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seemingly interesting paper. In stead
particular, his final coa[l]gebra theorem
Inductive logic programming at 30
https://arxiv.org/abs/2102.10556
The paper contains not a single reference to autoencoders!
Still they show this example:
Fig. 1 ILP systems struggle with structured examples that
exhibit observational noise. All three examples clearly
spell the word "ILP", with some alterations: 3 noisy pixels,
shifted and elongated letters. If we would be to learn a
program that simply draws "ILP" in the middle of the picture,
without noisy pixels and elongated letters, that would
be a correct program.
I guess ILP is 30 years behind the AI boom. An early autoencoder
turned into transformer was already reported here (*):
SERIAL ORDER, Michael I. Jordan - May 1986 https://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Jordan-TR-8604-OCRed.pdf
Well ILP might have its merits, maybe we should not ask
for a marriage of LLM and Prolog, but Autoencoders and ILP.
But its tricky, I am still trying to decode the da Vinci code of
things like stacked tensors, are they related to k-literal clauses?
The paper I referenced is found in this excellent video:
The Making of ChatGPT (35 Year History) https://www.youtube.com/watch?v=OFS90-FX6pg
**DIE ANTINOMIEN DER MENGENLEHRE**E. Specker, Dialectica, Vol. 8, No. 3 (15. 9. 1954) https://www.jstor.org/stable/42964119?seq=7
Hi,
That is extremly embarassing. I donrCOt know
what you are bragging about, when you wrote
the below. You are wrestling with a ghost!
Maybe you didnrCOt follow my superbe link:
seemingly interesting paper. In stead
particular, his final coa[l]gebra theorem
The link behind Hopcroft and Karp (1971) I
gave, which is a Bisimulation and Equirecursive
Equality hand-out, has a coalgebra example,
I used to derive pairs.pl from:
https://www.cs.cornell.edu/courses/cs6110/2014sp/Lectures/lec35a.pdf
Bye
Mild Shock schrieb:
Inductive logic programming at 30
https://arxiv.org/abs/2102.10556
The paper contains not a single reference to autoencoders!
Still they show this example:
Fig. 1 ILP systems struggle with structured examples that
exhibit observational noise. All three examples clearly
spell the word "ILP", with some alterations: 3 noisy pixels,
shifted and elongated letters. If we would be to learn a
program that simply draws "ILP" in the middle of the picture,
without noisy pixels and elongated letters, that would
be a correct program.
I guess ILP is 30 years behind the AI boom. An early autoencoder
turned into transformer was already reported here (*):
SERIAL ORDER, Michael I. Jordan - May 1986
https://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Jordan-TR-8604-OCRed.pdf
Well ILP might have its merits, maybe we should not ask
for a marriage of LLM and Prolog, but Autoencoders and ILP.
But its tricky, I am still trying to decode the da Vinci code of
things like stacked tensors, are they related to k-literal clauses?
The paper I referenced is found in this excellent video:
The Making of ChatGPT (35 Year History)
https://www.youtube.com/watch?v=OFS90-FX6pg
Hi,
My beloved Logic professor introduced Non-Wellfounded
in the form of library cards, sorry only German:
Wir denken uns dazu eine Kartothek, auf deren
Karten wieder Karten derselben Kartothek
aufgef|+hrt sind. Ein Beispiel einer solchen
Kartothek w|nre etwa das folgende : wir haben
drei Karten a, b, c; a f|+hrt a und b auf, b
die Karten a und c, c die Karte b a = (a, b),
b = (a, c), c = (b). Entsprechend den sich
nicht selbst als Element enthaltenden Mengen
fragen wir nach den Karten, die sich nicht
selbst auff|+hren. Die Karte a ist die einzige,
die sich selbst auff|+hrt ; b und c sind somit
die sich nicht selbst auff|+hrenden Karten.
