Studia Logica

, Volume 105, Issue 3, pp 649–664 | Cite as

Rasiowa–Harrop Disjunction Property



We show that there is a purely proof-theoretic proof of the Rasiowa–Harrop disjunction property for the full intuitionistic propositional calculus (\(\mathbf {IPC}\)), via natural deduction, in which commuting conversions are not needed. Such proof is based on a sound and faithful embedding of \(\mathbf {IPC}\) into an atomic polymorphic system. This result strengthens a homologous result for the disjunction property of \(\mathbf {IPC}\) (presented in a recent paper co-authored with Fernando Ferreira) and answers a question then posed by Pierluigi Minari.


Rasiowa–Harrop disjunction property Intuitionistic propositional calculus Predicative polymorphism Natural deduction Strong normalization 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Departamento de MatemáticaFaculdade de Ciências da Universidade de LisboaLisbonPortugal

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