From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction

Jan von Plato

Bulletin of the Section of Logic (2017)

  • Volume: 46, Issue: 1/2
  • ISSN: 0138-0680

Abstract

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The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.

How to cite

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Jan von Plato. "From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction." Bulletin of the Section of Logic 46.1/2 (2017): null. <http://eudml.org/doc/295558>.

@article{JanvonPlato2017,
abstract = {The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.},
author = {Jan von Plato},
journal = {Bulletin of the Section of Logic},
keywords = {proof systems; linear natural deduction; Gentzen; Jaśkowski},
language = {eng},
number = {1/2},
pages = {null},
title = {From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction},
url = {http://eudml.org/doc/295558},
volume = {46},
year = {2017},
}

TY - JOUR
AU - Jan von Plato
TI - From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction
JO - Bulletin of the Section of Logic
PY - 2017
VL - 46
IS - 1/2
SP - null
AB - The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.
LA - eng
KW - proof systems; linear natural deduction; Gentzen; Jaśkowski
UR - http://eudml.org/doc/295558
ER -

References

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  1. [1] H. Curry, (1965) Remarks on inferential deduction, [in:] A. Tyminiecka (ed.), Contributions to Logic and Methodology in Honor of J. M. Bochenski, North-Holland (1965), pp. 45–72. 
  2. [2] G. Gentzen, Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 39 (1934-35), pp. 176–210 and 405-431. 
  3. [3] S. Jaśkowski, On the rules of supposition in formal logic (1934), as reprinted [in:] S. McCall (ed.), Polish Logic 1920–1939, pp. 232–258, Oxford U. P. 1967. 
  4. [4] J. von Plato, Natural deduction with general elimination rules, Archive for Mathematical Logic, vol. 40 (2001), pp. 541–567. 
  5. [5] J. von Plato, Elements of Logical Reasoning, Cambridge, 2013. 
  6. [6] D. Prawitz, ABC i Symbolisk Logik, Mimeographed compendium. Later expanded and printed editions with Bokförlaget Thales, 1973. 

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