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FULL LAMBEK CALCULUS WITH CONTRACTION IS UNDECIDABLE

Published online by Cambridge University Press:  10 May 2016

KAREL CHVALOVSKÝ  and
ROSTISLAV HORČÍK
KAREL CHVALOVSKÝ
Affiliation:
INSTITUTE OF COMPUTER SCIENCE ACADEMY OF SCIENCES OF THE CZECH REPUBLIC POD VODÁRENSKOU VĚŽÍ 2 182 07 PRAGUE 8, CZECH REPUBLICE-mail: chvalovsky@cs.cas.cz
ROSTISLAV HORČÍK
Affiliation:
INSTITUTE OF COMPUTER SCIENCE ACADEMY OF SCIENCES OF THE CZECH REPUBLIC POD VODÁRENSKOU VĚŽÍ 2 182 07 PRAGUE 8, CZECH REPUBLICE-mail: horcik@cs.cas.cz
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Abstract

We prove that the set of formulae provable in the full Lambek calculus with the structural rule of contraction is undecidable. In fact, we show that the positive fragment of this logic is undecidable.

Keywords

substructural logicfull Lambek calculuscontraction rulesquare-increasing residuated latticeequational theorydecidability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 524 - 540
Copyright
Copyright © The Association for Symbolic Logic 2016 

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