Date: 31 May 2005

The basic logic of proofs

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Abstract

Propositional Provability Logic was axiomatized in [5]. This logic describes the behaviour of the arithmetical operator “y is provable”. The aim of the current paper is to provide propositional axiomatizations of the predicate “x is a proof of y”by means of modal logic, with the intention of meeting some of the needs of computer science.

Supported by the Swiss Nationalfonds (project 21-27878.89) during a stay at the University of Berne in January 1992.
Financed by the Union Bank of Switzerland (UBS/SBG) and by the Swiss Nationalfonds (projects 21-27878.89 and 20-32705.91).
The authors wish to thank the anonymous referee for his valuable suggestions.