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On the decidability of implicational ticket entailment

Published online by Cambridge University Press:  12 March 2014

Katalin Bimbó  and
J. Michael Dunn
Katalin Bimbó
Affiliation:
Department of Philosophy, University of Alberta, Edmonton, AB, T6G 2E7, Canada, E-mail: bimbo@ualberta.ca, URL: www.ualberta.ca/~bimbo
J. Michael Dunn
Affiliation:
School of Informatics and Computing, and Department of Philosophy, Indiana University, Bloomington, IN 47408-3912, USA, E-mail: dunn@indiana.edu
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Abstract

The implicational fragment of the logic of relevant implication, R→ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, T→ 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 the decidability problem of R→. The decidability of T→ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over the base {B, B′, I, W}.

Keywords

decidabilityAckermann constantssequent calculiadmissibility of cutrelevance logicsticket entailment
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 214 - 236
Copyright
Copyright © Association for Symbolic Logic 2013

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