Reasoning About Knowledge In Linear Logic: Modalities and Complexity

In this paper, we briefly argue, following ideas set forth by Jacques Dubucs, for a radical version of anti-realism and claim that it leads to the adoption of a ‘substructural’ logic, linear logic. We further argue that, in order to avoids problems such as that of ‘omniscience’, one should develop an epistemic linear logic, which would be weak enough so that the agents could still be described as omniscient, while this would not be problematic anymore. We then examine two possible ways to develop an epistemic linear logic, and eliminate one. We conclude on some remarks about complexity. The paper contains a coding in Coq of fragments of modal linear logic and a proof of the ‘wise men’ puzzle.

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