In the paper we investigate semantic properties of program-oriented 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 logics of quasiary non-deterministic predicates and investigate semantic properties of T-consequence relation for such logics. Specific properties of T-consequence relation for the class of deterministic predicates are also considered. Obtained results can be used to prove logic validity and completeness.