Skip to main content
Log in

The Distance Function in Commutative ℓ-semigroups and the Equivalence in Łukasiewicz Logic

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The equivalence connective in Łukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|xy| of a positive cone of a commutative ℓ-group. We make some observations on logically motivated algebraic structures involving the distance function.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blok, W. J., and I. M. A. Ferreirim, \lsOn the structure of hoops\rs, Algebra Universalis 43 (2000), 233–257.

    Article  Google Scholar 

  2. Bosbach, B., \lsKomplement\:are Halbgruppen\rs, Fundamenta Mathematicae 64 (1969), 257–287.

    Google Scholar 

  3. Chang, C. C., \lsA new proof of completeness of \kLukasiewicz axioms\rs, Trans. Amer. Math. Soc. 93 (1959), 74–80.

    Google Scholar 

  4. Davis, M., Y. Matijasevich, and J. Robinson, \lsHilbert's tenth problem. Diophantine equations: positive aspects of a negative solution\rs, Proc. Symp. Pure Math. 28 (1976), 323–378.

    Google Scholar 

  5. Freese, R., and R. McKenzie, Commutator Theory for Congruence Modular Varieties, vol. 125 of London Math. Soc. Lecture Notes Series, Cambridge University Press, Cambridge, 1987.

    Google Scholar 

  6. Henkin, L., \lsThe Logic of Equality\rs, The American Mathematical Monthly 84 (1977), 597–612.

    Google Scholar 

  7. Matijasevich, Y., \lsDiofantovost perechislimykh mnozhestv\rs, Dokl. Akad. Nauk SSSR 191 (1970), 278–282. English translation in Soviet Math. Doklady 11, 354–357.

    Google Scholar 

  8. McKenzie, R., \lsFinite equational bases for congruence modular varieties\rs, Algebra Universalis 24 (1987), 224–250.

    Google Scholar 

  9. Pixley, A. F., \lsThe ternary discriminator function in universal algebra\rs, Math. Ann. 191 (1971), 167–180.

    Google Scholar 

  10. Werner, H., \lsDiscriminator algebras\rs, Studium zur Algebra und ihre Andwendungen 6 (1978).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wroński, A. The Distance Function in Commutative ℓ-semigroups and the Equivalence in Łukasiewicz Logic. Studia Logica 77, 241–253 (2004). https://doi.org/10.1023/B:STUD.0000037128.76996.90

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:STUD.0000037128.76996.90

Navigation