Constructing fully complete models for multiplicative linear logic

Andrea Schalk; Hugh Steele

doi:10.1109/LICS.2012.67

Constructing fully complete models for multiplicative linear logic

Andrea Schalk, Hugh Steele

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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Abstract

We demonstrate how the Hyland-Tan double glueing construction produces a fully complete model of the unit-free multiplicative fragment of Linear Logic when applied to any of a large family of degenerative ones. This process explains as special cases a number of such models which appear in the literature. In order to achieve this result, we make use of 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 the construction adding to those already available from the original category. © 2012 IEEE.

Original language	English
Title of host publication	Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012\|Proc. Annu. ACM/IEEE Symp. Logic Comput. Sci., LICS
Place of Publication	http://www.computer.org/portal/site/store/index.jsp
Publisher	IEEE
Pages	571-580
Number of pages	9
ISBN (Print)	9780769547695
DOIs	https://doi.org/10.1109/LICS.2012.67
Publication status	Published - 2012
Event	2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012 - Dubrovnik Duration: 1 Jul 2012 → …

Conference

Conference	2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
City	Dubrovnik
Period	1/07/12 → …

Keywords

Compact Closure
Double Glueing
Full Completeness
Linear Logic

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abstract = "We demonstrate how the Hyland-Tan double glueing construction produces a fully complete model of the unit-free multiplicative fragment of Linear Logic when applied to any of a large family of degenerative ones. This process explains as special cases a number of such models which appear in the literature. In order to achieve this result, we make use of 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 the construction adding to those already available from the original category. {\textcopyright} 2012 IEEE.",

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booktitle = "Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012|Proc. Annu. ACM/IEEE Symp. Logic Comput. Sci., LICS",

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Schalk, A & Steele, H 2012, Constructing fully complete models for multiplicative linear logic. in Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012|Proc. Annu. ACM/IEEE Symp. Logic Comput. Sci., LICS. IEEE, http://www.computer.org/portal/site/store/index.jsp, pp. 571-580, 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, Dubrovnik, 1/07/12. https://doi.org/10.1109/LICS.2012.67

Constructing fully complete models for multiplicative linear logic. / Schalk, Andrea; Steele, Hugh.
Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012|Proc. Annu. ACM/IEEE Symp. Logic Comput. Sci., LICS. http://www.computer.org/portal/site/store/index.jsp: IEEE, 2012. p. 571-580.

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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Constructing fully complete models for multiplicative linear logic

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