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What is a Logic, and What is a Proof?

  • Lutz Straßurger

Abstract

I will discuss the two problems of how to define identity between logics and how to define identity between proofs. For the identity of logics, I propose to simply use the notion of preorder equivalence. This might be considered to be folklore, but is exactly what is needed from the viewpoint of the problem of the identity of proofs: If the proofs are considered to be part of the logic, then preorder equivalence becomes equivalence of categories, whose arrows are the proofs. For identifying these, the concept of proof nets is discussed.

Keywords

Modal Logic Classical Logic Category Theory Deductive System Intuitionistic Logic 
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

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Lutz Straßurger
    • 1
  1. 1.INRIA Futurs, Projet ParsifalÉcole Polytechnique — LIXPalaiseau CedexFrance

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