A set of assertions about properties of a system and how they are effected by program execution. The axiomatic semantics of a program could include pre- and post-conditions for operations. In particular if you view the program as a state transformer (or collection of state transformers), the axiomatic semantics is a set of invariants on the state which the state transformer satisfies.
sort_list :: [T] -> [T]
One interesting use of axiomatic semantics is to have a language that has a finitely computable sublanguage that is used for specifying pre and post conditions, and then have the compiler prove that the program will satisfy those conditions.