Source : Free On-Line Dictionary of Computing

symbolic inference
     
        The derivation of new facts from known facts and {inference
        rule}s.  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)