Propositional proof systems, the consistency of first order theories and the complexity of computations

1989 ◽  
Vol 54 (3) ◽  
pp. 1063-1079 ◽  
Author(s):  
Jan Krajíček ◽  
Pavel Pudlák
Keyword(s):  
First Order ◽  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

AbstractWe consider the problem about the length of proofs of the sentences saying that there is no proof of contradiction in S whose length is < n. We show the relation of this problem to some problems about propositional proof systems.

Disjoint NP-Pairs and Propositional Proof Systems

2014 ◽  
Vol 45 (4) ◽  
pp. 59-75 ◽  
Author(s):  
C. Glaßer ◽  
A. Hughes ◽  
A. L. Selman ◽  
N. Wisiol
Keyword(s):  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

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

2020 ◽  
Vol 54 (3 (253)) ◽  
pp. 127-136
Author(s):  
Anahit A. Chubaryan ◽  
Arsen A. Hambardzumyan
Keyword(s):  
Cut Rule ◽  
Proof Systems ◽  
Nonclassical Logics ◽  
Frege Systems ◽  
Sequent Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies ψn, every one of which has unique minimal tautologies φn such that for each n the minimal proof lines of φn are an order more than the minimal proof lines of ψn.

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