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Stanisław Jaśkowski and Natural Deduction Systems

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The Lvov-Warsaw School. Past and Present

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

In 1934 Stanisław Jaśkowski published his groundbreaking work on natural deduction. At the same year Gerhard Gentzen also published a work on the same topic. We aim at presenting (three versions) of Jaśkowski’s system and provide a comparison with Gentzen’s approach. We also try to outline the influence of Jaśkowski’s approach on the later development of natural deduction systems.

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Notes

  1. 1.

    This series after the War was revitalised as the well known logical journal.

  2. 2.

    This part is an excerpt from more detailed considerations contained in my [16] and [17].

  3. 3.

    In 1926 he was 20 years old.

  4. 4.

    Cf. historical remarks in Bencivenga [4]; in [5] he also pointed out that Jaśkowski’s system may be easily changed into a system of free logic.

  5. 5.

    The two examples provided in the footnote in [19] show only propositional proofs.

  6. 6.

    By the way, an innovation introduced by Jaśkowski (i.e. prefixes) may be classified in a different way; we may treat his second version as the first example of ND defined not on formulae but on labelled formulae.

  7. 7.

    Although this approach is by no means the only one possible. For example, in [16] we proposed a different general strategy of proving soundness for any ND system in Jaśkowski format.

  8. 8.

    The history of successive versions of Copi’s ND with numerous mistaken formulation of this rule is particularly instructive—see e.g. Annellis [1].

  9. 9.

    More detailed comparison of both approaches may be found in Hazen and Pelletier [15].

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Authors and Affiliations

  1. Department of Logic, University of Lodz, Lodz, Poland

    Andrzej Indrzejczak

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  1. Andrzej Indrzejczak
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Correspondence to Andrzej Indrzejczak .

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  1. Department of Fundamental Mathematics, UNED, Madrid, Spain

    Ángel Garrido

  2. Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland

    Urszula Wybraniec-Skardowska

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Indrzejczak, A. (2018). Stanisław Jaśkowski and Natural Deduction Systems. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_33

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