Logics of Quasiary Predicates in Formal Software Development

Logics of quasiary predicates are algebra-based logics constructed in a semantic-syntactic style on the methodological basis, which is common with programming. Such way of construction gives a possibility to use these logics in formal methods of software development. We demonstrate the main ideas of program logic construction and give formal definitions for an important fragment of program logics called many-sorted first-order composition-nominative logics. These logics are generalizations of classical logics for a case of partial predicates that do not have fixed arity; reasoning rules for such logics differ from classical ones. We study semantic properties of these logics used for investigation of satisfiability and validity problems.