He then concludes that Non-Wellfounded has still the
Russell Paradox, and hence also the productive form of it:
Es gibt somit in jeder Kartothek eine
Gesamtheit G von Karten, zu der es keine Karte
gibt, die genau jene aus G auff|+hrt. (F|+r endliche
Kartotheken ist dies ziemlich selbstverst|nndlich,
doch wollen wir auch unendliche Kartotheken in
Betracht ziehen.) Dieser Satz schliesst aber
nat|+rlich nicht aus, dass es stets m||glich ist,
eine genau die Karten aus G auff|+hrende Karte
herzustellen und diese in die Kartothek zu legen.
Nur m|+ssen wir mit der M||glich-
What is your opinion? Excerpt from:
**DIE ANTINOMIEN DER MENGENLEHRE**E. Specker, Dialectica, Vol. 8, No. 3 (15. 9. 1954) https://www.jstor.org/stable/42964119?seq=7
Bye
Mild Shock schrieb:
Hi,
That is extremly embarassing. I donrCOt know
what you are bragging about, when you wrote
the below. You are wrestling with a ghost!
Maybe you didnrCOt follow my superbe link:
seemingly interesting paper. In stead
particular, his final coa[l]gebra theorem
The link behind Hopcroft and Karp (1971) I
gave, which is a Bisimulation and Equirecursive
Equality hand-out, has a coalgebra example,
I used to derive pairs.pl from:
https://www.cs.cornell.edu/courses/cs6110/2014sp/Lectures/lec35a.pdf
Bye
Mild Shock schrieb:
Inductive logic programming at 30
https://arxiv.org/abs/2102.10556
The paper contains not a single reference to autoencoders!
Still they show this example:
Fig. 1 ILP systems struggle with structured examples that
exhibit observational noise. All three examples clearly
spell the word "ILP", with some alterations: 3 noisy pixels,
shifted and elongated letters. If we would be to learn a
program that simply draws "ILP" in the middle of the picture,
without noisy pixels and elongated letters, that would
be a correct program.
I guess ILP is 30 years behind the AI boom. An early autoencoder
turned into transformer was already reported here (*):
SERIAL ORDER, Michael I. Jordan - May 1986
https://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Jordan-TR-8604-OCRed.pdf >>>
Well ILP might have its merits, maybe we should not ask
for a marriage of LLM and Prolog, but Autoencoders and ILP.
But its tricky, I am still trying to decode the da Vinci code of
things like stacked tensors, are they related to k-literal clauses?
The paper I referenced is found in this excellent video:
The Making of ChatGPT (35 Year History)
https://www.youtube.com/watch?v=OFS90-FX6pg
I guess there is a bug in preparing flat terms vector
Hi,
Take this exercise. Exercise 4.1 Draw the tree
represented by the term n1(n2(n4),n3(n5,n6)). https://book.simply-logical.space/src/text/2_part_ii/4.1.html
Maybe there was a plan that SWISH can draw trees,
and it could be that something was implemented as well.
But I don't see anything dynamic working on the
above web site link. Next challenge for Simply Logical,
in another life. Draw a rational tree.
The Prolog system has them:
/* SWI-Prolog 9.3.26 */
?- X = a(Y,_), Y = b(X,_).
X = a(b(X, _A), _),
Y = b(X, _A).
Bye
I guess there is a bug in preparing flat terms vector
I give you a gold medal EfNc, if you can prove a
compare_index/3 correct that uses this rule. It
was already shown impossible by Matt Carlson.
There are alternative approaches that can reach
transitivity, but do not use the below step
inside some compare_index/3.
compare_term_args(I, C, X, Y, A, H):-
-a-a-a-a-a-a-a arg(I, X, K),
-a-a-a-a-a-a-a arg(I, Y, L),
-a-a-a-a-a-a-a !,
-a-a-a-a-a-a-a compare_index(D, K, L, A, H),
-a-a-a-a-a-a-a (-a-a-a D = (=) ->
-a-a-a-a-a-a-a-a-a-a-a I0 is I + 1,
-a-a-a-a-a-a-a-a-a-a-a compare_term_args(I0, C, X, Y, A, H)
-a-a-a-a-a-a-a ;-a-a-a C = D
-a-a-a-a-a-a-a ).
compare_term_args(_ ,= , _, _, _, _).
