Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normalform theorems. On the basis of these ...

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...