Skip to main content
SpringerLink
Log in

The implications in conditional logic

  • Contributed Papers
  • Conference paper
  • First Online:
Algebraic Logic and Universal Algebra in Computer Science (ALUACS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 425))

Abstract

Given a logical system with disjunction (V) and negation (¬), we call implication, the derived operation defined by p ⇒ q ≡ (¬p) V q. Conditional logic is the 3-valued logic associated with short-circuit evaluation, and up to anti-isomorphism, is the unique non-commutative regular extension of Boolean logic to 3 truth values. The two anti-isomorphic conditional logics (left to right and right to left evaluation) yield quite different implications. We study the 3-element algebras associated with each of these operations, and for each of them a complete set of laws and a recursive formula for the free spectrum is obtained.

This paper is in final form and no version of it will be submitted for publication elsewhere.

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.

References

  1. Abbott, J.C., Semi-Boolean Algebra, Matematicki Vesnik 4 (1967), 177–198.

    MATH  MathSciNet  Google Scholar 

  2. Berman, J., Free spectra of 3-element algebras, in “Universal Algebra and Lattice Theory,” (edited by Freese, R. and Garcia, O.), Springer Lecture Notes in Mathematics 1004, 1983.

    Google Scholar 

  3. Cleave, J.P., Some remarks on the interpretation of 3-valued logics, Ratio 22 (1980), 52–60.

    MathSciNet  Google Scholar 

  4. Dienes, Z.P., On an implication function on many-valued systems of logic, Journal of Symbolic Logic 14 (1949), 95–97.

    Article  MATH  MathSciNet  Google Scholar 

  5. Guzmán, F., Squier, C.C., The algebra of conditional logic, Algebra Universalis (To appear).

    Google Scholar 

  6. Kleene, S., “Introduction to Metamathematics,” Van Nostrand, New York, 1952.

    Google Scholar 

  7. Lukasiewicz, J., Tarski A., Untersuchungen über den Aussagenkalkül, Comptes rendus des séances de la Société des Lettres de Varsovie Class III 23 (1930), 30–50.

    MATH  Google Scholar 

  8. McCarthy, J., Predicate calculus with “undefined” as a truth value, Stanford Artificial Intelligence Project Memo 1 (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematical Sciences, SUNY-Binghamton, 13901, Binghamton, NY

    Fernando Guzmán

Authors
  1. Fernando Guzmán
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Clifford H. Bergman Roger D. Maddux Don L. Pigozzi

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Guzmán, F. (1990). The implications in conditional logic. In: Bergman, C.H., Maddux, R.D., Pigozzi, D.L. (eds) Algebraic Logic and Universal Algebra in Computer Science. ALUACS 1988. Lecture Notes in Computer Science, vol 425. Springer, New York, NY. https://doi.org/10.1007/BFb0043082

Download citation

  • DOI: https://doi.org/10.1007/BFb0043082

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97288-6

  • Online ISBN: 978-0-387-34804-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation