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Monoid based semantics for linear formulas

Published online by Cambridge University Press:  12 March 2014

W. P. R. Mitchell  and
H. Simmons
W. P. R. Mitchell
Affiliation:
Motorola UK Research Lab, Basingstoke. Rg22 4Dp., England, E-Mail: b.mitchell@motorola.com
H. Simmons
Affiliation:
Department of Computer Science, Manchester University, Manchester, M13 9PL., England, E-Mail: hsimmons@cs.man.ac.uk
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1597 - 1619
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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