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UNDECIDABILITY OF CONSEQUENCE RELATION IN FULL NON-ASSOCIATIVE LAMBEK CALCULUS

Published online by Cambridge University Press:  22 April 2015

KAREL CHVALOVSKÝ
KAREL CHVALOVSKÝ*
Affiliation:
INSTITUTE OF COMPUTER SCIENCE ACADEMY OF SCIENCES OF THE CZECH REPUBLIC POD VODÁRENSKOUVĚŽÍ 271/2, 182 07 PRAGUE 8, CZECH REPUBLICE-mail:karel@chvalovsky.czURL: http://karel.chvalovsky.cz
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Abstract

We prove that the consequence relation in the Full Non-associative Lambek Calculus is undecidable. An encoding of the halting problem for 2-tag systems using finitely many sequents in the language {⋅,∨} is presented. Therefore already the consequence relation in this fragment is undecidable. Moreover, the construction works even when the structural rules of exchange and contraction are added.

Keywords

Substructural logicsconsequence relationundecidabilitytag systemsword problemrewriting systems

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015 , pp. 567 - 586
Copyright
Copyright © The Association for Symbolic Logic 2015 

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