XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: polcott333@gmail.com   
      
   On 2/6/2026 1:42 AM, dart200 wrote:   
   > On 2/5/26 9:26 PM, olcott wrote:   
   >> On 2/5/2026 11:22 PM, dart200 wrote:   
   >>> On 2/5/26 9:01 PM, olcott wrote:   
   >>>> On 2/5/2026 10:36 PM, dart200 wrote:   
   >>>>> On 2/5/26 8:31 PM, olcott wrote:   
   >>>>>> On 2/5/2026 10:15 PM, dart200 wrote:   
   >>>>>>> On 2/5/26 8:08 PM, olcott wrote:   
   >>>>>>>> On 2/5/2026 9:23 PM, dart200 wrote:   
   >>>>>>>>> On 2/5/26 7:11 PM, olcott wrote:   
   >>>>>>>>>> On 2/5/2026 8:49 PM, dart200 wrote:   
   >>>>>>>>>>> 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 ...   
   >>>>>>>>>>>>>>>>>   
      
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