2020; Physical and Mathematical Sciences, 54(3 (253): 127–136
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ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS

Anahit Chubaryan*

Received: 2025-01-27 · Published: 2020-12-15

© 2020 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS
Author
Anahit Chubaryan
Published
2020-12-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2020.54.3.127

Abstract

We investigate the relations between the proof lines of non-minimaltautologies and its minimal tautologies for the Frege systems, the sequent systemswith cut rule and the systems of natural deductions of classical and nonclassicallogics. We show that for these systems there are sequences of tautologiesψn,every one of which has unique minimal tautologiesφnsuch that for eachntheminimal proof lines ofφnare an order more than the minimal proof lines ofψn
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