Advertisement

Advanced Topics in Logic

  • Gerard O’Regan
Chapter
Part of the Undergraduate Topics in Computer Science book series (UTICS)

Abstract

We consider some advanced topics in logic including fuzzy logic, temporal logic, intuitionist logic, undefined values in logic, logic and AI and theorem provers. Fuzzy logic is an extension of classical logic that acts as a mathematical model for vagueness. Temporal logic is concerned with the expression of properties that have time dependencies. Brouwer and others developed intuitionist logic as the logical foundation for intuitionism, which was a controversial theory of the foundations of mathematics based on a rejection of the law of the excluded middle and an insistence on constructive existence. We discuss several approaches that have been applied to dealing with undefined values that arise with partial functions including the logic of partial functions; Dijkstra’s approach with his cand and cor operators; and Parnas’s approach which preserves a classical two-valued logic.

References

  1. 1.
    E.M. Clarke, E.A. Emerson, Design and synthesis of synchronization skeletons using branching time temporal logic, in Logic of Programs: Work-shop, Yorktown Heights, NY, May 1981, volume 131 of LNCS (Springer, Berlin, 1981)Google Scholar
  2. 2.
    Stanford Enclyopedia of Philosophy, Temporal logic. http://plato.stanford.edu/entries/logic-temporal/
  3. 3.
    A. Heyting, Intuitionist Logic. An Introduction (North-Holland Publishing, 1966)Google Scholar
  4. 4.
    P. Martin Löf, Intuitionist Type Theory. Notes by Giovanni Savin of lectures given in Padua, June, 1980. Bibliopolis. Napoli (1984)Google Scholar
  5. 5.
    D.L. Parnas, Predicate calculus for software engineering. IEEE Trans. Softw. Eng. 19(9) (1993)Google Scholar
  6. 6.
    C. Jones, Systematic Software Development using VDM (Prentice Hall International, 1986)Google Scholar
  7. 7.
    J. McCarthy, Programs with common sense, in Proceedings of the Teddington Conference on the Mechanization of Thought Processes (1959)Google Scholar
  8. 8.
    A. Newell, H. Simon, The logic theory machine. IRE Trans. Inf. Theory 2, 61–79 (1956)Google Scholar
  9. 9.
    B. Russell, A.N. Whitehead, Principia Mathematica (Cambridge University Press, Cambridge, 1910)Google Scholar
  10. 10.
    R. Boyer, J.S. Moore, A Computational Logic. The Boyer Moore Theorem Prover (Academic Press, New York, 1979)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.SQC ConsultingMallow, County CorkIreland

Personalised recommendations