Shkilnyak O. Investigation of composition nominative modal and temporal logics

New classes of logics of partial predicates oriented on composition-nominative program models - composition nominative modal and temporal logics - are created. A special refinement of the notion of composition nominative modal system is introduced. General and temporal modal transition systems and logics based on such systems are specified. Semantic properties of general transition and temporal composition nominative logics of renominative and first-order levels are investigated. Functionally stable modal systems are defined for logics of functional-equational level. A relation of logical consequence for sets of specified with state names formulas is described and its properties are investigated. For general transition and temporal modal logics of propositional and nominative levels sequent calculi are constructed. Such calculi are based on relational semantics of introduced logics. Depending on properties of transition relation on states of the universe, various variants of the calculi can be obtained. For the defined calculi, soundness and completeness theorems are proved. The results of the dissertation can be used in program and information systems development; they are included to educational courses in a curriculum. Key words: program models, mоdal logic, temporal logic, partial predicate, logical consequence, semantics, sequent calculus.