This is a preview. Log in through your library . Abstract We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, φ, ...

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 ...

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 ...

The field of Reverse Mathematics explores the minimal axiomatic frameworks necessary to prove classical theorems, seeking to elucidate the logical foundations of mathematics. In parallel, ...