Monoid Based Semantics for Linear Formulas

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Journal of Symbolic Logic 66 (4):1597-1619 (2001)
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Abstract

Each Girard quantale provides a support for a semantics for linear propositional formulas. 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. 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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From if to bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.

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