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