Advertisement

Logical matrix generation and testing

  • Peter K. Malkin
  • Errol P. Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 310)

Abstract

Logical matrices are generalisations of truth-tables. They provide powerful computational tools for dealing with inference systems. A matrix in which all of the axioms and rules of a theory are true (or designated) but in which some query statement is false (or undesignated) shows that the query statement cannot be derived from the given theory. In this paper we discuss the use of matrices in logical research and in automated theorem-proving, and we conjecture further uses in the area of general constraint satisfaction. The computational ease of use of matrices is partly overshadowed by the computational difficulty of selecting the best or even a suitable matrix for a given task. Little is known about the relative efficiency of various matrices. We discuss our implementation of a general matrix generate and test algorithm which is designed to assist with research into these questions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Anderson A.R. and Belnap N.D. Jr. (1975), Entailment: The Logic of Relevance and Necessity, Princeton, Princeton University Press.Google Scholar
  2. [2]
    Gelernter, H. (1959), Realization of a geometry-theorem proving machine, Proceedings of the International Conference on Information Processing, UNESCO House, pp. 273–282. Reprinted in Siekmann and Wrightson (1983), pp. 99–117.Google Scholar
  3. [3]
    Jaffar, J. and Lassez, J-L. (1987), Constraint Logic Programming, Proceedings of the Fourteenth ACM Symposium on Principles of Programming Languages, pp.111–119.Google Scholar
  4. [4]
    Morishita, S., Numao, M. and Hirose, S. (1987), Symbolical construction of truth value domain for logic program, Proceedings of the 4th International Conference on Logic Programming (ed. J-L. Lassez), Cambridge, Mass., MIT Press.Google Scholar
  5. [5]
    Pritchard, P.A. (1978), And now for Something Completely Different, ms., Australian National University.Google Scholar
  6. [6]
    Pritchard, P.A. (1979), Son of Something Completely Different, ms., University of Queensland.Google Scholar
  7. [7]
    Pritchard, P.A. and Meyer, R.K., (1977), On computing matrix models of propositional calculi, ms. ANU.Google Scholar
  8. [8]
    Siekmann, J. and Wrightson, G. (1983), Automation of Reasoning: Classical Papers on Computational Logic, 2 vols. Springer-Verlag.Google Scholar
  9. [9]
    Slaney, J.K. (1980), Computers and Relevant Logic: A project in computing matrix model structures for propositional logics, Ph.D. thesis, Australian National University.Google Scholar
  10. [10]
    Thistlewaite, P.B., McRobbie, M.A., and Meyer, R.K. (1988). Automated Theorem-Proving in Non-Classical Logics, London, Pitman.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Peter K. Malkin
    • 1
  • Errol P. Martin
    • 1
  1. 1.Automated Reasoning ProjectRSSS, Australian National UniversityCanberraAustralia

Personalised recommendations