On the surface: The world would be premises and stories would be proofs.
Linear Logic for Non-Linear Storytelling by Anne-Gwenn Bosser and Marc Cavazza and Ronan Champagnat has an example.
Then generating proofs means generating valid stories. Linear logic is tough though, it is a logic that admits contradiction so straightaway most logicians are clueless in how to handle it.
I do not think the last sentence is an adequate description of what linear logic is, or how it's used and understood.
It is interesting in itself, I admit that. But I don't see how it would admit contradiction, or how logicians are clueless how to handle it. It is in fact well understood, and used in many places, e.g. computer science [1,2]
those interested in the link between math and literature might be interested in the link between narratives and linear logic.