A logic worth its salt should be understood as a method of correct reasoning about some class of entities, not as an empty formal game. For equational logic, the entities in question are sets, functions between them, and the relation of identity between elements. For rewriting logic, the entities in question are concurrent systems having states, and evolving by means of transitions. The signature of a rewrite theory describes a particular structure for the states of a system—e.g., multiset, binary tree, etc.—so that its states can be distributed according to such a structure.
― Dynamic Worlds: From the Frame Problem to Knowledge Management