Abstract

We give a definition of a "linear fibration", which is a hyperdoctrine model of polymorphic linear logic, and show how to internalise the fibration, generating topos models. This gives a constructive set theoretical context for the logic of Petri nets, as recently developed by N. Mart'i-Oliet and J. Meseguer. Also, we sketch how this can be further extended to include the exponential operator ! . In this context, the topos model we construct can be embedded in the model constructed by A.M. Pitts. 0 Introduction In [4], it is shown how to enrich the logic of Petri nets with gedanken states and processes, by embedding it into linear logic. Recently, Mart'i-Oliet and Meseguer have asked how to extend this even further to include polymorphism. It turns out that the process is fairly straightforward, and for maximal impact (so as to include constructive set theory), can be internalised to give topos models of polymorphic linear logic. Here we give the necessary definitions, and sketch the ...

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