A Note on Monothetic BCI

A Note on Monothetic BCI

Tomasz Kowalski and Sam Butchart

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

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.

Primary Subjects: 03B47

Keywords: substructural logics; BCI logic; monothetic BCI logic

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Links and Identifiers

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

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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).

Mathematical Reviews (MathSciNet): MR2211186

Digital Object Identifier: doi:10.1305/ndjfl/1143468315

Project Euclid: euclid.ndjfl/1143468315

[2] Kalman, J. A., Automated Reasoning with Otter, Rinton Press, Incorporated, Princeton, 2001. With a foreword by Larry Wos.

Mathematical Reviews (MathSciNet): MR1892796

Zentralblatt MATH: 1009.68145

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