Duality in Intuitionistic Propositional Logic

Author Paweł Urzyczyn

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Author Details

Paweł Urzyczyn
  • Institute of Informatics, University of Warsaw, Poland

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Paweł Urzyczyn. Duality in Intuitionistic Propositional Logic. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 11:1-11:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


It is known that provability in propositional intuitionistic logic is Pspace-complete. As Pspace is closed under complements, there must exist a Logspace-reduction from refutability to provability. Here we describe a direct translation: given a formula φ, we define ̅φ so that ̅φ is provable if and only if φ is not.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Constructive mathematics
  • Theory of computation → Complexity theory and logic
  • Intuitionistic logic
  • Complexity


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