XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: polcott333@gmail.com   
      
   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.   
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable for the entire body of knowledge.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)