||The reason for the
tremendous representation inefficiency of propositional logic is that it does
not contain the concept of an object.
When we think about the world, we always think about objects ---
people, cars, cities, even talks --- are viewed as separate entities. Each of these has its own properties, or
attributes. And, they are all linked
to each other via a complex network of interactions. A yet more transparent representation is
relational logic. In this case, the
possible worlds specify a set of objects, their properties, and the relations
between them. By making objects
explicit, we can now generalize over them, specifying universal patterns that
apply to all objects. This allows us
to state many things at once, and provide a much more compact
representation. In particular, the
rules of chess now require only about 100 axioms.