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.
This series after the War was revitalised as the well known logical journal.
- 2.
- 3.
In 1926 he was 20 years old.
- 4.
- 5.
The two examples provided in the footnote in [19] show only propositional proofs.
- 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.
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.
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.
More detailed comparison of both approaches may be found in Hazen and Pelletier [15].
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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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