XPost: comp.theory, sci.math, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/23/2025 9:34 AM, olcott wrote:   
   > A Turing-machine decider is a Turing machine D that   
   > computes a total function D : Σ∗ → {Accept,Reject},   
   > where Σ∗ is the set of all finite strings over the   
   > input alphabet. That is:   
   >   
   > 1. Totality: For every finite string input w ∈ Σ∗,   
   > D halts and outputs either Accept or Reject.   
   >   
   > 2. Decision basis: Each input string is evaluated   
   > according to one of two types of properties:   
   >   
   >    (a) Syntactic property: a property of the input   
   >    string itself, such as containing a particular   
   >    substring or satisfying a structural pattern.   
   >   
   >    (b) Semantic property: a property of the sequence of   
   >    computational steps explicitly encoded by the input   
   >    string, i.e., the behavior that the input itself   
   >    specifies when interpreted as a machine description.   
      
   (b) Semantic property: This only applies to the subset   
   of finite strings that are valid machine descriptions   
   a property of the sequence of computational steps explicitly   
   encoded by the input string, i.e., the behavior that the   
   input itself specifies.   
      
   >   
   > The decider outputs Accept if the corresponding property   
   > holds for the input and Reject otherwise.   
   >   
      
      
   --   
   Copyright 2025 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   
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