XPost: comp.theory, sci.math, comp.prolog   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 8.12.2025 klo 21.12:   
   > On 12/5/2025 4:49 AM, Tristan Wibberley wrote:   
   >> On 04/12/2025 14:06, olcott wrote:   
   >>   
   >>> % 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"   
   >>   
   >> No. I think I showed in one of my recent posts (using definition   
   >> extensions) that you need to formalise the mathematicians notion of   
   >> "proof /in/ [system]" vis-a-vis "let" and its stronger sibling   
   >> "suppose". That's a bigger job than you've done.   
   >>   
   >> I need a new quotation convention for referring to things whose name has   
   >> an existing meaning in my U-language, I quoted "let" and "suppose" as if   
   >> I were using their names; I mean to use the things themselves, but they   
   >> have to be quoted in some way to distinguish the objects of mathematical   
   >> language from the verbs of ordinary language without introducing such   
   >> incidental new names as I would otherwise need.   
      
   > Semantics tautologies that define finite strings in   
   > terms of other finite strings to give the LHS its   
   > semantic meaning on the basis of the RHS.   
      
   You havn't given a single example of a smenatic tautology that can be   
   interpreted as a definition nor a single example of defintion that is   
   a semantic tautology. Perhaps it is possible if you define "semantic   
   taultology" so that it needn't be anything like a tautology.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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