XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   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 ...   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> 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?   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
      
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