Jaśkowski and Gentzen Approaches to Natural Deduction and Related Systems

It is well known that Jaśkowski and Gentzen independently published their results concerning Natural Deduction (ND for short) in 1934. But details of their work are not well known, as one can see when faced with many publications concerning ND. In what follows we briefly describe two systems of ND due to (1929), (1934) and (1934), then the Sequent Calculus (SC) from (1934) and finally one more ND system from (1936). We focus on similarities and differences in the approaches of both authors. Moreover we try to show their influence (not always clearly recognised) on further works on ND and related systems. This picture is necessarily some-what sketchy and far from being complete so we would like to apologise in advance to the many logicians who are not even mentioned in this paper, but should be.

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