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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.

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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]

[1] https://en.m.wikipedia.org/wiki/Linear_logic

[2] https://plato.stanford.edu/entries/logic-linear/

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