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How to lie without being (easily) convicted and the lengths of proofs in propositional calculus
[chapter]

1995
*
Lecture Notes in Computer Science
*

We shall describe two general methods for proving lower bounds on

doi:10.1007/bfb0022253
fatcat:msdzmo6nqrf2barxsxxsiqob2u
*the**lengths**of**proofs**in**propositional**calculus**and*give examples*of*such lower bounds. ... One*of**the*methods is based on interactive*proofs*where one player is claiming that he has a falsifying assignment for a tautology*and**the*second player is trying*to**convict*him*of*a*lie*. ... What is he saying is a blatant*lie*for you, but*the*judge,*and*especially*the*jury, need a*proof**without*any doubts. ...##
###
Page 3437 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
*
Mathematical Reviews
*

3437
98f:03049 03F20 03B05 03D15 68Q15 Pudlak, Pavel (CZ-AOS; Prague); Buss, Samuel R. (1-UCSD; La Jolla, CA)

*How**to**lie**without**being*(*easily*)*convicted**and**the**lengths**of**proofs**in**propositional**calculus*... Summary: “We describe two general methods for proving lower bounds on*the**lengths**of**proofs**in**propositional**calculus**and*give examples*of*such lower bounds. ...##
###
Page 2545 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

Buss,

*How**to**lie**without**being*(*easily*)*convicted**and**the**lengths**of**proofs**in**propositional*calcu- lus (151-162); Bruno Courcelle, Monadic second-order logic*and*linear orderings*of*finite structures ... {*The*papers are*being*reviewed individually. } 98d:68015 68-06 68045 68R15 * Developments*in*language theory. II. At*the*crossroads*of*mathematics, computer science*and*biology. ...##
###
Duplication of directed graphs and exponential blow up of proofs

1999
*
Annals of Pure and Applied Logic
*

*Proofs*are two-dimensional objects

*and*di erences

*in*

*the*behavior

*of*their cut elimination can often

*be*accounted for by di erences

*in*their two-dimensional structure. ... Our purpose is

*to*determine geometrical conditions on

*the*graphs

*of*

*proofs*

*to*explain

*the*expansion

*of*

*the*size

*of*

*proofs*after cut elimination. ... It is

*the*Gentzen Cut Elimination Theorem [12] which says that any

*proof*

*in*

*the*sequent

*calculus*with cuts can always

*be*transformed

*in*some e ective way into a

*proof*

*without*cuts. ...

##
###
The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics

2013
*
Journal for the History of Analytical Philosophy
*

*In*

*the*decade following

*the*publication

*of*

*the*Contributions, he made a series

*of*mathematical breakthroughs, discovering

*how*epsilontics could

*be*used

*to*provide a foundation for

*the*infinitesimal

*calculus*... So, for example, from

*the*

*propositions*:

*The*point is

*the*simple

*in*space, it is

*the*boundary

*of*a line

*and*itself no part

*of*a line, it has nei-ther extension

*in*

*length*, breadth, nor depth, etc., anyone ... Kant limits its use

*to*phenomena, but, as Bolzano remarks, he tacitly assumes it

*in*claiming things

*in*themselves

*to*

*be*

*the*ground

*of*phenomena. ...

##
###
A Physical Quantum Model in a Smooth Topos
[article]

2002
*
arXiv
*
pre-print

governed by

arXiv:quant-ph/0202079v1
fatcat:omyuxcoiazchzeigj7yjrr7xeq
*the*less restrictive intuitionistic logic,*and*known*to*support*the*theory*of*synthetic differential geometry. ...*In*exploring some*of**the*aspects*of*construction*of*a simple quantum-mechanical system*in*a mathematical universe different from that represented by set theory, we show that more thought*and*a better appreciation ... It turns out that it is precisely*the*universal validity*of**the*law*of*excluded middle*in*CL that blocks any attempts*to*formulate*calculus**without*limits. ...##
###
The Development of Mathematical Logic from Russell to Tarski, 1900–1935
[chapter]

2009
*
The Development of Modern Logic
*

Principia, despite its

doi:10.1093/acprof:oso/9780195137316.003.0029
fatcat:ygiplet5oraf7fza6fsmf5j5ly
*length*, does not even manage*to*treat*the**calculus**in*full detail). ... He introduces*the*method as follows:*In*each*of**the*following independence*proofs*,*the**calculus*will*be*reduced*to*a finite system (a finite group*in**the*wider sense*of**the*word [footnote: that is,*without*...##
###
Classroom Notes

