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Proof Normalisation in a Logic Identifying Isomorphic Propositions

Authors Alejandro Díaz-Caro , Gilles Dowek

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Author Details

Alejandro Díaz-Caro
  • Instituto de Ciencias de la Computación (CONICET-Universidad de Buenos Aires), Ciudad Autónoma de Buenos Aires, Argentina
  • Universidad Nacional de Quilmes, Bernal (Buenos Aires), Argentina
Gilles Dowek
  • Inria, LSV, ENS Paris-Saclay, France

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Alejandro Díaz-Caro and Gilles Dowek. Proof Normalisation in a Logic Identifying Isomorphic Propositions. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 14:1-14:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We define a fragment of propositional logic where isomorphic propositions, such as A wedge B and B wedge A, or A ==> (B wedge C) and (A ==> B) wedge (A ==> C) are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Type theory
  • Mathematics of computing → Lambda calculus
  • Simply typed lambda calculus
  • Isomorphisms
  • Logic
  • Cut-elimination
  • Proof-reduction


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