The pq-system Axioms and Rules (from the book "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter) Axiom definition: xp-qx- is an axiom, whenever x is composed of hyphens only. Rule: if xpyqz is known to be a theorem, (where x, y, and z are strings containing only hyphens) then xpy-qz- is a theorem.
Note that x must stand for the same string of hyphens in both occurrences. For example, --p-q--- is an axiom. The literal expression 'xp-qx-' is not an axiom, of course (because 'x' does not belong to the pq-system); it is more like a mold in which all axioms are cast-and it is called an axiom schema.