Notre Dame Journal of Formal Logic

A Note on Monothetic BCI

Sam Butchart and Tomasz Kowalski

Abstract

In "Variations on a theme of Curry," Humberstone conjectured that a certain logic, intermediate between BCI and BCK, is none other than monothetic BCI—the smallest extension of BCI in which all theorems are provably equivalent. In this note, we present a proof of this conjecture.

Article information

Source
Notre Dame J. Formal Logic Volume 47, Number 4 (2006), 541-544.

Dates
First available in Project Euclid: 9 January 2007

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1168352666

Digital Object Identifier
doi:10.1305/ndjfl/1168352666

Mathematical Reviews number (MathSciNet)
MR2272087

Zentralblatt MATH identifier
1129.03006

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
substructural logics BCI logic monothetic BCI logic

Citation

Kowalski, Tomasz; Butchart, Sam. A Note on Monothetic BCI. Notre Dame J. Formal Logic 47 (2006), no. 4, 541--544. doi:10.1305/ndjfl/1168352666. http://projecteuclid.org/euclid.ndjfl/1168352666.


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References

  • [1] Humberstone, L., "Variations on a theme of Curry", Notre Dame Journal of Formal Logic, vol. 47 (2006), pp. 101--31 (electronic).
  • [2] Kalman, J. A., Automated Reasoning with Otter, Rinton Press, Incorporated, Princeton, 2001. With a foreword by Larry Wos.