scholarly journals On Some Universal Propositional Proof Systems for Many-Valued Logic

2020 ◽  
pp. 21-28
Author(s):  
Artur Khamisyan
Keyword(s):  
Proof System ◽  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

Some uniform Hilbert-like propositional proof system is suggested for all versions of many-valued logic to apply them to 3 versions of 3-valued logic, two of which have only one designated value, and the last one has two designated values

Dual weak pigeonhole principle, pseudo-surjective functions, and provability of circuit lower bounds

2004 ◽  
Vol 69 (1) ◽  
pp. 265-286 ◽  
Author(s):  
Jan Krajíček
Keyword(s):  
Lower Bounds ◽  
Sparse Matrix ◽  
Proof System ◽  
Direct Construction ◽  
Proof Systems ◽  
Circuit Lower Bounds ◽  
Iterable Functions ◽  
Propositional Proof Systems ◽  
Propositional Proof ◽  
Surjective Function

AbstractThis article is a continuation of our search for tautologies that are hard even for strong propositional proof systems like EF. cf. [14, 15]. The particular tautologies we study, the τ-formulas. are obtained from any /poly map g; they express that a string is outside of the range of g, Maps g considered here are particular pseudorandom generators. The ultimate goal is to deduce the hardness of the τ-formulas for at least EF from some general, plausible computational hardness hypothesis.In this paper we introduce the notions of pseudo-surjective and iterable functions (related to free functions of [15]). These two properties imply the hardness of the τ-formulas from the function but unlike the hardness they are preserved under composition and iteration. We link the existence of maps with these two properties to the provability of circuit lower bounds, and we characterize maps g yielding hard τ-formulas in terms of a hitting set type property (all relative to a propositional proof system). We show that a proof system containing EF admits a pseudo-surjective function unless it simulates a proof system WF introduced by Jeřábek [11]. an extension of EF.We propose a concrete map g as a candidate function possibly pseudo-surjective or free for strong proof systems. The map is defined as a Nisan-Wigderson generator based on a random function and on a random sparse matrix. We prove that it is iterable in a particular way in resolution, yielding the output/input ratio n3 −ε (that improves upon a direct construction of Alekhnovich et al. [2]).

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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