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Groups > comp.lang.prolog > #14647

Relation of the practical to the mathematical oracle (Was: What is practical choice point eliminaton then?)

From Mild Shock <janburse@fastmail.fm>
Newsgroups comp.lang.prolog
Subject Relation of the practical to the mathematical oracle (Was: What is practical choice point eliminaton then?)
Date 2025-07-10 21:35 +0200
Message-ID <104p4lv$22dsf$1@solani.org> (permalink)
References <vpceij$is1s$1@solani.org> <104osio$2281u$1@solani.org> <104p3so$22dce$1@solani.org> <104p4cr$22dou$1@solani.org>

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Hi,

Now one might ask, if we have a Prolog system
that anyway juggles with choice points, why
would we need a logical formula for choice points?

Well there is a funny correctness criteria,
for example in the top-level, if the top-level
doesn't prompt the end user anymore in such a scenario:

?- p(X).
X = a1 ;
X = a2 ;
...
X = ak-1 ;
X = ak

So the end user is not prompted because the
Prolog system founds CP = []. This is licensed
by this correctness statement for any choice

point elimination:

CP = [] => ~∃X ( p(X) & X =\= a1 & ... & X =\= ak)

Have Fun!

Bye

Mild Shock schrieb:
> 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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