In the paper we investigate semantic properties of programoriented algebras and logics defined for classes of quasiary predicates. Informally speaking, such predicates are partial predicates defined over partial states (partial assignments) of variables. Conventional n-ary predicates can be considered as a special case of quasiary predicates. We define first-order algebras and logics of quasiary non-deterministic predicates and investigate their semantic properties. Obtained results can be used to prove logic validity and completeness.