XPost: comp.theory, sci.logic, sci.math   
   XPost: comp.lang.prolog, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   On 2/5/26 12:20 PM, olcott wrote:   
   > On 2/5/2026 12:06 PM, dart200 wrote:   
   >> On 2/4/26 7:04 PM, olcott wrote:   
   >>> On 2/4/2026 8:52 PM, dart200 wrote:   
   >>>> On 2/4/26 6:50 PM, olcott wrote:   
   >>>>> On 2/4/2026 8:42 PM, dart200 wrote:   
   >>>>>> On 2/4/26 4:00 PM, olcott wrote:   
   >>>>>>> On 2/4/2026 5:43 PM, dart200 wrote:   
   >>>>>>>> On 2/4/26 2:27 PM, olcott wrote:   
   >>>>>>>>> On 2/4/2026 4:19 PM, dart200 wrote:   
   >>>>>>>>>> On 2/4/26 2:15 PM, olcott wrote:   
   >>>>>>>>>>> On 2/4/2026 2:41 PM, dart200 wrote:   
   >>>>>>>>>>>> On 2/1/26 9:35 AM, olcott wrote:   
   >>>>>>>>>>>>> On 2/1/2026 6:11 AM, Richard Damon wrote:   
   >>>>>>>>>>>>>> On 1/31/26 12:49 PM, olcott wrote:   
   >>>>>>>>>>>>>>> Source code of fully operational system   
   >>>>>>>>>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> int DD()   
   >>>>>>>>>>>>>>> {   
   >>>>>>>>>>>>>>>    int Halt_Status = HHH(DD);   
   >>>>>>>>>>>>>>>    if (Halt_Status)   
   >>>>>>>>>>>>>>>      HERE: goto HERE;   
   >>>>>>>>>>>>>>>    return Halt_Status;   
   >>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> HHH simulates DD step-by-step according to   
   >>>>>>>>>>>>>>> the semantics of the C programming language.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> IT CAN'T, as you have been told, as your above program,   
   >>>>>>>>>>>>>> without the C CODE for HHH, has undefined behavior by the   
   >>>>>>>>>>>>>> semantics of the C programming language.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> HHH as executed by polcott is exhibiting a classifier   
   >>>>>>>>>>>> interface i'm calling a *partial recognizer*   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> (machine) -> {   
   >>>>>>>>>>>>    TRUE iff machine HALTS and DECIDABLE,   
   >>>>>>>>>>>>    FALSE iff machine LOOPS or UNDECIDABLE,   
   >>>>>>>>>>>> }   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> it doesn't do so quite so intelligently, but HHH(DD) needs   
   >>>>>>>>>>>> to return FALSE because DD is an UNDECIDABLE input to HHH   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> polcott does this by detecting the infinite recursion and   
   >>>>>>>>>>>> returning FALSE because of that   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> this approach of returning FALSE upon encountering an   
   >>>>>>>>>>>> infinite recursion on self (which i believe all paradoxes   
   >>>>>>>>>>>> will involve) will either be accurate or inaccurate in   
   >>>>>>>>>>>> regards to actually halting/ not... but it doesn't matter   
   >>>>>>>>>>>> because returning FALSE for halting yet UNDECIDABLE input is   
   >>>>>>>>>>>> acceptable for a *partial recognizer*   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> where this wouldn't work is:   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> int ND()   
   >>>>>>>>>>>> {   
   >>>>>>>>>>>>      int Halt_Status = HHH(ND);   
   >>>>>>>>>>>>      return Halt_Status;   
   >>>>>>>>>>>> }   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> HHH(ND) -> FALSE because HHH(ND) will recognize the infinite   
   >>>>>>>>>>>> recursion and return FALSE ... but that's not an acceptable   
   >>>>>>>>>>>> response for a *partial recognizer* for ND because ND is not   
   >>>>>>>>>>>> an UNDECIDABLE input, and it clearly should HALT   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> sorry polcott   
   >>>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> That is merely a text message that has not been updated.   
   >>>>>>>>>>>   
   >>>>>>>>>>> See my other post:   
   >>>>>>>>>>> When halt provers are allowed to reject bad   
   >>>>>>>>>>> inputs the remaining domain is decidable   
   >>>>>>>>>>>   
