What is a Logic, and What is a Proof?

Lutz Straßurger
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Lutz Straßurger: École Polytechnique — LIX, INRIA Futurs, Projet Parsifal

A chapter in Logica Universalis, 2007, pp 135-152 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-7643-8354-1_8

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