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