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Erkenntnis

, Volume 43, Issue 1, pp 81–109 | Cite as

A pragmatic interpretation of intuitionistic propositional logic

  • Carlo Dalla Pozza
  • Claudio Garola
Article

Abstract

We construct an extensionP of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) ofP;rfs preceded by theassertion sign ⊢ constituteelementary assertive formulas ofP, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf ofP is endowed with atruth value defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity inP and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part ofP and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic.

Keywords

Classical Problem Classical Logic Propositional Calculus Intuitionistic Logic Constructive Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Carlo Dalla Pozza
    • 1
  • Claudio Garola
    • 1
  1. 1.Dipartimento Di FisicaUniversita Degli Studi Di LecceLecceItaly

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