Shkilniak S. Spectrum of logics of partial predicates oriented on composition-nominative program models

Various classes of logics of partial predicates oriented on composition-nominative program models are created and investigated. Semantic properties of composition-nominative logics of quasi-ary predicates of renominative and first-order levels are studied. Neoclassical logics such as logics of equitone predicates and their extensions are defined and investigated. They preserve main properties of classical predicate logic. For neoclassical logics, Hilbert and Gentzen (sequent) calculi are constructed and investigated, soundness and completeness theorems are proved, and important corollaries of completeness theorem are obtained. Many of the obtained results are generalizations of well-known statements of classical logic. Different formalizations of relation of logical consequence of composition-nominative logics of partial single-valued, total and partial ambiguous quasi-ary predicates are proposed and investigated. Logics of quasi-ary predicates can be considered as a foundation for creation of specific logics. On its basis, composition-nominative modal and temporal logics are introduced, and logics over hierarchical nominative data are constructed and investigated. The results obtained in the dissertation can be used in program and information systems development, particularly for program verification and specification systems. Key words: program models, logic, partial predicate, logical consequence, semantics, calculus, soundness, completeness.