Reminds me of Baez's Rosetta stone paper [1]. It's about some common threads in physics, math, logic, and programming. A completely different set of connections that what you'd see in Gödel, Escher, Bach.
I kinda sorta remember linear logic having the option for an infinite source, and an infinite sink for things you might want to deal with. A business has an infinite number of customers, but each specific transaction needs to be handled in a very specific way. You give me a dollar, and i give you a hamburger or french fries, your choice.
A light, accessible overview of linear logic is here [2]. That has a few nice, simple examples. It's easier than the wikipedia article.