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A SAHLQVIST THEOREM FOR SUBSTRUCTURAL LOGIC

Published online by Cambridge University Press:  18 March 2013

TOMOYUKI SUZUKI
TOMOYUKI SUZUKI*
Affiliation:
Department of Computer Science, University of Leicester
*
*DEPARTMENT OF INFORMATICS, UNIVERSITY OF PISA, LARGO PONTECORVO 3C, 56127 PISA, ITALY, E-mail: tomoyuki.suzuki@di.unipi.it
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Abstract

In this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic. Our result is not limited to substructural logic but is also easily applicable to other lattice-based logics.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 229 - 253
Copyright
Copyright © Association for Symbolic Logic 2013 

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