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Monoid Based Semantics for Linear Formulas

Monoid Based Semantics for Linear Formulas
Monoid Based Semantics for Linear Formulas
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.
0022-4812
505-527
Mitchell, Bill
5d045751-9ef4-4375-9e89-dbae07c90049
Simmons, Harold
065ba5cb-352a-4f3b-824f-85cad8d352d9
Mitchell, Bill
5d045751-9ef4-4375-9e89-dbae07c90049
Simmons, Harold
065ba5cb-352a-4f3b-824f-85cad8d352d9

Mitchell, Bill and Simmons, Harold (2002) Monoid Based Semantics for Linear Formulas. Journal of Symbolic Logic, JSL, 67 (2), 505-527.

Record type: Article

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.

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Published date: 2002
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Organisations: Electronics & Computer Science, IT Innovation
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Identifiers

Local EPrints ID: 266046
URI: http://eprints.soton.ac.uk/id/eprint/266046
ISSN: 0022-4812
PURE UUID: d0334d65-224b-4171-9c78-f32f449f4e43

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Date deposited: 03 Jul 2008 22:32
Last modified: 14 Mar 2024 08:19

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Contributors

Author: Bill Mitchell
Author: Harold Simmons

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