For AI as engineering, this is all straightforward. Many AI programs are written in the languages Lisp or Prolog, and the elementary symbols will usually correspond to numeric and string constants. In Prolog, they'd include what are called ``atoms''. You should look at a few examples: see for instance the description of Evans' Analogy program in pages 24-32 of Artificial Intelligence by P Winston (2nd edition Addison-Wesley 1992: PSY KH:W 072).
These references do not explicitly state the symbols, syntax rules, and so on, but you can easily get some idea of what they should be. In all three references, at least some of the notation rather resembles logic. This is no accident.