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An Analytic Propositional Proof System on Graphs
[article]

2021
*
arXiv
*
pre-print

In this paper we present a

arXiv:2012.01102v3
fatcat:wjbgni4unfhs3ohxwp2253firq
*proof**system*that operates on graphs instead of formulas. ... For our*proof**system*we show the admissibility of cut and a generalization of the splitting property. ... The main challenge is to design an analytic*propositional**proof**system*. ...##
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Reflection principles, propositional proof systems, and theories
[article]

2020
*
arXiv
*
pre-print

In this paper we will revisit some results about the reflection principles for

arXiv:2007.14835v1
fatcat:rxl2clf4cvgv5aepilk5zya3x4
*propositional**proofs**systems*using a finer scale of reflection principles. ... We will also survey some results about arithmetical theories and*proof**systems*associated with them. ... Basic concepts 2.1*Propositional**proof**systems*In this paper "a*proof**system*" will always mean a*proof**system*for classical*propositional*logic. ...##
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Propositional proof systems and fast consistency provers
[article]

2020
*
arXiv
*
pre-print

Krajíček and Pudlák proved that the existence of an optimal

arXiv:2004.05431v1
fatcat:3bgdita2nfa3bhnvpvra4alaze
*propositional**proof**system*is equivalent to the existence of a fast consistency prover. ... A fast consistency prover is a consistent poly-time axiomatized theory that has short*proofs*of the finite consistency statements of any other poly-time axiomatized theory. ... A pps P is an optimal*propositional**proof**system*, an opps for short, if P ≥ Q for any*propositional**proof**system*Q. It is easy to see that a pps is optimal whenever it is super. ...##
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A Propositional Proof System for Log Space
[chapter]

2005
*
Lecture Notes in Computer Science
*

The

doi:10.1007/11538363_35
fatcat:aejccivfb5hbdf34obkw43jjhu
*proof**system*G * 0 of the quantified*propositional*calculus corresponds to N C 1 , and G * 1 corresponds to P , but no formula-based*proof**system*that corresponds log space reasoning has ever been ... The*proof**system*G * is a tree-like*proof**system*for the quantified*propositional*calculus based on Gentzen's LK [2] . ... The*Proof**System*The*proof**system*P K is the Gentzen-style sequent calculus for*propositional*logic [5, 6] . The initial sequents are ⊥ →, → , and A → A, for any*propositional*formula A. ...##
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Disjoint NP-Pairs from Propositional Proof Systems
[chapter]

2006
*
Lecture Notes in Computer Science
*

We exhibit structural properties of

doi:10.1007/11750321_23
fatcat:6legyood6nat3lx3rgj7tcmoue
*proof**systems*which make the previously defined canonical NP-pairs of these*proof**systems*hard or complete for DNPP(P ). ... For a*proof**system*P we introduce the complexity class DNPP(P ) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the*proof**system*P . ... By using*Proposition*24 we can also establish a version of*Proposition*30 for other line based*proof**systems*which admit efficient deduction.*Proposition*32 . 32 Let P be a*proof**system*. ...##
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Propositional Proof Systems and Fast Consistency Provers

2007
*
Notre Dame Journal of Formal Logic
*

Krajíček and Pudlák proved in [5] that the existence of an optimal

doi:10.1305/ndjfl/1187031410
fatcat:6lkusc3dujbkvbb2dpi2d4roki
*propositional**proof**system*is equivalent to the existence of a fast consistency prover. ... A fast consistency prover is a consistent poly-time axiomatized theory that has short*proofs*of the finite consistency statements of any other poly-time axiomatized theory. ... A pps P is an optimal*propositional**proof**system*, an opps for short, if P ≥ Q for any*propositional**proof**system*Q. It is easy to see that a pps is optimal whenever it is super. ...##
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The relative efficiency of propositional proof systems

1979
*
Journal of Symbolic Logic (JSL)
*

We are interested in studying the length of the shortest

doi:10.2307/2273702
fatcat:2ckq23nvuzb25pkrziawtzrrym
*proof*of a*propositional*tautology in various*proof**systems*as a function of the length of the tautology. ... The smallest upper bound known for this function is exponential, no matter what the*proof**system*. ...*PROPOSITION*. If a*proof**system*f2 for L p-simulates a polynomially bounded*proof**system*f1 for L, then f2 is also polynomially bounded. ...##
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A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic
[article]

