Quasiary predicates can be defined as partial predicates over partial states (partial assignments) of variables. Such predicates have flexible arity. They are used to represent conditions in programs and program requirements, therefore logics of quasiary predicates are program-oriented logics. The main semantic idea of free logic is to allow singular terms not to denote an object. Therefore free logic has fewer existential presuppositions than classical logic. Free logic as well as classical predicate logic is based on total n-ary predicates. We demonstrate how different variants of free logic can be represented as logics of quasiary predicates. Properties of such representation are investigated. The obtained results can be useful for program verification and theory of definite descriptions.