XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   On 1/14/2026 8:57 PM, Richard Damon wrote:   
   > On 1/13/26 1:43 PM, olcott wrote:   
   >> On 1/13/2026 6:10 AM, Richard Damon wrote:   
   >>> On 1/12/26 11:46 PM, olcott wrote:   
   >>>> On 1/12/2026 9:16 PM, Richard Damon wrote:   
   >>>>> On 1/12/26 4:41 PM, olcott wrote:   
   >>>>>> How The Well-Founded Semantics for General Logic Programs   
   >>>>>>   
   >>>>>> of (Van Gelder, Ross & Schlipf, 1991)   
   >>>>>> Journal of the Association for Computing Machinery,   
   >>>>>> volume 38, number 3, pp. 620{650 (1991).   
   >>>>>> https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf   
   >>>>>>   
   >>>>>> handle the Liar Paradox when we construe   
   >>>>>> non-well-founded / undefined as not a truth-bearer?   
   >>>>>>   
   >>>>>> % This sentence is not true.   
   >>>>>> ?- LP = not(true(LP)).   
   >>>>>> LP = not(true(LP)).   
   >>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).   
   >>>>>> false.   
   >>>>>>   
   >>>>>> WFS assigns undefined to self-referential paradoxes   
   >>>>>> without external support.   
   >>>>>>   
   >>>>>> When we interpret undefined as lack of truth-bearer   
   >>>>>> status the Liar sentence fails to be about anything   
   >>>>>> that can bear truth values   
   >>>>>>   
   >>>>>> The paradox dissolves - there's no contradiction   
   >>>>>> because there's no genuine proposition   
   >>>>>>   
   >>>>>> This is actually similar to how some philosophers   
   >>>>>> (like the "gap theorists") handle the Liar: sentences   
   >>>>>> that fail to achieve determinate truth conditions   
   >>>>>> simply aren't truth-bearers. WFS's undefined value   
   >>>>>> provides a formal mechanism for identifying exactly   
   >>>>>> these cases.   
   >>>>>>   
   >>>>>> A Subtle Point The occurs-check failure in Prolog is   
   >>>>>> slightly different from WFS's undefined assignment -   
   >>>>>> it's a structural constraint on term formation. But   
   >>>>>> both point to the same insight: circular, unsupported   
   >>>>>> self-reference doesn't create genuine semantic content.   
   >>>>>>   
   >>>>>>   
   >>>>>   
   >>>>>   
   >>>>> I thought you said that no one in the past handled the liar paradox?   
   >>>>>   
   >>>>   
   >>>> That is no one in the past handling the Liar Paradox.   
   >>>> That all happened today.   
   >>>   
   >>> So, today is 1991?   
   >>>   
   >>   
   >> The paper provides the basis for me to   
   >> handle the Liar Paradox today. The Paper   
   >> does not mention the Liar Paradox it   
   >> only shows how to implement Proof Theoretic   
   >> semantics in a logic programming system.   
   >>   
   >>>>   
   >>>>> I guess you are just admitting you are just a liar.   
   >>>>>   
   >>>>>   
   >>>>> Note, since Prolog's logic is not sufficient to handle PA,   
   >>>>   
   >>>> I never said it was. A formal system anchored in   
   >>>> Proof Theoretic Semantics is powerful enough.   
   >>>   
   >>> Nope. It can't handle PA.   
   >>>   
   >>   
   >> It definitely can. I already showed you the details   
   >> of how.   
   >   
   > Nope,  you PRESUME that Godel is non-sense.   
   >   
      
   “When PA is interpreted within proof‑theoretic semantics, only   
   well‑founded inferential structures are admissible as meaningful   
   statements. Gödel’s diagonal construction produces an ungrounded,   
   self‑referential formula whose proof‑dependency graph contains a cycle.   
   Since such expressions are not truthbearers in this framework, the   
   classical incompleteness phenomenon does not arise. PA itself remains   
   sound and complete with respect to its grounded proof rules.”   
      
   > But, you can't show the step in his proof that he uses an incorrect   
   > logic step.   
   >   
   > All you are doing is proving that you are just a pathological liar that   
   > can't cover his own lies.   
   >   
   > And, your claim that it is just non-smese means that you claim of making   
   > truth computable CAN'T be true.   
   >   
   > A fundamental of Godel's proof is showing that a proof checker is a   
   > computatble operation. That is the essense of what all of Godel's   
   > numbering and the relation he derives.   
   >   
   > If you define that you can't even build a proof checker, how do you   
   > expect to be able to determine if a statement is actually true?   
   >   
   >>   
   >>>>   
   >>>>> your argument here doesn't affect the logic system that you are   
   >>>>> trying to argue about, and you are just showing that you don't   
   >>>>> understand that difference.   
   >>>>>   
   >>>>> Many system can handle some self-references, which Prolog, and   
   >>>>> yours, can't.   
   >>>>   
   >>>>   
   >>>   
   >>   
   >>   
   >   
      
      
   --   
   Copyright 2026 Olcott

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

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