From Newsgroup: sci.logic

Hi,

Now toying around with a model finder,
for some rewritng problems. Not bad, I
didn't see that before on my computer:

?- time(mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, _)).
% Zeit 166.140 ms, GC 0.000 ms, Lips 18616 k
true

?- mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, R).
R = [d-2, c-1, 5*2-3, 5*5-4, 4*3-2, 3*5-2, 3*2-5, 4*4-5, 2*4-3,
2*3-4, 3*4-1, 3*1-4, 5*3-1, 4*1-3, 1*5-3, 1*3-5, 2*1-5, 2*5-1,
5*1-2, 4*2-1, 1*4-2, 1*2-4, 5*0-5, 4*0-4, 4*5-0, 5^ -1-4, 5*4-0,
4^ -1-5, 3*0-3, 3*3-0, 3^ -1-3, 2*0-2, 2*2-0, 2^ -1-2, 1*0-1,
1*1-0, 1^ -1-1, 0^ -1-0, 0*5-5, 0*4-4, 0*3-3, 0*2-2,
0*1-1, 0*0-0, e-0]

But still not as good as Mc Cune, wo reported
0.010 seconds , so 10 ms (*). I guess I need to
explore more heuristics. But will it include

union find? The payback of union find in such
search examples is so low. If |D| = n is the
domain size, then although |D x D| has size n^2,

the diagonal E_D, namely E_D = { (x,y) | x e D,
y e D, x = y } has only size n. So the probability
of a pair in certain problem domains, is around 1/n,

getting smaller and smaller with larger and larger n.

Bye

(*)
https://www.mcs.anl.gov/research/projects/AR/mace4/July-2005/doc/mace4.pdf

Mild Shock schrieb:

Hi,

Current AI is split between two worlds that don't play well together:

Deep Learning (neural networks, transformers, ChatGPT) - great at
learning from data, terrible at logical reasoning
Symbolic AI (logic programming, expert systems) - great at logical reasoning, terrible at learning from messy real-world data

Tensor Logic unifies both. It's a single language where you can:
Write logical rules that the system can actually learn and modify
Do transparent, verifiable reasoning (no hallucinations)
Mix "fuzzy" analogical thinking with rock-solid deduction

The Killer Feature: The Temperature Knob

https://www.youtube.com/watch?v=4APMGvicmxY

Bye

Mild Shock schrieb:

Hi,

The English had Aristoteles (*), the French had
Descartes, and the Dutch have their national
Flag. The culmination of the Enlighment was

the distinction between analytic and synthetic
truth. But this doesn't help to understand
Generative AI, which produces a mish mash

of the factual and the plausible. But the logical
and non-logical distinction lead to abominations
like ascribing to Wittgenstein the maxim,

"All logical differences are big differences", with
the even worse conjecture "All nonlogical differences
are small differences". But an early conceptual

prototype of ChatGPT was given by:

"Mirror (**) Mirror on the Wall who is the Fairest of them All?"
- Snow White, Brothers Gri

So its all about retrieving mirror texts and images and
transforming them, the retrieval having good old metrics like
recall and precision, and the transformation having also metrics,

metrics all relative to a group preferences assumption of
the end-user, so that the end-user can more cost effictively
and more market penetratingly act, in a totally

new AI Boom infected environment.

Bye

(*)
we have powers and faculties fitted to deal with
them, and are **happy or miserable** in proportion
as we know how to **frame** a right judgment of things
The elements of logic. In four books
by Duncan, William, 1717-1760
https://archive.org/details/elementsoflogic00dunc/page/n5/mode/2up

(**)

An earlier version of "Mirrors" (Chapter 7) was written for a
volume in honor of Thomas A. Sebeok (He was among the
founders of biosemiotics, and coined the term "zoosemiotics"
in 1963 to describe the development of signals and signs by
non-human animal species) for his sixty-fifth birthday.
Umberto Eco, ''Semiotics and the Philosophy of Language'',
Bloomington: Indiana U.P., 1984
https://monoskop.org/images/b/b3/Eco_Umberto_Semiotics_and_the_Philosophy_of_Language_1986.pdf

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.logic

Hi,

One challenge is that the example has
not only anti-unification, like the c*d\=d*c,
the Mc Cune style model finder implementation

makes also heavy use of backtracking. So
I even donrCOt know whether ISAMORE papers
with saturation would help:

Finding Reusable Instructions via E-Graph Anti-Unification
Youwei Xiao et al. - ASPLOS rCO26
https://github.com/pku-liang/ISAMORE

But I guess ISAMORE also delivers
rewriting challenges.

