XPost: comp.theory, sci.math, comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 12/5/2025 3:38 AM, Mikko wrote:   
   > olcott kirjoitti 4.12.2025 klo 16.06:   
   >> On 12/4/2025 2:58 AM, Mikko wrote:   
   >>> Tristan Wibberley kirjoitti 4.12.2025 klo 4.32:   
   >>>> On 30/11/2025 09:58, Mikko wrote:   
   >>>>   
   >>>>> Note that the meanings of   
   >>>>>   ?- G = not(provable(F, G)).   
   >>>>> and   
   >>>>>   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >>>>> are different. The former assigns a value to G, the latter does not.   
   >>>   
   >>>> For sufficiently informal definitions of "value".   
   >>>> And for sufficiently wrong ones too!   
   >>>   
   >>> It is sufficiently clear what "value" of a Prolog variable means.   
   >   
   >> % This sentence cannot be proven in F   
   >> ?- G = not(provable(F, G)).   
   >> G = not(provable(F, G)).   
   >> ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >> false.   
   >>   
   >> I would say that the above Prolog is the 100%   
   >> complete formal specification of:   
   >>   
   >> "This sentence cannot be proven in F"   
   >   
   > The first query can be regarded as a question whether "G = not(provable(   
   > F, G))" can be proven for some F and some G. The answer is that it can   
   > for every F and for (at least) one G, which is not(provable(G)).   
   >   
   > The second query can be regarded as a question whether "G = not(provable   
   > (F, G))" can be proven for some F and some G that do not contain cycles.   
   > The answer is that in the proof system of Prolog it cannot be.   
   >   
      
   No that it flatly incorrect. The second question is this:   
   Is "G = not(provable(F, G))." semantically sound?   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
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