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

Pavel Pudlák, Samuel R. Buss
1995 Lecture Notes in Computer Science  
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  
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

A. Carbone
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.  ... 
doi:10.1016/s0168-0072(99)00009-3 fatcat:6eegfmivandt7iqunywe7wm7rm

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

Jan Sebestik, Paul Rusnock
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.  ... 
doi:10.4148/jhap.v1i8.1460 fatcat:moigliznajfpjlih3b2u5pb55y

A Physical Quantum Model in a Smooth Topos [article]

John D. Fearns
2002 arXiv   pre-print
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]

Paolo Mancosu, Richard Zach, Calixto Badesa
2009 The Development of Modern Logic  
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

J. L. Synge, L. M. Kelly, H. S. M. Coxeter, R. G. Helsel, T. Radó
1948 The American mathematical monthly  
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

Taylor
2010 Journal of Logic and Analysis  
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

Arnold H. Loewy
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.  ... 
doi:10.1007/s10609-007-9041-x fatcat:ow7h66ifr5dcrho3sv3erewdii

Systemic Changes that Could Reduce the Conviction of the Innocent

Arnold H. Loewy
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.  ... 
doi:10.2139/ssrn.927223 fatcat:f4uujj5nlvcgheo5xiiogb6sxi

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

K. VELA VELUPILLAI
2012 New Mathematics and Natural Computation  
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

Eli Ben-Sasson, Prahladh Harsha
2010 ACM Transactions on Computational Logic  
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]

John Stillwell
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  ... 
doi:10.5281/zenodo.6080488 fatcat:duf7ea2kpbemvj4yfg4ewizlw4

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

Alex D.D. Craik
2009 Historia Mathematica  
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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