We give a deenition of a \linear bration", which is a hyperdoctrine model of polymorphic linear logic, and show how to internalise the bration, generating topos models. This gives a constructive set theoretical context for the logic of Petri nets, as recently developed by N. Mart-Oliet and J. Meseguer. Also, we sketch how this can be further extended to include the exponential operator !. In th...

– In this paper, a sheaf-theoretic approach toward fundamental problems in quantum physics is made. For example, the particle-wave duality depends upon whether or not a presheaf is evaluated at a specified object. The t-topos theoretic interpretations of doubleslit interference, uncertainty principle(s), and the EPR-type non-locality are given. As will be explained, there are more than one type...

Many of Eugene O’Neill’s characters deal with the complications love. That is, declarations love are not necessarily reciprocated. When this is case, lovers suffer unrequited love, which has been a frequent topos in classical as well modern texts. Unrequited encompasses three stages: rejection, betrayal, or death beloved; lover’s frustration; and finally, his her reaction to issue. This article...

We introduce a new topos in order to give a semantic account of the nonstandard functional interpretation introduced by Eyvind Briseid, Pavol Safarik and the author.

We define filter quotients of $(\infty,1)$-categories and prove that preserve the structure an elementary $(\infty,1)$-topos in particular lift quotient underlying topos. then specialize to case products a characterization theorem for equivalences product. Then we use construct large class $(\infty,1)$-toposes are not Grothendieck $(\infty,1)$-toposes. Moreover, give one detailed example intere...

This dissertation investigates what may be termed the model theory of higher-order logic using the methods of category theory. Of course, there is no such eld of logic as \higher-order model theory," and so our rst concern in chapter I will be to specify the basic objects under investigation, viz. higher-order logical theories and their models. This is a fairly straightforward generalization|in...