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First-Order Logic as a Constraint Programming Language

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2514))

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Abstract

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic maintenance of the constraint store takes place.

We prove that the resulting semantics is sound with respect to the truth definition. By instantiating it by specific forms of constraint management policies we obtain several sound evaluation policies of first-order formulas. This semantics can also be used a basis for sound implementation of constraint maintenance in presence of block declarations and conditionals.

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References

  1. R. Apt and A. Schaerf. The Alma project, or how first-order logic can help us in imperative programming. In E.-R. Olderog and B. Steffen, editors, Correct System Design, Lecture Notes in Computer Science 1710, pages 89–113, 1999.

    Chapter  Google Scholar 

  2. K.R. Apt. A denotational semantics for first-order logic. In Proc. of the computational logic conference (CL2000), Lecture Notes in Artificial Intelligence 1861, pages 53–69. Springer Verlag, 2000.

    Google Scholar 

  3. K.R. Apt and M.A. Bezem. Formulas as programs. In K.R. Apt, V.W. Marek, M. Truszcyński, and D.S. Warren, editors, The Logic Programming Paradigm: A 25 Year Perspective, pages 75–107, 1999.

    Google Scholar 

  4. K.R. Apt, J. Brunekreef, V. Partington, and A. Schaerf. Alma-0: An imperative language that supports declarative programming. ACM Toplas, 20(5):1014–1066, 1998.

    Article  Google Scholar 

  5. F.S. De Boer, M. Gabbrielli, E. Marchiori, and C. Palamidessi. Proving concurrent constraint programs correct. In ACM Transactions on Programming Languages and Systems, volume 19(5), pages 685–725, 1997.

    Article  Google Scholar 

  6. A. Colmerauer. Equations and inequations on finite and infinite trees. In John Lloyd, editor, Proc. of International Conference of Fifth Generation Computer Systems (FGCS’84), pages 85–99. OHMSHA Ltd. Tokyo and North-Holland, 1984.

    Google Scholar 

  7. F.S. de Boer, A. Di Pierro, and C. Palamidessi. Nondeterminism and infinite computations in constraint programming. Theoretical Computer Science, 151(1):37–78, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Fages, P. Ruet, and S. Soliman. Linear concurrent constraint programming: Operational and phase semantics. Information and Computation, 165(1):14–41, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Jaffar and J.M. Maher. Constraint logic programming: a survey. Journal of Logic Programming, 19/20, 1994.

    Google Scholar 

  10. J. Jaffar, J.M. Maher, K. Marriott, and P. Stuckey. The semantics of constraint logic programs. Journal of Logic Programming, 37(1):1–46, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  11. J.W. Lloyd and R.W. Topor. Making Prolog more expressive. Journal of Logic Programming, 1:225–240, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Palamidessi, F.S. de Boer, and A. Di Pierro. An algebraic perspective of constraint logic programming. Journal of Logic and Computation, 7, 1997.

    Google Scholar 

  13. V. A. Saraswat, M. Rinard, and P. Panangaden. Semantic foundations of concurrent constraint programming. In Conference Record of the Eighteenth Annual ACM Symposium on Principles of Programming Languages, pages 333–352, Orlando, Florida, 1991.

    Google Scholar 

  14. Vijay Saraswat. Concurrent Constraint Programming. MIT Press, 1993.

    Google Scholar 

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Author information

Authors and Affiliations

  1. CWI, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands

    K. R. Apt

  2. University of Amsterdam, The Netherlands

    K. R. Apt & C. F. M. Vermeulen

Authors
  1. K. R. Apt
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  2. C. F. M. Vermeulen
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Editor information

Editors and Affiliations

  1. Abteilung für Theoretische Informatik, Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Matthias Baaz

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13, 9PL, UK

    Andrei Voronkov

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© 2002 Springer-Verlag Berlin Heidelberg

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Apt, K.R., Vermeulen, C.F.M. (2002). First-Order Logic as a Constraint Programming Language. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_2

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  • DOI: https://doi.org/10.1007/3-540-36078-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00010-5

  • Online ISBN: 978-3-540-36078-0

  • eBook Packages: Springer Book Archive

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