Maybe there is a grain of salt of invoking the
Axiom of Choice (AC) in some previous posts.
Although the Axiom of Choice is not needed for
finite sets, they have anyway some choice.
BTW: When Peter Aczel writes ZFC-, he then
means ZFC without AC, right? But he doesnrCOt
show some compare/3 .
Mild Shock schrieb:
Hi,
Take this exercise. Exercise 4.1 Draw the tree
represented by the term n1(n2(n4),n3(n5,n6)).
https://book.simply-logical.space/src/text/2_part_ii/4.1.html
Maybe there was a plan that SWISH can draw trees,
and it could be that something was implemented as well.
But I don't see anything dynamic working on the
above web site link. Next challenge for Simply Logical,
in another life. Draw a rational tree.
The Prolog system has them:
/* SWI-Prolog 9.3.26 */
?- X = a(Y,_), Y = b(X,_).
X = a(b(X, _A), _),
Y = b(X, _A).
Bye
Hi,
Did the old School Logicians waste time
with compare/3 ? I guess no:
Ernst Specker, my beloved Professor, and
Dana Scott made only a partial order. A
partial order might have transitivity
of (<') lacking:
"Scott's model construction is in fact
closely related to Specker's but there
is a subtle difference in the notion of
tree that they use. In fact neither of
them formulate their notion of tree in
terms of graphs but rather in terms of
what it will be convenient here to
call tree-partial-orderings."
See here:
NON-WELL-FOUNDED SETS
Peter Aczel - 1988 https://les-mathematiques.net/vanilla/uploads/editor/fh/v4pi6qyxfbel.pdf
There is also the notion of co-well-
foundedness, something like Noetherian but
up side down, i.e. certain ascending
chains stabilizing.
Bye
Mild Shock schrieb:
I guess there is a bug in preparing flat terms vector
I give you a gold medal EfNc, if you can prove a
compare_index/3 correct that uses this rule. It
was already shown impossible by Matt Carlson.
There are alternative approaches that can reach
transitivity, but do not use the below step
inside some compare_index/3.
compare_term_args(I, C, X, Y, A, H):-
-a-a-a-a-a-a-a-a arg(I, X, K),
-a-a-a-a-a-a-a-a arg(I, Y, L),
-a-a-a-a-a-a-a-a !,
-a-a-a-a-a-a-a-a compare_index(D, K, L, A, H),
-a-a-a-a-a-a-a-a (-a-a-a D = (=) ->
-a-a-a-a-a-a-a-a-a-a-a-a I0 is I + 1,
-a-a-a-a-a-a-a-a-a-a-a-a compare_term_args(I0, C, X, Y, A, H)
-a-a-a-a-a-a-a-a ;-a-a-a C = D
-a-a-a-a-a-a-a-a ).
compare_term_args(_ ,= , _, _, _, _).
Maybe there is a grain of salt of invoking the
Axiom of Choice (AC) in some previous posts.
Although the Axiom of Choice is not needed for
finite sets, they have anyway some choice.
BTW: When Peter Aczel writes ZFC-, he then
means ZFC without AC, right? But he doesnrCOt
show some compare/3 .
Mild Shock schrieb:
Hi,
Take this exercise. Exercise 4.1 Draw the tree
represented by the term n1(n2(n4),n3(n5,n6)).
https://book.simply-logical.space/src/text/2_part_ii/4.1.html
Maybe there was a plan that SWISH can draw trees,
and it could be that something was implemented as well.
But I don't see anything dynamic working on the
above web site link. Next challenge for Simply Logical,
in another life. Draw a rational tree.
The Prolog system has them:
/* SWI-Prolog 9.3.26 */
?- X = a(Y,_), Y = b(X,_).
X = a(b(X, _A), _),
Y = b(X, _A).
Bye