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Buddos Waterloo: Checkpoint McCune (Was: Tensor Logic "Unifies" AI Paradigms [Pedro Domingos]=

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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 
>>
> 

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Buddos Waterloo: Checkpoint McCune (Was: Tensor Logic "Unifies" AI Paradigms [Pedro Domingos]= Mild Shock <janburse@fastmail.fm> - 2026-05-10 16:18 +0200
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