Self-implications in BCI

Notre Dame Journal of Formal Logic 49 (3):295-305 (2008)
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Abstract

Humberstone asks whether every theorem of BCI provably implies $\phi\to\phi$ for some formula $\phi$. Meyer conjectures that the axiom $\mathbf{B}$ does not imply any such "self-implication." We prove a slightly stronger result, thereby confirming Meyer's conjecture

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Tomasz Kowalski
La Trobe University

Citations of this work

Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.
BCK is not Structurally Complete.Tomasz Kowalski - 2014 - Notre Dame Journal of Formal Logic 55 (2):197-204.
An Abelian Rule for BCI—and Variations.Tomasz Kowalski & Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (4):551-568.

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References found in this work

Fragments of R-Mingle.W. J. Blok & J. G. Raftery - 2004 - Studia Logica 78 (1-2):59-106.
Variations on a Theme of Curry.Lloyd Humberstone - 2006 - Notre Dame Journal of Formal Logic 47 (1):101-131.
A Note on Monothetic BCI.Tomasz Kowalski & Sam Butchart - 2006 - Notre Dame Journal of Formal Logic 47 (4):541-544.
On a property of BCK-identities.Misao Nagayama - 1994 - Studia Logica 53 (2):227 - 234.

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