1948
*
The American mathematical monthly
*

Such

doi:10.1080/00029890.1948.11991898
fatcat:2ydsrdmrfjbjneigqkazndc5nu
*proofs*would hardly*be*tolerated, let 26 CLASSROOM NOTES [January, alone encouraged,*in**the*ordinary*calculus*course. ... Very often*the*synthetic approach makes*the**proof**of*an interest- ing*proposition*accessible*to*a larger group than would*be**the*case if more sophisticated methods were employed. ...##
###
A lambda calculus for real analysis

2010
*
Journal of Logic and Analysis
*

Every expression

doi:10.4115/jla.2010.2.5
fatcat:mrzmjsyeergy7m5rqdobj6yysa
*in**the**calculus*denotes both a continuous function*and*a program,*and**the*reasoning looks remarkably like a sanitised form*of*that*in*classical topology. ... Expressing topology*in*terms*of*continuous functions rather than sets*of*points leads*to*treatments*of*open*and*closed concepts that are very closely lattice-(or de Morgan-) dual,*without**the*double negations ... We need these*in*order*to**be*able*to*reason entirely within*the**calculus*itself,*without*referring back*to**the*model. ...##
###
Systemic Changes that Could Reduce the Conviction of the Innocent

2007
*
Criminal Law Forum
*

*Without*

*in*any way endorsing these

*propositions*, it seems clear that

*the*

*calculus*is drastically altered when we know that we

*convict*innocent people. ... For

*the*reasons given

*in*

*the*introduction

*to*this paper, juries may not take

*the*burden

*of*

*proof*seriously. ...

##
###
Systemic Changes that Could Reduce the Conviction of the Innocent

2006
*
Social Science Research Network
*

*Without*

*in*any way endorsing these

*propositions*, it seems clear that

*the*

*calculus*is drastically altered when we know that we

*convict*innocent people. ... For

*the*reasons given

*in*

*the*introduction

*to*this paper, juries may not take

*the*burden

*of*

*proof*seriously. ...

##
###
TAMING THE INCOMPUTABLE, RECONSTRUCTING THE NONCONSTRUCTIVE AND DECIDING THE UNDECIDABLE IN MATHEMATICAL ECONOMICS

2012
*
New Mathematics and Natural Computation
*

fantastic universe which they knew

doi:10.1142/s1793005712400017
fatcat:iuupodfe2jflnjtwdqhejvwtoi
*how**to*manipulate admirably,*and*almost faultlessly,*without*ever*being*able*to*justify anything. ... Now here is my alternative statement*of**Proposition*1:*Proposition*17 For any given n,*the*largest value that can*be*printed by a program*of**length*(at most) n, is uncomputable. ...##
###
Lower bounds for bounded depth Frege proofs via Pudlák-Buss games

2010
*
ACM Transactions on Computational Logic
*

We present a simple

doi:10.1145/1740582.1740587
fatcat:5t6yvoen5nbxndqy2z3gakd2tq
*proof**of**the*bounded-depth Frege*proof*lower bounds*of*Pitassi et al. [1993]*and*Krajíček et al. [1995] for*the*pigeonhole principle. ... This makes*the*lower bound*of*Pitassi et al. [1993]*and*Krajíček et al. [1995] accessible*to**the*general computational complexity audience. ... ACKNOWLEDGMENTS We thank*the*anonymous referees for pointing an error*in**the*earlier presentation*of**the*article. ...##
###
Elements of Mathematics
[article]

2022
*
Zenodo
*

*The*present chapter introduces

*the*fields

*of*mathematics that will

*be*considered "elementary"

*in*this book. ... They have all been considered "elementary" at some stage

*in*

*the*history

*of*mathematics education,

*and*they are all still taught at school level

*in*some places today. ... For

*the*germ

*of*

*the*idea that led

*to*this book, credit should go

*to*Vagn Lundsgaard Hansen

*and*Jeremy Gray, who commissioned my article on Klein,

*and*later suggested that I write a book

*of*a similar kind ...

##
###
A proportional view: The mathematics of James Glenie (1750–1817)

2009
*
Historia Mathematica
*

Among them are many new geometrical constructions

doi:10.1016/j.hm.2008.12.001
fatcat:cnpfw3pxbzcqjhq42oyiq25hdq
*and**proofs*, a novel demonstration*of**the*binomial theorem,*and*an alternative approach*to**the*differential*calculus*. ... His mathematical achievements, underestimated by previous historians, were deeply rooted*in*Euclidean geometry*and*his own generalized theory*of*proportion. ... Acknowledgments*The*permission*of**the*Royal Society*of*London*to*quote brief extracts from unpublished manuscripts*in*their care is gratefully acknowledged. ...
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