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Groups > comp.lang.prolog > #14646

What is practical choice point eliminaton then? (Was: The ideal choice point as a logical formula)

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Hi,

Now what does a Prolog system do? Well when
it prompts the end-user it has somewhere
a list of the current query choice points:

CPs = [CP1, CP2, .., CPn]

This is implementation specific, what choice
points a system creates, also the ISO core standard
shows a machine in its more procedural explanation,

that depicts something that has also somewhere
choice points. Since it is implementation specific
a Prolog System A and Prolog System B might

use different choice points:

System A:
CPs = [CP1, CP2, .., CPn]

System B:
CP's = [CP'1, CP'2, .., CP'n]

We say a System B could eliminate a choice point CP,
relative to a System A, if we have:

System A:
CP ∈ CPs

System B:
CP ∉ CPs

So System B might have an advantage over System A,
since it will not backtrack over CP.

When it comes to answer substitution display,
it is now very common, that a Prolog system checks
its own choice points, and when it finds that

CP = []

It knows that the query left no choice points,
either because there were never any, because
there was no branching in the executed code, or

because a cut removed branching, or because
they were eliminated somehow. Like through
some index analysis.

Bye

Mild Shock schrieb:
> Hi,
> 
> This is nothing for Bart Demoen, Physics PhD,
> academic fraud. The ideal choice point can
> be formulated as a logical formula, involving
> 
> an existential quantifier. Assume we have
> a query and already these answers, and the
> Prolog system is prompting the interactive user:
> 
> ?- p(X).
> X = a1 ;
> X = a2 ;
> ...
> X = ak-1 ;
> X = ak
> 
> A mathematical oracle that could indicate whether
> it is even necessary to prompt the user could be:
> 
>     ∃X ( p(X) & X =\= a1 & ... & X =\= ak)
> 
> It doesn't match 100% Prolog since Prolog might
> give duplicate answers or non-ground answers,
> but assume for the moment the query q(X),
> 
> produces only distinct and ground results.
> Nice existential FOL formula we have in the above.
> 
> Bye
> 
> Mild Shock schrieb:
>>
>> Henri Poincaré believed that mathematical
>> and scientific creativity came from a deep,
>> unconscious intuition that could not be
>>
>> captured by mechanical reasoning or formal
>> systems. He famously wrote about how insights
>> came not from plodding logic but from sudden
>>
>> illuminations — leaps of creative synthesis.
>>
>> But now we have generative AI — models like GPT — that:
>>
>> - produce poetry, proofs, stories, and code,
>>
>> - combine ideas in novel ways,
>>
>> - and do so by processing patterns in massive
>>    datasets, without conscious understanding.
>>
>> And that does seem to contradict Poincaré's belief
>> that true invention cannot come from automation.
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> But I shouldn't waste too much time.
>>> One shouldn't punish people for just
>>> being plain stupid.
>>>
>>> Like for example this clueless french
>>> philosopher who had a lot of troubles
>>> with non-classical logic.
>>>
>>> His brain tried to eliminate non-classical
>>> logic, it was keen on avoiding non-classical
>>> logic. A typical species of a human with
>>>
>>> an extremly small brain, again working
>>> in the wrong place!
>>>
>>> Bye
>>>
>>> P.S.: Maybe this a Poincaré thingy? Poincaré
>>> was a strong critic of logicism (as championed
>>> by Frege and Russell) and of Hilbert’s
>>> formalist program.
>>>
>>> But, he did not formally use or promote systems
>>> like intuitionistic logic, modal logic, or
>>> relevance logic. His logical framework remained
>>> within the bounds of classical logic,
>>>
>>> though he was skeptical of excessive formalism.
>>> He thought formal systems could miss the creative
>>> and synthetic nature of mathematical
>>> invention. 
>>
> 

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