Notre Dame Journal of Formal Logic

BCK is not Structurally Complete

Tomasz Kowalski


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

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

First available in Project Euclid: 24 April 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

BCK logic structural completeness admissible rules


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

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