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