   >>>>>>>>>>> A bad input is any input that does not have   
   >>>>>>>>>>> *a well-founded justification tree within Proof*   
   >>>>>>>>>>> *theoretic semantics*   
   >>>>>>>>>>>   
   >>>>>>>>>>> For a simulating halt prover as soon as it detects   
   >>>>>>>>>>> that its simulated input cannot possibly reach its   
   >>>>>>>>>>> own simulated final halt state for any reason   
   >>>>>>>>>>> what-so-ever then this input  a bad input.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> so ur just banning self-referential analysis?   
   >>>>>>>>>>   
   >>>>>>>>>   
   >>>>>>>>> When we reject inputs not having   
   >>>>>>>>> *a well-founded justification tree within Proof*   
   >>>>>>>>> *theoretic semantics*   
   >>>>>>>>>   
   >>>>>>>>> Then undecidability utterly ceases to exist.   
   >>>>>>>>   
   >>>>>>>> i agree it's impossible to demonstrated undecidability without   
   >>>>>>>> self- reference,   
   >>>>>>>>   
   >>>>>>>> and filtering out paradoxes is a path to turing complete and   
   >>>>>>>> fully decidable subset of turing machines,   
   >>>>>>>>   
   >>>>>>>> but ND is a halting function, and i don't see a particular   
   >>>>>>>> reason why a more intelligent HHH couldn't return that given a   
   >>>>>>>> more in- depth analysis of how the self-reference interplays   
   >>>>>>>> with the rest of the machine   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> It cannot do that because that is not what it sees.   
   >>>>>>   
   >>>>>> once it sees the infinite recursion on itself ...   
   >>>>>>   
   >>>>>> why can't it do analysis on the effects of various possible return   
   >>>>>> values for itself ... like what we do when we talk thru it?   
   >>>>>>   
   >>>>>   
   >>>>> The job of a simulating halt prover is to determine   
   >>>>> whether or not it must abort its simulation to prevent   
   >>>>> its own non-termination. If for-any-reason the answer   
   >>>>> is yes then it is always correct to abort and reject   
   >>>>> this input.   
   >>>>>   
   >>>>   
   >>>> it's still a partial recognizer, just with worse power than perhaps   
   >>>> a more optimal one that can do more than just abort it's simulation,   
   >>>> but upon doing so recognize the self-reference and perform more in-   
   >>>> depth analysis beyond pure simulation.   
   >>>>   
   >>>   
   >>> Like I tell the LLM systems it is a partial halt prover   
   >>   
   >> i simple see that a more powerful partial halting recognizer can   
   >> return TRUE to the input ND just fine,   
   >>   
   >   
   > When an input does the opposite of whatever value   
      
   bro u didn't read what i posted before, please refer to the definition:   
      
      int ND()   
      {   
           int Halt_Status = HHH(ND);   
           return Halt_Status;   
      }   
      
   *ND* does not do the oppose of whatever HHH(ND) reports 🫩, it halts   
   regardless of what HHH(ND) reports.   
      
   yet HHH will still fail to report it's behavior properly because HHH   
   will decide that the self-referential recursion implies an infinite   
   execution that doesn't actually execute.   
      
   > its halt decider returns the only correct choice   
   > is to reject this input.   
   >   
   > Thanks to LLM systems I now finally have the proper   
   > conventional terms-of-the-art to say this, we correctly   
   > reject any input not having:   
   >   
   > *a well-founded justification tree within Proof*   
   > *theoretic semantics*   
   >   
   > I may have said that same thing not using conventional   
   > terms-of-the-art as much as 22 years ago. I only had   
   > the actual algorithm to do that about six years ago.   
   >   
   >> because i can map out the essential steps on paper...   
   >>   
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)