ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS

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Submitted: 2025-01-27; Published: 2025-01-27

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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