XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   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;   
   >>    }   
   >>   
   >> *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.   
   >>   
   >   
   > When HHH is a simulating proof theoretic halt prover (SPTHP)   
   > any input that does not have a well-founded justification   
      
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