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 ...

Studia Logica: An International Journal for Symbolic Logic, Vol. 106, No. 2 (April 2018), pp. 219-235 (17 pages) We prove that for any recursively axiomatized consistent extension of Peano Arithmetic, ...

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 ...

Non-classical logics, encompassing modal, intuitionistic, fuzzy and other alternative logical systems, have increasingly benefitted from an algebraic treatment that elucidates the underlying structure ...