Journal of Symbolic Logic

On the decidability of implicational ticket entailment

Katalin Bimbó and J. Michael Dunn

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The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over the base $\{\mathsf{B, B', I, W}\}$.

Article information

J. Symbolic Logic, Volume 78, Issue 1 (2013), 214-236.

First available in Project Euclid: 23 January 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: Primary: 03F52, Secondary: 03B47, 03F05

decidability Ackermann constants sequent calculi admissibility of cut relevance logics ticket entailment


Bimbó, Katalin; Dunn, J. Michael. On the decidability of implicational ticket entailment. J. Symbolic Logic 78 (2013), no. 1, 214--236. doi:10.2178/jsl.7801150.

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