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CANONICITY RESULTS OF SUBSTRUCTURAL AND LATTICE-BASED LOGICS

Published online by Cambridge University Press:  20 September 2010

TOMOYUKI SUZUKI
TOMOYUKI SUZUKI*
Affiliation:
University of Leicester
*
*DEPARTMENT OF COMPUTER SCIENCE, UNIVERSITY OF LEICESTER, LEICESTER LE1 7RH, UNITED KINGDOM. E-mail: tomoyuki.suzuki@mcs.le.ac.uk
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Abstract

In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of ε-join preserving operations, ε-meet preserving operations, ε-additive operations, ε-multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in Dunn et al. (2005) and Gehrke et al. (2005).

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 1 , March 2011 , pp. 1 - 42
Copyright
Copyright © Association for Symbolic Logic 2010

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