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Goals in the Propositional Horn ⊃  Language Are Monotone Boolean Circuits

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Mathematical Foundations of Computer Science 2005 (MFCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3618))

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Abstract

Horn  ⊃  is a logic programming language which extends usual Horn clauses by adding intuitionistic implication in goals and clause bodies. This extension can be seen as a form of structuring programs in logic programming. Restricted to the propositional setting of this language, we prove that any goal in Horn  ⊃  can be translated into a monotone Boolean circuit which is linear in the size of the goal.

This work has been partially supported by the projects TIN2004-07925-C03-03 and UPV 00141.226-E-15965/2004.

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References

  1. Angluin, D., Kharitonov, M.: When won’t Membership Queries Help? Journal of Computer and System Sciences 50(2), 336–355 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arruabarrena, R., Lucio, P., Navarro, M.: A strong logic programming view for static embedded implications. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 56–72. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Baldoni, M., Giordano, L., Martelli, A.: Translating a Modal Language with Embedded Implication into Horn Clause Logic. In: Proc. of \(5\check{z}\) Int. Workshop of Extensions of Logic Programming, ELP 1996. Lect. Notes in Comput.Sciences, vol. 1050, Springer, Heidelberg (1996)

    Google Scholar 

  4. Bugliesi, M., Lamma, E., Mello, P.: Modularity in Logic Programming. Journal of Logic Programming (19-20), 443–502 (1994)

    Google Scholar 

  5. Gabbay, D.M.: N-Prolog: An Extension of Prolog with Hypothetical Implications. II. Logical Foundations and Negation as Failure. Journal of Logic Programming 2(4), 251–283 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gaintzarain, J., Hermo, M., Navarro, M.: On Learning Conjunctions of Horn  ⊃  Clauses. In: CiE 2005, New Computational Paradigms, Amsterdam, June 8-12 (2005)

    Google Scholar 

  7. Giordano, L., Martelli, A.: Structuring Logic Programs: A Modal Approach. Journal of Logic Programming 21, 59–94 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. Giordano, L., Martelli, A., Rossi, G.: Extending Horn Clause Logic with Implication Goals. Theoretical Computer Science 95, 43–74 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kearns, M., Valiant, L.: Criptographic Limitations on Learning Boolean Formulae and Finite Automata. Journal of the ACM 41(1), 67–95 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lucio, P.: Structured Sequent Calculi for Combining Intuitionistic and Classical First-Order Logic. In: Kirchner, H. (ed.) FroCos 2000. LNCS, vol. 1794, pp. 88–104. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  11. Meseguer, J.: Multiparadigm Logic Programming. In: Kirchner, H., Levi, G. (eds.) ALP 1992. LNCS, vol. 632, pp. 158–200. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  12. Miller, D.: A Logical Analysis of Modules in Logic Programming. Journal of Logic Programming 6, 79–108 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  13. Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform Proofs as a Foundation for Logic Programming. Annals of Pure and App. Logic 51, 125–157 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Monteiro, L., Porto, A.: Contextual Logic Programming. In: Proc. 6th International Conf. on Logic Programming, pp. 284–299 (1989)

    Google Scholar 

  15. Moscowitz, Y., Shapiro, E.: Lexical Logic Programs. In: Proc. 8th International Conf. on Logic Programming, pp. 349–363 (1991)

    Google Scholar 

  16. Navarro, M.: From Modular Horn Programs to Flat Ones: a Formal Proof for the Propositional Case. In: Proc. of ISIICT 2004 (Int. Symp. on Innovation in Information and Communication Technology), Amman, Jordan, Technical Report UPV-EHU/ LSI/ TR 01- (April 2004)

    Google Scholar 

  17. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley Publishing Company, Inc, Reading (1995)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dpto de L.S.I., Facultad de Informática, P.O. Box 649, 20080, San Sebastián, Spain

    J. Gaintzarain, M. Hermo & M. Navarro

Authors
  1. J. Gaintzarain
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  2. M. Hermo
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  3. M. Navarro
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80 952, Gdansk, Poland

    Joanna Jȩdrzejowicz  & Andrzej Szepietowski  & 

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Gaintzarain, J., Hermo, M., Navarro, M. (2005). Goals in the Propositional Horn ⊃  Language Are Monotone Boolean Circuits. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_33

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  • DOI: https://doi.org/10.1007/11549345_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28702-5

  • Online ISBN: 978-3-540-31867-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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