Abstract
In this paper, we study some interconnections amongst the three disciplines mentioned in the title of the paper. To begin with we quote some definitions and observations from Pratt [4]. There are lots of connectives in the closed unit interval [0, 1] , we present some of them. We replace the set of natrual numbers ℕ by a semi ring K = [0, 1] in the definition of a petrinet and discuss the firing rule of this petrinet. We also define a dual net and see that a transition t fires at a marking μ to produce precisely the dual of what it produces when it dual fires at μ . The last section of this paper is devoted exclusively to a “petrinet corresponding to a lineale” (which is a model for linear logic) we will discuss two special cases of a lineale and with the help of these cases, we offer a definition of a ‘complementary net’, a kind of dual, based on the complementation. This is another link to linear logic.
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