Bye

Mild Shock schrieb:

Hi,

Now toying around with a model finder,
for some rewritng problems. Not bad, I
didn't see that before on my computer:

?- time(mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, _)).
% Zeit 166.140 ms, GC 0.000 ms, Lips 18616 k
true

?- mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, R).
R = [d-2, c-1, 5*2-3, 5*5-4, 4*3-2, 3*5-2, 3*2-5, 4*4-5, 2*4-3,
2*3-4, 3*4-1, 3*1-4, 5*3-1, 4*1-3, 1*5-3, 1*3-5, 2*1-5, 2*5-1,
5*1-2, 4*2-1, 1*4-2, 1*2-4, 5*0-5, 4*0-4, 4*5-0, 5^ -1-4, 5*4-0,
4^ -1-5, 3*0-3, 3*3-0, 3^ -1-3, 2*0-2, 2*2-0, 2^ -1-2, 1*0-1,
1*1-0, 1^ -1-1, 0^ -1-0, 0*5-5, 0*4-4, 0*3-3, 0*2-2,
0*1-1, 0*0-0, e-0]

But still not as good as Mc Cune, wo reported
0.010 seconds , so 10 ms (*). I guess I need to
explore more heuristics. But will it include

union find? The payback of union find in such
search examples is so low. If |D| = n is the
domain size, then although |D x D| has size n^2,

the diagonal E_D, namely E_D = { (x,y) | x e D,
y e D, x = y } has only size n. So the probability
of a pair in certain problem domains, is around 1/n,

getting smaller and smaller with larger and larger n.

Bye

(*) https://www.mcs.anl.gov/research/projects/AR/mace4/July-2005/doc/mace4.pdf

Mild Shock schrieb:

Hi,

Current AI is split between two worlds that don't play well together:

Deep Learning (neural networks, transformers, ChatGPT) - great at
learning from data, terrible at logical reasoning
Symbolic AI (logic programming, expert systems) - great at logical
reasoning, terrible at learning from messy real-world data

Tensor Logic unifies both. It's a single language where you can:
Write logical rules that the system can actually learn and modify
Do transparent, verifiable reasoning (no hallucinations)
Mix "fuzzy" analogical thinking with rock-solid deduction

The Killer Feature: The Temperature Knob

https://www.youtube.com/watch?v=4APMGvicmxY

Bye

Mild Shock schrieb:

Hi,

The English had Aristoteles (*), the French had
Descartes, and the Dutch have their national
Flag. The culmination of the Enlighment was

the distinction between analytic and synthetic
truth. But this doesn't help to understand
Generative AI, which produces a mish mash

of the factual and the plausible. But the logical
and non-logical distinction lead to abominations
like ascribing to Wittgenstein the maxim,

"All logical differences are big differences", with
the even worse conjecture "All nonlogical differences
are small differences". But an early conceptual

prototype of ChatGPT was given by:

"Mirror (**) Mirror on the Wall who is the Fairest of them All?"
- Snow White, Brothers Gri

So its all about retrieving mirror texts and images and
transforming them, the retrieval having good old metrics like
recall and precision, and the transformation having also metrics,

metrics all relative to a group preferences assumption of
the end-user, so that the end-user can more cost effictively
and more market penetratingly act, in a totally

new AI Boom infected environment.

Bye

(*)
we have powers and faculties fitted to deal with
them, and are **happy or miserable** in proportion
as we know how to **frame** a right judgment of things
The elements of logic. In four books
by Duncan, William, 1717-1760
https://archive.org/details/elementsoflogic00dunc/page/n5/mode/2up

(**)

An earlier version of "Mirrors" (Chapter 7) was written for a
volume in honor of Thomas A. Sebeok (He was among the
founders of biosemiotics, and coined the term "zoosemiotics"
in 1963 to describe the development of signals and signs by
non-human animal species) for his sixty-fifth birthday.
Umberto Eco, ''Semiotics and the Philosophy of Language'',
Bloomington: Indiana U.P., 1984
https://monoskop.org/images/b/b3/Eco_Umberto_Semiotics_and_the_Philosophy_of_Language_1986.pdf

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.logic

Hi,

One challenge is that the example has
not only anti-unification, like the c*d\=d*c,
the Mc Cune style model finder implementation

makes also heavy use of backtracking. So
I even donrCOt know whether ISAMORE papers
with saturation would help:

Finding Reusable Instructions via E-Graph Anti-Unification
Youwei Xiao et al. - ASPLOS rCO26
https://github.com/pku-liang/ISAMORE

But I guess ISAMORE also delivers
rewriting challenges. But their subject
matter in the above paper is LLVM/GEM5,

so maybe I rather buy a new Mac Neo
and enjoy local AI.

