The Free On-line Dictionary of Computing (30 December 2018):

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)