Notre Dame Journal of Formal Logic

BCK is not Structurally Complete

Tomasz Kowalski

Abstract

We exhibit a simple inference rule, which is admissible but not derivable in BCK, proving that BCK is not structurally complete. The argument is proof-theoretical.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 2 (2014), 197-204.

Dates
First available in Project Euclid: 24 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1398345780

Digital Object Identifier
doi:10.1215/00294527-2420642

Mathematical Reviews number (MathSciNet)
MR3201832

Zentralblatt MATH identifier
1327.03017

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 06F35: BCK-algebras, BCI-algebras [See also 03G25] 03F07: Structure of proofs

Keywords
BCK logic structural completeness admissible rules

Citation

Kowalski, Tomasz. BCK is not Structurally Complete. Notre Dame J. Formal Logic 55 (2014), no. 2, 197--204. doi:10.1215/00294527-2420642. https://projecteuclid.org/euclid.ndjfl/1398345780


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References

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