Higher-order logic

All higher-order logics, which refer to a series of logical systems where universal and existential quantifiers can be applied to variables referring to relations or relations of relations, can be considered as subsystems of ω-order logic. For example, in second-order logic, variables can refer to individuals and predicates, and predicates can denote properties of sets of individuals or relations. Third-order logic includes second-order predicates as variables, and predicates can denote properties of second-order predicates.