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