XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   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   
      
   >   
   > and   
   >   
   > "true on the basis of meaning expressed in language"   
   > becomes reliably computable for the entire body of knowledge.   
   >   
      
   --   
   arising us out of the computing dark ages,   
   please excuse my pseudo-pyscript,   
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
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