Skip to main content

Gaggle theory: An abstraction of Galois connections and residuation, with applications to negation, implication, and various logical operators

  • Invited Papers
  • Conference paper
  • First Online:
Logics in AI (JELIA 1990)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 478))

Included in the following conference series:

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • A. R. Anderson and N. D. Belnap et al (1975), Entailment: The Logic of Relevance and Necessity, vol. 1, Princeton (Princeton University Press).

    Google Scholar 

  • G. Birkhoff (1940, 1948, 1967), Lattice Theory, Providence (American Mathematical Society).

    Google Scholar 

  • T. S. Blyth and M. F. Janowitz (1972), Residuation Theory, New York (Pergamon Press Inc.).

    Google Scholar 

  • J. M. Dunn (1966), The Algebra of Intensional Logics. Doctoral Dissertation, University of Pittsburgh, Ann Arbor (University Microfilms). Portions relevant to this paper are reprinted in Anderson, Belnap, et al. as §8 and §28.2.

    Google Scholar 

  • C. J. Everett (1944), "Closure Operators and Galois Theory in Lattices," Transactions of the American Mathematical Society, 55, 514–525.

    Google Scholar 

  • L. Fuchs (1963), Partially-Ordered Algebraic Systems, New York (Pergamon Press Inc.).

    Google Scholar 

  • R. I. Goldblatt (1974), "Semantic Analysis of Orthologic," Journal of Philosophical Logic, 3, 19–35.

    Google Scholar 

  • B. Jónsson and A. Tarski (1951–52), "Boolean Algebras with Operators," American Journal of Mathematics, 73–74, 891–939, 127–162.

    Google Scholar 

  • J. Lambek (1981), "The Influence of Heraclitus on Modern Mathematics," in Scientific Philosophy Today, eds. J. Agassi and R. S. Cohen, Dordrecht (D. Reidel Publishing Company).

    Google Scholar 

  • E. J. Lemmon (1966), "Algebraic Semantics for Modal Logics, I and II," The Journal of Symbolic Logic, 32, 46–65, 191–218.

    Google Scholar 

  • S. MacLane (1971), Categories for the Working Mathematician, New York (Springer-Verlag).

    Google Scholar 

  • R. K. Meyer and R. Routley (1972), "Algebraic Analysis of Entailment," Logique et Analyse, n.s. 15, 407–428.

    Google Scholar 

  • O. Ore (1944), "Galois Connexions," Transactions of the American Mathematical Society, 55, 493–513.

    Google Scholar 

  • R. Routley and R. K. Meyer (1972–73), "The Semantics of Entailment I" in Truth, Syntax and Modality, ed. H. Leblanc, Amsterdam (North-Holland Publishing Company), pp. 199–243.

    Google Scholar 

  • M. Stone (1936), "The Theory of Representations for Boolean Algebras, Transactions of the American Mathematical Society, 40, 37–111.

    Google Scholar 

  • M. Stone (1937), "Topological Representations of Distributive Lattices and Brouwerian Logics," Casopsis pro Pestov ani Matematiky a Fysiky, 67, 1–25.

    Google Scholar 

  • M. Ward and R. P. Dilworth (1939), "Residuated Lattices," Transactions of the American Mathematical Society, 45, 335–54.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. van Eijck

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dunn, J.M. (1991). Gaggle theory: An abstraction of Galois connections and residuation, with applications to negation, implication, and various logical operators. In: van Eijck, J. (eds) Logics in AI. JELIA 1990. Lecture Notes in Computer Science, vol 478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018431

Download citation

  • DOI: https://doi.org/10.1007/BFb0018431

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53686-4

  • Online ISBN: 978-3-540-46982-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics