XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   On 1/15/2026 5:50 AM, Richard Damon wrote:   
   > On 1/15/26 12:24 AM, olcott wrote:   
   >> 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.”   
   >   
   > In other words, you are just admitting to be an idiot that deosn't care   
   > what your words actually mean.   
   >   
      
   The term *proof‑theoretic semantics* has always   
   proved my point long before I ever heard of it.   
      
      
   --   
   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)