Order algebras as models of linear logic

Studia Logica 76 (2):201 - 225 (2004)
  Copy   BIBTEX


The starting point of the present study is the interpretation of intuitionistic linear logic in Petri nets proposed by U. Engberg and G. Winskel. We show that several categories of order algebras provide equivalent interpretations of this logic, and identify the category of the so called strongly coherent quantales arising in these interpretations. The equivalence of the interpretations is intimately related to the categorical facts that the aforementioned categories are connected with each other via adjunctions, and the compositions of the connecting functors with co-domain the category of strongly coherent quantales are dense. In particular, each quantale canonically induces a Petri net, and this association gives rise to an adjunction between the category of quantales and a category whose objects are all Petri nets.



    Upload a copy of this work     Papers currently archived: 74,594

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The Block Relation in Computable Linear Orders.Michael Moses - 2011 - Notre Dame Journal of Formal Logic 52 (3):289-305.
First-Order Logical Duality.Steve Awodey - 2013 - Annals of Pure and Applied Logic 164 (3):319-348.
The Logic of Peirce Algebras.Maarten De Rijke - 1995 - Journal of Logic, Language and Information 4 (3):227-250.
A General Notion of Realizability.Lars Birkedal - 2002 - Bulletin of Symbolic Logic 8 (2):266-282.
Nonexistence of Universal Orders in Many Cardinals.Menachem Kojman & Saharon Shelah - 1992 - Journal of Symbolic Logic 57 (3):875-891.


Added to PP

26 (#443,839)

6 months
1 (#419,510)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Han Zhang
University of New South Wales

Citations of this work

Prior’s OIC Nonconservativity Example Revisited.Lloyd Humberstone - 2014 - Journal of Applied Non-Classical Logics 24 (3):209-235.

Add more citations

References found in this work

No references found.

Add more references