Re: Categorically exhaustive reasoning applied to the decision to abort

On 3/27/2024 4:55 AM, Fred. Zwarts wrote:

Op 26.mrt.2024 om 15:43 schreef olcott:

On 3/26/2024 3:51 AM, Fred. Zwarts wrote:

Op 25.mrt.2024 om 23:50 schreef olcott:

On 3/24/2024 11:42 AM, Mikko wrote:

On 2024-03-24 03:39:12 +0000, olcott said:
>

On 3/23/2024 9:54 PM, immibis wrote:

On 24/03/24 03:40, olcott wrote:

On 3/23/2024 9:34 PM, immibis wrote:

On 24/03/24 03:15, olcott wrote:

On 3/23/2024 8:40 PM, immibis wrote:

On 24/03/24 00:29, olcott wrote:

On 3/23/2024 5:58 PM, immibis wrote:

On 23/03/24 16:02, olcott wrote:

(b) H(D,D) that DOES abort its simulation is correct
     (ABOUT THIS ABORT DECISION)
     because it would halt and all deciders must always halt.

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To be a decider it has to give an answer.
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To be a halt decider it has to give an answer that is the same as whether the direct execution of its input would halt.

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That would entail that

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Tough shit. That is the requirement.

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I proved otherwise in the parts you erased.

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You proved that the requirement is not actually the requirement?

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I proved that it cannot be a coherent requirement, it can still
be an incoherent requirement. Try and think it through for yourself.

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Every program/input pair either halts some time, or never halts.
Determining this is a coherent requirement.

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That part is coherent.

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The part that this determination must be done by a Turing machine
using descriptions of the program and input is coherent, too.
>

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Every decider is required by definition to only report on what
this input specifies.
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int sum(int x, int y){ return x + y; }
sum(3,4) is not allowed to report on the sum of 5 + 6
even if you really really believe that it should.
>

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Exactly! Therefore H(D,D), where D is based on H that aborts and returns false, so that D halts, should not return a report about another D that does not halt, even if you really really believe that it should.

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There is enough information for sum(3,4) to compute the sum of 3+4.
There is NOT enough information for sum(3,4) to compute the sum of 5+6.
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There is enough information for H1(D,D) to compute Halts(D,D).
There is NOT enough information for H(D,D) to compute Halts(D,D).
>

 But it is possible to create a simulating sum decider that aborts sum and returns the sum of 5+6 and then claim that it is right, because it has not enough information to calculate 3+4. It is possible, but wrong.
The only reason it has not enough information, is that it aborts prematurely. That makes the decision to abort wrong. This holds for H as well.

Why are you denying reality?
Can D correctly simulated by H terminate normally?
01 int D(ptr x)  // ptr is pointer to int function
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 void main()
10 {
11   H(D,D);
12 }
*Execution Trace*
Line 11: main() invokes H(D,D);
*keeps repeating* (unless aborted)
Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
*Simulation invariant*
D correctly simulated by H cannot possibly reach past its own line 03.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer