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Using the prover ANDP to simplify orthogonality

2003
*
Annals of Pure and Applied Logic
*

Recently,

doi:10.1016/s0168-0072(03)00051-4
fatcat:aoch76uzlnh7xjhrwqspst5vpa
*von*Plato used di erent concepts to*axiomatize*the*geometry*: he used 14 axioms to describe the*axiomatization*for*apartness**geometry*. ... In the 1920s, Heyting attempted at*axiomatizing**constructive**geometry*. ... The experiments whose results are reported in this paper were executed at RRL*of*department*of*computer science*of*SUNY Albany. ...##
###
Simplifying the axiomatization for the order affine geometry
[article]

2022
*
arXiv
*
pre-print

Based on an ordering with directed lines and using

arXiv:2205.05162v1
fatcat:buqt2ocsnncvpg6od56ffyfcby
*constructions*instead*of*existential axioms,*von*Plato proposed a*constructive**axiomatization**of*ordered affine*geometry*. ... There are 22 axioms for the ordered affine*geometry*,*of*which the axiom I.7 is about the convergence*of*three lines (ignoring their directions). ... By using theorem prover ANDP [9, 10] , we found a natural deduction*of*Halting problem [11] , and*simplified**von**Plato's**axiomatization**of**constructive**apartness**geometry*and orthogonality [12, 13] ...##
###
Index

2000
*
Annals of Pure and Applied Logic
*

*von*

*Plato's*

*axiomatization*

*of*

*Constructive*

*Apartness*

*Geometry*(1}2) 1} 26 Pynko, A.P., Erratum to &&De"nitional equivalence and algebraizability

*of*generalized logical systems'' Annals

*of*Pure and Applied ... , M., see Jensen, R.B. (1}2) 101}138 Kanovei, V., Linearization

*of*de"nable order relations (1}2) 69}100 Kohlenbach, U., Things that can and things that cannot be done in PRA (3) 223}245 Li, D.,

*Simplifying*...

##
###
Page 8375 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

Dafa (PRC-TSI; Beijing); Jia, Peifa (PRC-TSI-IT; Beijing);
Li, Xinxin (1-WYNS-C; Detroit, MI)

*Simplifying**von**Plato’s**axiomatization**of**constructive**apartness**geometry*. ... By replacing three pairs*of*axioms with three axioms, as well as*simplifying*one*of**von**Plato’s*axioms for*apartness**geometry*, the authors obtain a new, equivalent axiom system with 11 axioms. ...##
###
A Decision Procedure for Geometry in Coq
[chapter]

2004
*
Lecture Notes in Computer Science
*

The idea

doi:10.1007/978-3-540-30142-4_17
fatcat:6ho42opbsjhg3cnybu33255ot4
*of*the method is to express the goal to be proved using three geometric quantities and eliminate points in the reverse order*of*their*construction*thanks to some elimination lemmas. ... We present in this paper the development*of*a decision procedure for affine plane*geometry*in the Coq proof assistant. ... I want to thank Hugo Herbelin for his help during the elaboration*of*this work. ...##
###
The axiomatic melting pot. Teaching probability theory in Prague during the 1930's
[article]

2006
*
arXiv
*
pre-print

In this paper, we are interested in the teaching

arXiv:math/0607217v1
fatcat:lp3oa4ekyvftjfnlcoreo6ho2i
*of*probability theory in Prague and Czechoslovakia, in particular during the 1930's. ... We focus specially on a textbook, published in Prague by Karel Rychlik in 1938, which uses Kolmogorov's*axiomatization*, a very exceptional fact before World War II. ... Let us just mention*Von**Plato's*book [74] whose subject is precisely to describe this new emergence*of*probability and renewal*of*the theory after the creations*of*the 17-18th centuries and the Laplacian ...##
###
Mathematical Interpretation of Plato's Third Man Argument
[article]

2014
*
arXiv
*
pre-print

Thus, the notion

arXiv:1406.1973v1
fatcat:2l2fdvdsjjdzvaqivtwbsrvlvu
*of*convergence is consistent with*Plato's*apprehension*of*mathematical concepts, and in particular these*of*"density"*of*magnitudes and the complete continuum in the sense that they include ... I also claim and prove that within this framework the logic*of*the TMA is consistent with that*of*the Third Bed Argument (TBA) as presented in*Plato's*"Republic". ... His*construction*is in accordance with*Von*Neumann set-theoretic one 19 . ...##
###
A Half-Century of Mathematics

