XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: news.x.richarddamon@xoxy.net   
      
   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.   
      
   You CAN NOT consistantly interpreted PA withiing proof-theoretic semantics.   
      
   Godels statement *WAS* built bu well-founded inferential methods.   
      
   His statement *IS* a truth bearer by the rules of the logic.   
      
   You can't just say otherwise.   
      
   Your problem is you just can't "redefine" what a word, like truth means,   
   in a system.   
      
   You don't seem to understand that the paper you are reading admits that   
   it isn't handling thw whole of the space, but only giving PARTIAL answers.   
      
   >   
   >> 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.   
   >>>>>   
   >>>>>   
   >>>>   
   >>>   
   >>>   
   >>   
   >   
   >   
      
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