Poset-valued sets or how to build models for linear logics

Authors:
Andrea Schalk;Valeria de Paiva
Affiliations:
Department of Computer Science, University of Manchester, Oxford Rd, Manchester, M13 gPL, UK;Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA
Venue:
Theoretical Computer Science - Mathematical foundations of programming semantics
Year:
2004

Citing 6
Cited 0

Linear logic

Theoretical Computer Science
Proofs and types

Proofs and types
Games and full completeness for multiplicative linear logic

Journal of Symbolic Logic
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
Glueing and orthogonality for models of linear logic

Theoretical Computer Science - Category theory and computer science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We describe a method for constructing models of linear logic based on the category of sets and relations. The resulting categories are non-degenerate in general; in particular they are not compact closed nor do they have biproducts. The construction is simple, lifting the structure of a poset to the new category. The underlying poset thus controls the structure of this category, and different posets give rise to differently-flavoured models. As a result, this technique allows the construction of models for both, intuitionistic or classical linear logic as desired. A number of well-known models, for example coherence spaces and hypercoherences, are instances of this method.