Journal of Automated Reasoning

, Volume 62, Issue 1, pp 127–167 | Cite as

Goal-Oriented Proof-Search in Natural Deduction for Intuitionistic Propositional Logic

  • Mauro Ferrari
  • Camillo FiorentiniEmail author


We address the problem of proof-search in the natural deduction calculus for Intuitionistic propositional logic. Our aim is to improve the usual proof-search procedure where introduction rules are applied upwards and elimination rules downwards. In particular, we introduce \(\mathbf {Nbu} \), a variant of the usual natural deduction calculus for Intuitionistic Propositional Logic, and we show that it can be used as a base for a goal-oriented proof-search procedure. We also show that the implementation of our proof-search procedure is competitive with those based on sequent or tableaux calculi.


Natural deduction Intuitionistic propositional logic Proof-search procedures 

Mathematics Subject Classification

03B20 03F07 03B35 



We thank the anonymous reviewers for their valuable remarks which helped us to improve the paper.

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Authors and Affiliations

  1. 1.Dipartimento di Scienze Teoriche e ApplicateUniversità degli Studi dell’InsubriaVareseItaly
  2. 2.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly

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