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Reasoning About Knowledge In Linear Logic: Modalities and Complexity

  • Mathieu Marion
  • Mehrnouche Sadrzadeh
Part of the Logic, Epistemology, And The Unity Of Science book series (LEUS, volume 1)

Abstract

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.

Keywords

Intuitionistic Logic Linear Logic Epistemic Logic Sequent Calculus Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Mathieu Marion
    • 1
  • Mehrnouche Sadrzadeh
    • 1
  1. 1.Département de philosophieUniversité du Québec à Montréal, C.P. 8888, Succursale Centre-VilleMontréalQuébec

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