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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

Funding

Partially supported by ECOS-Sud A17C03, PICT 2015-1208, and the French-Argentinian laboratory SINFIN.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.FSCD.2019.14

Abstract

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
Keywords
  • Simply typed lambda calculus
  • Isomorphisms
  • Logic
  • Cut-elimination
  • Proof-reduction

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Related Versions

  • A variant of the system presented in this paper, has been published in https://arxiv.org/abs/1303.7334v1 (LSFA 2012 [Alejandro Díaz-Caro and Gilles Dowek, 2013]), with a sketch of a subject reduction proof but no normalisation or consistency proofs.

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