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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*
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

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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