Unconventional partial halt decider and grounding to a truthmaker

On 5/16/2024 5:42 AM, Mikko wrote:

On 2024-05-15 15:06:26 +0000, olcott said:
 

On 5/15/2024 3:06 AM, Mikko wrote:

On 2024-05-14 14:32:26 +0000, olcott said:
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On 5/14/2024 4:44 AM, Mikko wrote:

On 2024-05-12 15:58:02 +0000, olcott said:
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On 5/12/2024 10:21 AM, Mikko wrote:

On 2024-05-12 11:34:17 +0000, Richard Damon said:
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On 5/12/24 5:19 AM, Mikko wrote:

On 2024-05-11 16:26:30 +0000, olcott said:
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I am working on providing an academic quality definition of this
term.

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The definition in Wikipedia is good enough.
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I think he means, he is working on a definition that redefines the field to allow him to claim what he wants.

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Here one can claim whatever one wants anysay.
In if one wants to present ones claims on some significant forum then
it is better to stick to usual definitions as much as possible.
>

Sort of like his new definition of H as an "unconventional" machine that some how both returns an answer but also keeps on running.

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There are systems where that is possible but unsolvable problems are
unsolvable even in those systems.
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When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

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This notation does not work with machines that can, or have parts
that can, return a value without (or before) termination.

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00 int H(ptr x, ptr x)  // ptr is pointer to int function
01 int D(ptr x)
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 int main()
10 {
11   H(D,D);
12 }

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That notation is not any better for the purpose.
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I refer to transitioning through a specific state to indicate
a specific halt status value, for Turing Machines.

 That does not satisfy the usual definition of "halt decider".

Yet it <is> an incremental improvement over both YES and NO are
the wrong answer for input D. YES <is> the correct answer and H
can not SAY this answer in the conventional way.

However, we could accept that as a solution to the halting problem
if one could prove that there is a Turing machine that can indicate
halting or non-halting that way for all computations.
 

Refuting the HP pathological program/input pair is the the full scope
of my theory of computation work. Even without my POD24 diagnosis I
would have no time to verify this against an infinite set of programs.
Validation of POD24 as a robust early clinical end point of poor
survival in FL from 5225 patients on 13 clinical trials
https://pubmed.ncbi.nlm.nih.gov/34614146/

However, it is possible to prove that every Turing machine that
indicates halting that way fails to indicate correctly at least
some computations.
 

Once I conquer the HP pathological program/input pair and
apply to to the foundation of {true on the basis of meaning}
expressed as finite strings, then I am done.
"a sentence may fail to make a statement if it is paradoxical or ungrounded."
*Outline of a Theory of Truth --- Saul Kripke*
https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
How to define a True(L, x) predicate that refutes Tarski Undefinability:
*AKA The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth preserving
operations from finite string expressions of language that have been
stipulated to have the semantic value of Boolean true. False(L,x) is
defined as True(L,~x).   Copyright 2022 PL Olcott
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer