XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   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.   
      
   >>   
   >>> 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)