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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Unconventional partial halt decider and grounding to a truthmaker
Date: Thu, 16 May 2024 09:48:21 -0500
Organization: A noiseless patient Spider
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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:
>>>
>>>> On 5/14/2024 4:44 AM, Mikko wrote:
>>>>> On 2024-05-12 15:58:02 +0000, olcott said:
>>>>>
>>>>>> On 5/12/2024 10:21 AM, Mikko wrote:
>>>>>>> On 2024-05-12 11:34:17 +0000, Richard Damon said:
>>>>>>>
>>>>>>>> On 5/12/24 5:19 AM, Mikko wrote:
>>>>>>>>> On 2024-05-11 16:26:30 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> I am working on providing an academic quality definition of this
>>>>>>>>>> term.
>>>>>>>>>
>>>>>>>>> The definition in Wikipedia is good enough.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think he means, he is working on a definition that redefines 
>>>>>>>> the field to allow him to claim what he wants.
>>>>>>>
>>>>>>> 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.
>>>>>>>
>>>>>>> There are systems where that is possible but unsolvable problems are
>>>>>>> unsolvable even in those systems.
>>>>>>>
>>>>>>
>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> This notation does not work with machines that can, or have parts
>>>>> that can, return a value without (or before) termination.
>>>>
>>>> 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 }
>>>
>>> That notation is not any better for the purpose.
>>>
>>
>> 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