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A Finite-Model-Theoretic View on Propositional Proof Complexity
[article]

2018
*
arXiv
*
pre-print

We establish new, and surprisingly tight, connections between

arXiv:1802.09377v2
fatcat:uliyrq6kgjh3fnskxcuq6kq7py
*propositional**proof**complexity*and*finite**model*theory. ... By exploring these connections further, we establish*finite*-*model*-*theoretic*tools for proving lower bounds for the polynomial calculus over the rationals and over*finite*fields. ... bounds*on*the*complexity*of*proofs*(size and/or width/degree) for families of*propositional*formulas using arguments from*finite**model*theory. ...##
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A Finite-Model-Theoretic View on Propositional Proof Complexity

2019

Our novel, uniform approach to these lower bounds, Vol. 15:1

doi:10.18154/rwth-2019-00950
fatcat:3pbaatf56vctfmvsbhhwo4ncae
*A**FINITE*-*MODEL*-*THEORETIC**VIEW**ON**PROPOSITIONAL**PROOF**COMPLEXITY*4:5 also suggests*a*way to capture*a*common weakness of many*propositional**proof*...*VIEW**ON**PROPOSITIONAL**PROOF**COMPLEXITY*4:3 4:4 E. ...*VIEW**ON**PROPOSITIONAL**PROOF**COMPLEXITY*4:21 Vol. 15:1*A**FINITE*-*MODEL*-*THEORETIC**VIEW**ON**PROPOSITIONAL**PROOF**COMPLEXITY*4:41 Vol. 15:1*A**FINITE*-*MODEL*-*THEORETIC**VIEW**ON**PROPOSITIONAL**PROOF**COMPLEXITY*...##
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On the Asymptotic Nullstellensatz and Polynomial Calculus Proof Complexity

2008
*
Logic in Computer Science
*

translation of any FO formula (that fails in all

doi:10.1109/lics.2008.30
dblp:conf/lics/Riis08
fatcat:hij6dbovtvgirjnlph24ztbifu
*finite**models*), has degree*proof**complexity*over fields of characteristic p, that behave in 4 distinct ways: (i) The degree*complexity*is bound by*a*constant ... (ii) The degree*complexity*is at least l(n) for all values of n. (iii) The degree*complexity*is bound by*a*constant*on*an infinite set S, and is at least l(n)*on*the complement N \ S. ... Another interesting question is if it possible to extend Krajicek's*model**theoretic*approach to include*model**theoretical*criteria that correspond to the fluctuating NS-degree (PC-degree) refutation*complexity*...##
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Page 1543 of Mathematical Reviews Vol. 58, Issue 3
[page]

1979
*
Mathematical Reviews
*

The aim of this note is to prove that for any wif D of E there is

*a**finite*set of wffs having properties similar to some properties of*a**finite**model*.” 02D _*Proof*theory See also 10293, 10332, 10334, ... - sions of formalized w-consistency; formalized completeness no- tions; unique and explicitly definable fixed points*on**propositions*; conservation results based*on*formalized consistency;*model*-theo- retic ...##
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On purity and applications to coderived and singularity categories
[article]

2014
*
arXiv
*
pre-print

Our main tools are (

arXiv:1412.1615v1
fatcat:ieemca6vqncsnioxiuvgdqwkoi
*a*)*model**theoretic*techniques and (b)*a*systematic study of the pure derived category of an additive*finitely*accessible category. ... Given*a*locally coherent Grothendieck category G, we prove that the homotopy category of*complexes*of injective objects (also known as the coderived category of G) is compactly generated triangulated. ... Since each perfect*complex*has*finitely*presentable cohomology by the above*proposition*, we can*view*D perf (fp G) as*a*thick subcategory of D b (fp G). ...##
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Page 1472 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

“In this paper, we introduce the notion of

*a**model*-*theoretic*property and formulate general principles of defining lists of prop- erties that are important in constructions of*finitely*axiomatizable theories ...*On*the basis of these results, existence theorems and estimates for the algorithmic*complexity*of natural semantic classes of sentences were also obtained. ...##
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Page 8487 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

Special topics include

*a*chapter*on*transducers (*finite*state automata with output strings) and*a*section*on*random access machines (*modelling*the classical von Neumann-style computer), the latter shown ... the isomorphism front (25-41); Paul Beame and Toniann Pitassi,*Propositional**proof**complexity*: past, present, and future (42-70); Neil Immer- man, Progress in descriptive*complexity*(71-82); Jack H. ...##
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Reasoning about infinite computation paths

1983
*
24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
*

We investigate extensions of tenlporal logic by

doi:10.1109/sfcs.1983.51
dblp:conf/focs/WolperVS83
fatcat:5j7n26m36vbyfcri4zfpc3qque
*finite*automata*on*infinite words. ... There are three different types of acceptance conditions (*finite*, looping and repeating) that*one*can give for these*finite*automata. This gives rise to three different logics. ... automata-*theoretic*point of*view*. ...##
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The prospects for mathematical logic in the twenty-first century
[article]

2002
*
arXiv
*
pre-print

The areas of recursion theory,

arXiv:cs/0205003v1
fatcat:i3rpwamx6nfdzi5kqkrt34twkq
*proof*theory and logic for computer science,*model*theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin for their comments*on*an earlier draft of this section. ... More broadly, much work in weak first-order theories and*on**propositional**proof**complexity*is motivated by the desire to find*a*logical*proof*that P = NP. Future problems in*proof**complexity*. ...##
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Expressing versus Proving: Relating Forms of Complexity in Logic

2010
*
Journal of Logic and Computation
*

In

doi:10.1093/logcom/exq008
fatcat:lpla27ghunf5fmmvdanaoasaei
*finite**model*theory, it is the*complexity*of describing properties, whereas in*proof**complexity*it is the*complexity*of proving properties in*a**proof*system. ... In particular, we show how the*complexity*of logics in the setting of*finite**model*theory is used to obtain results in bounded arithmetic, stating which functions are provably total in certain weak systems ... The results*on*connections between*finite**model*theory and bounded arithmetic mentioned here come from my joint work with Stephen Cook (which resulted in my PhD thesis). ...##
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Page 3542 of Mathematical Reviews Vol. , Issue 91G
[page]

1991
*
Mathematical Reviews
*

The author

*views*this system as*a*use- ful bridge between the tree*proof*rules for*propositional*logic and those for first-order logic. ... Summary: “We define minimal consequence in sentential logic and present*a*number of results of*a**model*-*theoretic*and recursion-*theoretic*character about this newly introduced nonmonotonic con- sequence ...##
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A Criticism of Kripke's Semantic for Intuitionistic Logic

2016
*
O que nos faz pensar
*

This note aims to examine critically Kripke's semantics for

doaj:1e58cf2d10594ad599a45c0a9b49d64a
fatcat:kg4y6ev2jffdfkc4dyibhtnxle
*propositional*intuitionistic logic. ... Kripke's semantic is extensionally correct with respect to*propositional*intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. ...*Proof*: straightforward induction*on*the*complexity*of*A*. ...##
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The Prospects for Mathematical Logic in the Twenty-First Century

2001
*
Bulletin of Symbolic Logic
*

The areas of recursion theory,

doi:10.2307/2687773
fatcat:mdamfnfy55atzalpnh7ul3xv6m
*proof*theory and logic for computer science,*model*theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin for their comments*on*an earlier draft of this section. ... More broadly, much work in weak first-order theories and*on**propositional**proof**complexity*is motivated by the desire to find*a*logical*proof*that P j-NP. Future problems in*proof**complexity*. ...##
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Yes fellows, most human reasoning is complex

2007
*
Synthese
*

It contains

doi:10.1007/s11229-007-9268-4
fatcat:if5ehjgolba7pat3vw3gp25nze
*a*description of the standard format of adaptive logics, analyses the notion of dynamic*proof*required by those logics, discusses the means to turn such*proofs*into demonstrations, and argues ... that, notwithstanding their formal*complexity*, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense ...*A**proof*-*theoretic*procedure was devised, first for*propositional*CL by Batens and Provijn (2001) , and next for*propositional*CLuN r by Batens (2005) . ...##
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Page 6170 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

(2) What is the

*complexity*of deciding whether M is an undominated*model*of*a*pair (I',*A*), where I is*a**propositional*formula in conjunctive normal form and*A*is*a*set of 2-literal defaults? ... H. 03 MATHEMATICAL LOGIC AND FOUNDATIONS 6170 Papadimitriou: (1) What is the*complexity*of finding*a*minimal*model*of*a**propositional*formula when all the letters are mini- mized? ...
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