Translator Disclaimer
June 2002 Monoid based semantics for linear formulas
W. P. R. Mitchell, H. Simmons
J. Symbolic Logic 67(2): 505-527 (June 2002). DOI: 10.2178/jsl/1190150094

Abstract

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.

Citation

Download Citation

W. P. R. Mitchell. H. Simmons. "Monoid based semantics for linear formulas." J. Symbolic Logic 67 (2) 505 - 527, June 2002. https://doi.org/10.2178/jsl/1190150094

Information

Published: June 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1024.03063
MathSciNet: MR1905151
Digital Object Identifier: 10.2178/jsl/1190150094

Subjects:
Primary: 03F52
Secondary: 03G30

Rights: Copyright © 2002 Association for Symbolic Logic

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.67 • No. 2 • June 2002
Back to Top