Schalk, Andrea and Steele, Hugh Paul - Constructing Fully Complete Models of Multiplicative Linear Logic

lmcs:1582 - Logical Methods in Computer Science, September 3, 2015, Volume 11, Issue 3
Constructing Fully Complete Models of Multiplicative Linear Logic

Authors: Schalk, Andrea and Steele, Hugh Paul

The multiplicative fragment of Linear Logic is the formal system in this family with the best understood proof theory, and the categorical models which best capture this theory are the fully complete ones. We demonstrate how the Hyland-Tan double glueing construction produces such categories, either with or without units, when applied to any of a large family of degenerate models. This process explains as special cases a number of such models from the literature. In order to achieve this result, we develop a tensor calculus for compact closed categories with finite biproducts. We show how the combinatorial properties required for a fully complete model are obtained by this glueing construction adding to the structure already available from the original category.


Source : oai:arXiv.org:1505.06056
DOI : 10.2168/LMCS-11(3:6)2015
Volume: Volume 11, Issue 3
Published on: September 3, 2015
Submitted on: December 17, 2014
Keywords: Computer Science - Logic in Computer Science


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