel, J.B. (2016). Index Sets for Finite Normal Predicate Logic Programs with Function Symbols. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-27683-0_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-27683-0

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