Re: Every computable function can be construed as --- finite string transformation rules applied to finite strings.

On 10/26/24 9:33 AM, olcott wrote:

On 10/26/2024 8:22 AM, olcott wrote:

On 10/25/2024 11:07 PM, Richard Damon wrote:

On 10/25/24 6:11 PM, olcott wrote:

On 10/25/2024 10:45 AM, Richard Damon wrote:

On 10/25/24 9:56 AM, olcott wrote:

On 10/25/2024 7:27 AM, Richard Damon wrote:

On 10/24/24 8:56 PM, olcott wrote:

On 10/24/2024 6:23 PM, Richard Damon wrote:

On 10/24/24 9:36 AM, olcott wrote:

On 10/23/2024 9:48 PM, Richard Damon wrote:

On 10/23/24 9:51 PM, olcott wrote:

ChatGPT does completely understand this.
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But, it is just a stupid idiot that has been taught to repeat what it has been told.
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It is a brilliant genius that seems to infallibly deduce all
of the subtle nuances of each of the consequences on the basis
of a set of premises.

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I guess you don't undetstand how "Large Language Models work, do you.
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It has NO actual intelegence, or ability to "deduce" nuances, it is just a massive pattern matching system.
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All you are doing is proving how little you understand about what you are talking about,
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Remember, at the bottom of the page is a WARNING that it can make mistakes. And feeding it LIES, like you do is one easy way to do that.
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There is much more to this than your superficial
understanding.  Here is a glimpse:
https://www.technologyreview.com/2024/03/04/1089403/large- language- models-amazing-but-nobody-knows-why/
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The bottom line is that ChatGPT made no error in its
evaluation of my work when this evaluation is based on
pure reasoning. It is only when my work is measured
against arbitrary dogma that cannot be justified with
pure reasoning that makes me and ChatGPT seem incorrect.
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If use your same approach to these things we could say that
ZFC stupidly fails to have a glimmering of understanding of
Naive set theory. From your perspective ZFC is a damned liar.
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The articles says no such thing.
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*large-language-models-amazing-but-nobody-knows-why*
They are much smarter and can figure out all kinds of
things. Their original designers have no idea how they
do this.
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In fact, it comments about the problem of "overfitting" where the processing get the wrong answers because it over generalizes.
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This is because the modeling process has no concept of actual meaning, and thus of truth, only the patterns that it has seen.
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AI's don't "Reason", they patern match and compare.
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Note, that "arbitrary dogma" that you try to reject, are the RULES and DEFINITONS of the system that you claim to be working in.
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How about we stipulate that the system that I am
working in is termination analysis for the x86 language.
as my system software says in its own name: x86utm.

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But it doesn;t actually know
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I said the the underlying formal mathematical system
of DDD/HHH <is> the x86 language.

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Can't be.
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That isn't a formal logic system.
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Sure it is. A formal logic system is any system
tat applies finite string transformation rules
to finite strings.
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The simplest concrete example of such a system
transforms pairs of ASCII digits into their sum.
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 Every computable function can be construed as applying
finite string transformation rules to an input finite
string and deriving an output finite string.
 

Which is a concept not in the x86 language, but in Computation Theory, so you just proved that you were lying with your statement that you were working in the "logic system of the x86 language semantics". (Which isn't a thing).
And it isn't even correctly stated, as what are called "Functions" in Computation Theory, is the mathematical abstraction that maps one domain to another. That mapping can be thought of as a mapping between finite strings that represents the elements of those domains.
A "Computable Function" is a Function (that mathematical concept of mapping) that can be computed with a finite algorithm, that is a finite string transformation of input finite strings to output finite strings, that match the full mapping of that function.
The Computable Function is not that resulting program, and that program is not called a Computable Function. But, since all programs that always halt (called deciders by some) end up computing some mapping, we can talk about the computable function it generates. But it is NOT that function, it computes that funcition, and its existsance is what makes that function "computable".
The key point is that if the Function it computes doesn't exactly match the Function it was claimed to compute, it is just wrong and doesn't match its claim.
The domain that does call the thing that does the mapping functions is other parts of Computer Science, but those don't use the adjective "computable", as ALL funtions (that return values) compute something.
And the question of if the program is correct, becomes parts of Requirements analysis.