Notre Dame Journal of Formal Logic

An Abelian Rule for BCI—and Variations

Tomasz Kowalski and Lloyd Humberstone

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We show the admissibility for $\mathsf{BCI}$ of a rule form of the characteristic implicational axiom of abelian logic, this rule taking us from $(\alpha\to\beta)\to\beta$ to $\alpha$. This is done in Section 8, with surrounding sections exploring the admissibility and derivability of various related rules in several extensions of $\mathsf{BCI}$.

Article information

Notre Dame J. Formal Logic Volume 57, Number 4 (2016), 551-568.

Received: 6 November 2012
Accepted: 9 November 2013
First available in Project Euclid: 12 September 2016

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Zentralblatt MATH identifier

Primary: 03F03: Proof theory, general 03F52: Linear logic and other substructural logics [See also 03B47]
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

admissible rules structural completeness BCI BCK abelian logic


Kowalski, Tomasz; Humberstone, Lloyd. An Abelian Rule for BCI—and Variations. Notre Dame J. Formal Logic 57 (2016), no. 4, 551--568. doi:10.1215/00294527-3679398.

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