XPost: comp.theory, sci.math, comp.ai.philosophy   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   The halting problem proof fails not because finite computation   
   is insufficient, but because it asks finite computation   
   to decide a judgment that is not finitely grounded under   
   operational semantics.   
      
   By “operational semantics” I mean the standard proof-theoretic   
   account of program meaning in which execution judgments are   
   defined by inference rules and termination corresponds to the   
   existence of a finite derivation.   
      
   By proof-theoretic semantics I mean the standard approach in   
   which the meaning of a statement is given by its rules of   
   proof rather than by truth conditions in a model.   
      
   This is the same sense in which operational semantics gives   
   meaning to programs via execution rules rather than denotations.   
      
   By denotational semantics I mean the standard approach in which   
   every well-formed program or statement is assigned a mathematical   
   object such as a function or truth value---independently of how   
   it is computed or proved.   
      
   This contrasts with operational or proof-theoretic semantics,   
   where meaning is given by execution or proof rules rather than   
   by an abstract denotation.   
      
   I use ‘denotational semantics’ simply to refer to any semantics   
   that assigns abstract mathematical meanings to programs independently   
   of their operational behavior.   
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)