Relations of Logical Consequence in Program-oriented Logics of Quasiary Predicates

We study new classes of program-oriented logical formalisms-pure first-order logics of quasiary predicates with extended renominations. Logics with predicates of weak equality and strong equality are considered; special attention is paid to logics with composition of predicate complement. For the introduced logics, composition algebras and languages are described and various logical consequence relations are specified including relations with undefinedness conditions. Relationships between different logical consequence relations are defined and conditions for elimination of undefinedness for the logical consequence relations of types T and F are determined.