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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
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We shall describe two general methods for proving lower bounds on 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. ...
doi:10.1007/bfb0022253
fatcat:msdzmo6nqrf2barxsxxsiqob2u
Page 3437 of Mathematical Reviews Vol. , Issue 98F
[page]
1998
Mathematical Reviews
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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
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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
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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. ...
doi:10.1016/s0168-0072(99)00009-3
fatcat:6eegfmivandt7iqunywe7wm7rm
The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics
2013
Journal for the History of Analytical Philosophy
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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. ...
doi:10.4148/jhap.v1i8.1460
fatcat:moigliznajfpjlih3b2u5pb55y
A Physical Quantum Model in a Smooth Topos
[article]
2002
arXiv
pre-print
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governed by 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. ...
arXiv:quant-ph/0202079v1
fatcat:omyuxcoiazchzeigj7yjrr7xeq
The Development of Mathematical Logic from Russell to Tarski, 1900–1935
[chapter]
2009
The Development of Modern Logic
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Principia, despite its 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 ...
doi:10.1093/acprof:oso/9780195137316.003.0029
fatcat:ygiplet5oraf7fza6fsmf5j5ly
Classroom Notes
1948
The American mathematical monthly
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Such 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. ...
doi:10.1080/00029890.1948.11991898
fatcat:2ydsrdmrfjbjneigqkazndc5nu
A lambda calculus for real analysis
2010
Journal of Logic and Analysis
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Every expression 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. ...
doi:10.4115/jla.2010.2.5
fatcat:mrzmjsyeergy7m5rqdobj6yysa
Systemic Changes that Could Reduce the Conviction of the Innocent
2007
Criminal Law Forum
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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. ...
doi:10.1007/s10609-007-9041-x
fatcat:ow7h66ifr5dcrho3sv3erewdii
Systemic Changes that Could Reduce the Conviction of the Innocent
2006
Social Science Research Network
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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. ...
doi:10.2139/ssrn.927223
fatcat:f4uujj5nlvcgheo5xiiogb6sxi
TAMING THE INCOMPUTABLE, RECONSTRUCTING THE NONCONSTRUCTIVE AND DECIDING THE UNDECIDABLE IN MATHEMATICAL ECONOMICS
2012
New Mathematics and Natural Computation
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fantastic universe which they knew 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. ...
doi:10.1142/s1793005712400017
fatcat:iuupodfe2jflnjtwdqhejvwtoi
Lower bounds for bounded depth Frege proofs via Pudlák-Buss games
2010
ACM Transactions on Computational Logic
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We present a simple 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. ...
doi:10.1145/1740582.1740587
fatcat:5t6yvoen5nbxndqy2z3gakd2tq
Elements of Mathematics
[article]
2022
Zenodo
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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 ...
doi:10.5281/zenodo.6080488
fatcat:duf7ea2kpbemvj4yfg4ewizlw4
A proportional view: The mathematics of James Glenie (1750–1817)
2009
Historia Mathematica
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Among them are many new geometrical constructions 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. ...
doi:10.1016/j.hm.2008.12.001
fatcat:cnpfw3pxbzcqjhq42oyiq25hdq
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