## Journal of Symbolic Logic

### On the decidability of implicational ticket entailment

#### Abstract

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

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

Dates
First available in Project Euclid: 23 January 2013

https://projecteuclid.org/euclid.jsl/1358951110

Digital Object Identifier
doi:10.2178/jsl.7801150

Mathematical Reviews number (MathSciNet)
MR3087072

Zentralblatt MATH identifier
1275.03159

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

#### Citation

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. https://projecteuclid.org/euclid.jsl/1358951110