Journal of Symbolic Logic

On the decidability of implicational ticket entailment

Katalin Bimbó and J. Michael Dunn

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
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

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

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


Export citation