Bye

Mild Shock schrieb:

Hi,

Now toying around with a model finder,
for some rewritng problems. Not bad, I
didn't see that before on my computer:

?- time(mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, _)).
% Zeit 166.140 ms, GC 0.000 ms, Lips 18616 k
true

?- mccune([e*X=X,X^(-1)*X=e,X*(Y*Z)=(X*Y)*Z, c*d\=d*c], 6, R).
R = [d-2, c-1, 5*2-3, 5*5-4, 4*3-2, 3*5-2, 3*2-5, 4*4-5, 2*4-3,
2*3-4, 3*4-1, 3*1-4, 5*3-1, 4*1-3, 1*5-3, 1*3-5, 2*1-5, 2*5-1,
5*1-2, 4*2-1, 1*4-2, 1*2-4, 5*0-5, 4*0-4, 4*5-0, 5^ -1-4, 5*4-0,
4^ -1-5, 3*0-3, 3*3-0, 3^ -1-3, 2*0-2, 2*2-0, 2^ -1-2, 1*0-1,
1*1-0, 1^ -1-1, 0^ -1-0, 0*5-5, 0*4-4, 0*3-3, 0*2-2,
0*1-1, 0*0-0, e-0]

But still not as good as Mc Cune, wo reported
0.010 seconds , so 10 ms (*). I guess I need to
explore more heuristics. But will it include

union find? The payback of union find in such
search examples is so low. If |D| = n is the
domain size, then although |D x D| has size n^2,

the diagonal E_D, namely E_D = { (x,y) | x e D,
y e D, x = y } has only size n. So the probability
of a pair in certain problem domains, is around 1/n,

getting smaller and smaller with larger and larger n.

Bye

(*) https://www.mcs.anl.gov/research/projects/AR/mace4/July-2005/doc/mace4.pdf

Mild Shock schrieb:

Hi,

Current AI is split between two worlds that don't play well together:

Deep Learning (neural networks, transformers, ChatGPT) - great at
learning from data, terrible at logical reasoning
Symbolic AI (logic programming, expert systems) - great at logical
reasoning, terrible at learning from messy real-world data

Tensor Logic unifies both. It's a single language where you can:
Write logical rules that the system can actually learn and modify
Do transparent, verifiable reasoning (no hallucinations)
Mix "fuzzy" analogical thinking with rock-solid deduction

The Killer Feature: The Temperature Knob

https://www.youtube.com/watch?v=4APMGvicmxY

Bye

Mild Shock schrieb:

Hi,

The English had Aristoteles (*), the French had
Descartes, and the Dutch have their national
Flag. The culmination of the Enlighment was

the distinction between analytic and synthetic
truth. But this doesn't help to understand
Generative AI, which produces a mish mash

of the factual and the plausible. But the logical
and non-logical distinction lead to abominations
like ascribing to Wittgenstein the maxim,

"All logical differences are big differences", with
the even worse conjecture "All nonlogical differences
are small differences". But an early conceptual

prototype of ChatGPT was given by:

"Mirror (**) Mirror on the Wall who is the Fairest of them All?"
- Snow White, Brothers Gri

So its all about retrieving mirror texts and images and
transforming them, the retrieval having good old metrics like
recall and precision, and the transformation having also metrics,

metrics all relative to a group preferences assumption of
the end-user, so that the end-user can more cost effictively
and more market penetratingly act, in a totally

new AI Boom infected environment.

Bye

(*)
we have powers and faculties fitted to deal with
them, and are **happy or miserable** in proportion
as we know how to **frame** a right judgment of things
The elements of logic. In four books
by Duncan, William, 1717-1760
https://archive.org/details/elementsoflogic00dunc/page/n5/mode/2up

(**)

An earlier version of "Mirrors" (Chapter 7) was written for a
volume in honor of Thomas A. Sebeok (He was among the
founders of biosemiotics, and coined the term "zoosemiotics"
in 1963 to describe the development of signals and signs by
non-human animal species) for his sixty-fifth birthday.
Umberto Eco, ''Semiotics and the Philosophy of Language'',
Bloomington: Indiana U.P., 1984
https://monoskop.org/images/b/b3/Eco_Umberto_Semiotics_and_the_Philosophy_of_Language_1986.pdf

--- Synchronet 3.22a-Linux NewsLink 1.2