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On the decidability of implicational ticket entailment

Published online by Cambridge University Press:  12 March 2014

Katalin Bimbó
Affiliation:
Department of Philosophy, University of Alberta, Edmonton, AB, T6G 2E7, Canada, E-mail: [email protected], 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: [email protected]

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}.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2013

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