XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   On 16/01/2026 01:40, olcott wrote:   
   > 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.   
      
   A term does not prove anything. Only a proof proves.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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