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From Classical Extensional Higher-Order Tableau to Intuitionistic Intentional Natural Deduction

16 pagesPublished: May 27, 2013

Abstract

We define a translation that maps higher-order formulas provable in a classical extensional setting to semantically equivalent formulas provable in an intuitionistic intensional setting. For the classical extensional higher-order proof system we define a Henkin-complete tableau calculus. For the intuitionistic intensional higher-order proof system we give a natural deduction calculus. We prove that tableau provability of a formula implies provability of a translated formula in the natural deduction calculus. Implicit in this proof is a method for translating classical extensional tableau refutations into intuitionistic intensional natural deduction proofs.

Keyphrases: analytic tableaux, classical, extensional, higher-order logic, intensional, Intuitionistic, proof theory, simple type theory, tableaux

In: Jasmin Christian Blanchette and Josef Urban (editors). PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving, vol 14, pages 27--42

Links:
BibTeX entry
@inproceedings{PxTP2013:From_Classical_Extensional_Higher_Order,
  author    = {Chad E. Brown and Christine Rizkallah},
  title     = {From Classical Extensional Higher-Order Tableau to Intuitionistic Intentional Natural Deduction},
  booktitle = {PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving},
  editor    = {Jasmin Christian Blanchette and Josef Urban},
  series    = {EPiC Series in Computing},
  volume    = {14},
  pages     = {27--42},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/Ps},
  doi       = {10.29007/8p9q}}
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