Re: Categorically exhaustive reasoning applied to the decision to abort

On 2024-03-29 14:26:50 +0000, olcott said:

On 3/29/2024 6:10 AM, Mikko wrote:

On 2024-03-28 15:38:08 +0000, olcott said:
 

On 3/28/2024 9:44 AM, Mikko wrote:

On 2024-03-27 14:04:17 +0000, olcott said:
 

On 3/27/2024 4:32 AM, Mikko wrote:

On 2024-03-26 14:41:08 +0000, olcott said:
 

On 3/26/2024 3:50 AM, Mikko wrote:

On 2024-03-25 22:52:18 +0000, olcott said:
 

On 3/24/2024 9:27 AM, Mikko wrote:

On 2024-03-24 02:11:34 +0000, olcott said:
 

On 3/23/2024 7:31 PM, Richard Damon wrote:

On 3/23/24 7:29 PM, 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.

 To be a decider it has to give an answer.
 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.
 

 That would entail that H must report on different behavior
than the behavior that H actually sees thus violate the
definition of a decider that must compute the mapping from
its inputs...

 Nope.
You are just showing yourself to be a stupid liar.
 Where in the DEFINITION of Compute the Mapping of the Input to the Mapped Output does it say that the decider has to be able to "see" that property of the input?
 

 In order to compute the mapping from an input there must be
some basis that is directly provided by this input.

 If no such basis is in the input the problem has no soution.
 

 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.

 Your and my beliefs don't matter. Testers call the function with
various pairs of inputs and compare the result to the specification.
If the result is not what the specification requires then the function
is wrong and needs be fixed or rejected.
 

 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.
 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).

 There is enough information to determine whether the result is as
required by the specification.
 

 This specification only requires a mapping from H(D,D)
to Halts(Simulated_by_H(D,D)) and it gets that one correctly.
D(D) does not halt from the POV of H.

 What "this pecification"? This means the one you refer or point to
but you didn't.
 

 Every implementation of H(D,D) that simulates its input must abort
this simulation or never itself halt.
 int main() { D(D); }   is not a D simulated by H.
int main() { H(D,D); } is a D simulated by H.

 Does not answer what "this specification" means above.
 

 *THIS SPECIFICATION*
Every implementation of H(D,D) that simulates its input must abort
this simulation or never itself halt.

Are you sure you want to allow that H(D,D) may run un a loop and never
halt and never continue the simulation?
--
Mikko