Theoretical Computer Science
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
What is a Categorical Model of Intuitionistic Linear Logic?
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
A Dialectica-like Model of Linear Logic
Category Theory and Computer Science
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A generic method for constructing categorical models of Linear Logic is provided and instantiated to yield traditional models such as coherence spaces, hypercoherences, phase spaces, relations, etc. The generic construction is modular, as expected. Hence we discuss multiplicative connectives, modalities and additive connectives in turn. Modelling the multiplicative connectives of Linear Logic is a generalisation of previous work, requiring a few non-standard concepts. More challenging is the modelling of the modalities '!' (and, respectively '?'), which is achieved in the surprisingly general setting of this construction by considering !-candidates and showing that they exist and constitute a modality, under appropriate conditions.