Skip to main content
Springer Nature Link
Log in

A Denotational Semantics for First-Order Logic

  • Conference paper
  • First Online:
Computational Logic — CL 2000 (CL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1861))

Included in the following conference series:

Abstract

In Apt and Bezem [AB99] we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables.

The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to “don’t know” nondeterminism, existential quantification to declaration of a local variable, and negation to the “negation as finite failure” rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. K. R. Apt and M. A. Bezem. Formulas as programs. In K.R. Apt, V.W. Marek, M. Truszczyński, and D.S. Warren, editors, The Logic Programming Paradigm: A 25 Year Perspective, pages 75–107, 1999. Available via http://xxx.lanl.gov/archive/cs/.

  2. 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 

  3. K. L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Databases, pages 293–322. Plenum Press, New York, 1978.

    Google Scholar 

  4. E. M. Clarke. Programming language constructs for which it is impossible to obtain good Hoare axiom systems. J. of the ACM, 26(1):129–147, January 1979.

    Google Scholar 

  5. J W. de Bakker. Mathematical Theory of Program Correctness. Prentice-Hall International, Englewood Cliffs, N.J., 1980.

    MATH  Google Scholar 

  6. DVS+88._M. Dincbas, P. Van Hentenryck, H. Simonis, A. Aggoun, T. Graf, and F. Berthier. The Constraint Logic Programming Language CHIP. In FGCS-88: Proceedings International Conference on Fifth Generation Computer Systems, pages 693–702, Tokyo, December 1988. ICOT.

    Google Scholar 

  7. P. M. Hill and J. W. Lloyd. The Gödel Programming Language. The MIT Press, 1994.

    Google Scholar 

  8. J. Jaffar, S. Michayov, P. Stuckey, and R. Yap. The CLP(R) language and system. ACM Transactions on Programming Languages and Systems, 14(3):339–395, July 1992.

    Google Scholar 

  9. R.A. Kowalski and D. Kuehner. Linear resolution with selection function. Artificial Intelligence, 2:227–260, 1971.

    Article  MATH  MathSciNet  Google Scholar 

  10. R.A. Kowalski. Predicate logic as a programming language. In Proceedings IFIP’74, pages 569–574. North-Holland, 1974.

    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. M.J. Maher. Complete axiomatizations of the algebras of finite, rational and infinite trees. In Proceedings of the Fifth Annual Symposium on Logic in Computer Science, pages 348–357. The MIT Press, 1988.

    Google Scholar 

  13. J.A. Robinson. A machine-oriented logic based on the resolution principle. J. A CM, 12(1):23–41, 1965.

    MATH  Google Scholar 

  14. D. S. Scott and C. Strachey. Towards a mathematical semantics for computer languages. Technical Report PRG-6, Programming Research Group, University of Oxford, 1971.

    Google Scholar 

  15. P. Van Hentenryck. Constraint Satisfaction in Logic Programming. Logic Programming Series. MIT Press, Cambridge, MA, 1989.

    Google Scholar 

  16. J. van Eijck. Programming with dynamic predicate logic. Technical Report INS-R9810, CWI, Amsterdam, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Krzysztof R. Apt

  2. University of Amsterdam, The Netherlands

    Krzysztof R. Apt

Authors
  1. Krzysztof R. Apt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Australian National University, Australia

    John Lloyd

  2. Simon Fraser University, Canada

    Veronica Dahl

  3. Universität Koblenz, Germany

    Ulrich Furbach

  4. The University of Birmingham, UK

    Manfred Kerber

  5. University of Manchester, UK

    Kung-Kiu Lau

  6. The Pennsylvania State University, USA

    Catuscia Palamidessi

  7. Universidade Nova de Lisboa, Portugal

    Luís Moniz Pereira

  8. The Hebrew University of Jerusalem, Israel

    Yehoshua Sagiv

  9. The University of Melbourne, Australia

    Peter J. Stuckey

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Apt, K.R. (2000). A Denotational Semantics for First-Order Logic. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-44957-4_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67797-0

  • Online ISBN: 978-3-540-44957-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation