Computer Laboratory

Technical reports

Categorical multirelations, linear logic and petri nets (draft)

Valeria de Paiva

May 1991, 29 pages

Abstract

This note presents a categorical treatment of multirelations, which is, in a loose sense a generalisation of both our previous work on the categories GC, and of Chu’s construction A_NC [Barr’79]. The main motivation for writing this note was the utilisation of the category GC by Brown and Gurr [BG90] to model Petri nets. We wanted to extend their work to deal with multirelations, as Petri nets are usually modelled using multirelations pre and post. That proved easy enough and people interested mainly in concurrency theory should refer to our joint work [BGdP’91], this note deals with the mathematics underlying [BGdP’91]. The upshot of this work is that we build a model of Intuitionistic Linear Logic (without modalities) over any symmetric monoidal category C with a distinguished object (N, ≤, ∘, e −∘) – a closed poset. Moreover, if the category C is cartesian closed with free monoids, we build a model of Intuitionistic Linear Logic with a non-trivial modality ‘!’ over it.

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BibTeX record

@TechReport{UCAM-CL-TR-225,
  author =	 {de Paiva, Valeria},
  title = 	 {{Categorical multirelations, linear logic and petri nets
         	   (draft)}},
  year = 	 1991,
  month = 	 may,
  url = 	 {http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-225.pdf},
  institution =  {University of Cambridge, Computer Laboratory},
  number = 	 {UCAM-CL-TR-225}
}