Notre Dame Journal of Formal Logic

Self-implications in BCI

Tomasz Kowalski

Abstract

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

Article information

Source
Notre Dame J. Formal Logic, Volume 49, Number 3 (2008), 295-305.

Dates
First available in Project Euclid: 15 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1216152552

Digital Object Identifier
doi:10.1215/00294527-2008-013

Mathematical Reviews number (MathSciNet)
MR2428556

Zentralblatt MATH identifier
1167.03018

Subjects
Primary: 03F07: Structure of proofs 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
BCI logic sequent system self-implication

Citation

Kowalski, Tomasz. Self-implications in BCI. Notre Dame J. Formal Logic 49 (2008), no. 3, 295--305. doi:10.1215/00294527-2008-013. https://projecteuclid.org/euclid.ndjfl/1216152552


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References

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