Journal of Symbolic Logic

Monoid based semantics for linear formulas

W. P. R. Mitchell and H. Simmons

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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.

Article information

Source
J. Symbolic Logic, Volume 67, Issue 2 (2002), 505-527.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1190150094

Digital Object Identifier
doi:10.2178/jsl/1190150094

Mathematical Reviews number (MathSciNet)
MR1905151

Zentralblatt MATH identifier
1024.03063

Subjects
Primary: 03F52: Linear logic and other substructural logics [See also 03B47]
Secondary: 03G30: Categorical logic, topoi [See also 18B25, 18C05, 18C10]

Citation

Mitchell, W. P. R.; Simmons, H. Monoid based semantics for linear formulas. J. Symbolic Logic 67 (2002), no. 2, 505--527. doi:10.2178/jsl/1190150094. https://projecteuclid.org/euclid.jsl/1190150094


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