1951
*
The American mathematical monthly
*

In the domain

doi:10.1080/00029890.1951.11999734
fatcat:tzhuvhvwynegnghcouhf4fp4d4
*of*elementary*axiomatic**geometry*one strange discovery, that*of**von*Neumann’s pointless “continuous*geometries*” stands out, because it is intimately inter- related with quantum mechanics, ... The*axiomatic*approach has often revealed inner relations between, and has made for unification*of*methods within, domains that apparently lie far*apart*. ...##
###
The Logic of Brouwer and Heyting
[chapter]

2009
*
Handbook of the History of Logic
*

*axiomatic*extensions, each necessarily contained in classical logic (which is

*axiomatically*complete). ... The logic

*of*Brouwer and Heyting is effective. The conclusion

*of*an intuitionistic derivation holds with the same degree

*of*

*constructivity*as the premises. ... Mark van Atten, Garyfallia Vafeiadou, Richard Vesley, Richard Zach and Yiannis Moschovakis generously read and commented on an earlier version

*of*the manuscript. ...

##
###
Page 1249 of Mathematical Reviews Vol. 32, Issue Index
[page]

*
Mathematical Reviews
*

(English summary) 2000d:51019
Li, Dafa (with Jia, Peifa; Li, Xinxin)

*Simplifying**von**Plato’s**axiomatization**of*construc- tive*apartness**geometry*. ... On non-spread representations*of*projective planes*of*order q’ in PG(2i,q). (English summary) 2000a:51008*von*Plato, Jan A*constructive*theory*of*ordered affine*geometry*. ...##
###
Page 74 of Mathematical Reviews Vol. 32, Issue Index
[page]

*
Mathematical Reviews
*

., (2000h:03006)
Leblanc, Hugues see Roeper, Peter, 2000k:03030
Li, Dafa (with Jia, Peifa; Li, Xinxin)

*Simplifying**von**Plato’s**axiomatization**of*construc- tive*apartness**geometry*. ... Uber einen Satz*von*Krasner. II. [On a theorem*of*Krasner. ...##
###
The Nature of Physical Knowledge

1961
*
Physics today
*

Even though the elementary bodies are

doi:10.1063/1.3057656
fatcat:w72z4itk3rdilnb7oywx5estzi
*constructed**of*mathematical figures, they retain much*of*the mutability characteristic*of*the primordial source. 12 How modern*Plato's*assessment*of*the mutability ... The use*of*the*axiomatic*method amounts to this: one starts with postulates-these postulates are part*of*the*axiomatic*system. ... To the man who pursues his studies in the proper way all geo metrical*constructions*, all systems*of*numbers, all duly constituted melodic progressions, the single ordered scheme*of*all celestial revolutions ...##
###
The Rhetoric of Failure: A Hyper-Dialog About Method in Economics and How to Get Things Going

2012
*
Social Science Research Network
*

*of*methodology. ... This paper gives first an overview

*of*the methodological questions at issue. The frame

*of*reference includes J. S. Mill, Jevons, Popper, Keynes, and Lawson. ... and at the same time its failure to

*construct*any sort

*of*

*axiomatic*theoretical framework led to its marginalization. ...

##
###
Quantum groups and noncommutative geometry

2000
*
Journal of Mathematical Physics
*

generalisation

doi:10.1063/1.533331
fatcat:iyelepep4jddvij5vykvnq6xla
*of**geometry*itself powerful enough to make sense in the quantum domain. ... Just as the last century saw the birth*of*classical*geometry*, so the present century sees at its end the birth*of*this quantum or noncommutative*geometry*, both as an elegant mathematical reality and in ...*of*Cambridge, England, where some*of*the work was completed. ...##
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The problem of the invariance of dimension in the growth of modern topology, part I

1979
*
Archive for History of Exact Sciences
*

Several mathematicians argued that

doi:10.1007/bf00327627
fatcat:yxt26tgq2zeqbdac7tizcbeabe
*geometry*ought to be*constructed*as a pure autonomous science and not on the basis*of*numbermanifolds. This is the*axiomatic*-deductive trend. ... KLEIN pointed the way to a solution avoiding the vicious circle, through*VON*STAUDT'S quadrilateral*construction*. By means*of*this*construction*we can avoid the usual metric. ... Dictionary*of*Scientific Biography. Ed. C.C. GILLISPIE. New York. Vol. X, p. 24. ...
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