XPost: comp.theory, sci.math, comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 12/6/2025 3:30 AM, Mikko wrote:   
   > olcott kirjoitti 5.12.2025 klo 19.43:   
   >> 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?   
   >   
   > When "G = not(provable(F, G))." is used as a Prolog goal the   
   > applied semantics is what Prolog lauguage definition specifies.   
   > Does "semantically sound" mean something in that context?   
   >   
   > At least your Prolog interpretation finds it meaningful. It determines   
   > that the excution of that goal succeeds and assigns a value G but not   
   > to F.   
   >   
      
   Is this sentence true or false:   
   "This sentence is not true"   
   It is not semantically sound.   
      
   Is this sentence true or false:   
   "This sentence cannot be proved"   
   It is not 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   
    * Origin: you cannot sedate... all the things you hate (1:229/2)