  We develop a classical propositional logic for reasoning about combinatory
logic. We define its syntax, axiomatic system and semantics. The syntax and
axiomatic system are presented based on classical propositional logic, with
typed combinatory terms as basic propositions, along with the semantics based
on applicative structures extended with special elements corresponding to
primitive combinators. Both the equational theory of untyped combinatory logic
and the proposed axiomatic system are proved to be sound and complete w.r.t.
the given semantics. In addition, we prove that combinatory logic is sound and
complete w.r.t. the given semantics.