2019
*
arXiv
*
pre-print

We additionally investigate

arXiv:1905.06143v2
fatcat:uuia4dlgpfcknmmzu3ozc7jlpy
*proof*-search strategies in the cyclic*system*for the fragment of PDL without tests. ... A finitarily representable cyclic*system*, G3PDL^ω, is then given. We show that both are sound and complete with respect to standard models of PDL and, further, that G3PDL^∞ is cut-free complete. ... This*proof**system*has two important features. The first is that it is a labelled*proof**system*. ...##
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Canonical Disjoint NP-Pairs of Propositional Proof Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

A

doi:10.1007/11549345_35
fatcat:p53fmhpbkrgl3nhohfixm3zovq
*proof**system*is optimal if it simulates every other*propositional**proof**system*. ... Although it is an open question whether optimal*proof**systems*exist, as we stated above, Razborov showed that if there exists an optimal*propositional**proof**system*f , then its canonical pair is a complete ... Specifically, Razborov [Raz94] defined the canonical disjoint NP-pair, (SAT * , REF f ), for every*propositional**proof**system*f , and he showed that if there exists an optimal*propositional**proof**system*...##
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The Deduction Theorem for Strong Propositional Proof Systems

2008
*
Theory of Computing Systems
*

even polynomially bounded

doi:10.1007/s00224-008-9146-6
fatcat:tn76ejrx25fp3j6wg4i725v7c4
*proof**systems*. ... This paper focuses on the deduction theorem for*propositional*logic. ... Preliminaries*Propositional**Proof**Systems*. ...##
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The Model-Theoretic Expressiveness of Propositional Proof Systems

2017
*
Leibniz International Proceedings in Informatics
*

The Model-Theoretic Expressiveness of

doi:10.18154/rwth-2020-09507
fatcat:s4ojkqjawbf4pf5wmi2xbnq6em
*Propositional**Proof**Systems*in such*systems*, and usually have completeness for relevant fragments of*propositional*logic, such as Horn-logic or 2-CNF. ... , provably require*proofs*of super-polynomial size even in quite strong*proof**systems*. ... Since Cook and Reckhow [14] made the notion of an efficient*propositional**proof**system*precise, a huge body of research on the power of various*propositional**proof**system*has been established. ...##
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Canonical disjoint NP-pairs of propositional proof systems

2007
*
Theoretical Computer Science
*

A

doi:10.1016/j.tcs.2006.10.006
fatcat:a7nnhnetbvcbhngebbzbdveyfe
*proof**system*is optimal if it simulates every other*propositional**proof**system*. ... Although it is an open question whether optimal*proof**systems*exist, as we stated above, Razborov showed that if there exists an optimal*propositional**proof**system*f , then its canonical pair is a complete ... Specifically, Razborov [Raz94] defined the canonical disjoint NP-pair, (SAT * , REF f ), for every*propositional**proof**system*f , and he showed that if there exists an optimal*propositional**proof**system*...##
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The Deduction Theorem for Strong Propositional Proof Systems
[chapter]

2007
*
Lecture Notes in Computer Science
*

even polynomially bounded

doi:10.1007/978-3-540-77050-3_20
fatcat:2b7dlniphnfv3ofvduq62i3tce
*proof**systems*. ... This paper focuses on the deduction theorem for*propositional*logic. ... Preliminaries*Propositional**Proof**Systems*. ...##
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Optimal proof systems for propositional logic and complete sets
[chapter]

1998
*
Lecture Notes in Computer Science
*

whose range is the set of tautologies in

doi:10.1007/bfb0028583
fatcat:dftglwhnqfbvzprqbdgwd6qtt4
*Propositional*Logic (TAUT), is called a*proof**system*. ...*proof**systems*exist. ... A*propositional**proof**system*(or just*proof**system*) is a polynomial time computable function h : ! ...##
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Propositional Proofs in Frege and Extended Frege Systems (Abstract)
[chapter]

2015
*
Lecture Notes in Computer Science
*

We discuss recent results on the

doi:10.1007/978-3-319-20297-6_1
fatcat:vjlmno4i3bc3tgdds37zgc7f7m
*propositional**proof*complexity of Frege*proof**systems*, including some recently discovered quasipolynomial size*proofs*for the pigeonhole principle and the Kneser-Lovász ... Frege*systems*are arguably the most important fully expressive, sound and complete*proof**system*for*propositional**proofs*: Frege*proofs*are "textbook"*propositional**proof**systems*usually formulated with ... for*propositional*logic and as an underpinning for stronger*systems*such as SMT solvers, modal logics and first-order logics. ...
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