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From The Free On-line Dictionary of Computing (27 SEP 03) :   [ foldoc ]

  symbolic inference
       
          The derivation of new facts from known facts and inference
          rules.  This is one of the fundamental operations of
          artificial intelligence and logic programming languages
          like Prolog.
       
          Inference is a basic part of human reasoning.  For example
          given that all men are mortal and that Socrates is a man, it
          is a trivial step to infer that Socrates is mortal.  We might
          express these symbolically:
       
          	man(X) => mortal(X).
          	man(socrates).
       
          ("if X is a man then X is mortal" and "Socrates is a man").
          Here, "man", "mortal" and "socrates" are just arbitrary
          symbols which the computer manipulates without reference to or
          knowledge of their external meaning.  A forward chaining
          system (a production system) could use these to infer the
          new fact
       
          	mortal(socrates).
       
          simply by matching the left-hand-side of the implication
          against the fact and substituting socrates for the variable X.
       
          (1994-10-28)
       
       

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