XPost: comp.theory, sci.math, comp.lang.prolog   
   From: mikko.levanto@iki.fi   
      
   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?   
      
   Where is the definition of Prolog semantics is that said?   
      
   --   
   Mikko   
      
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