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 ...

Computational logic and formal languages form a cornerstone of modern computer science and mathematics, providing the theoretical framework by which algorithms, automated reasoning systems and even ...

We present a dynamic approach to Peirce's original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic ...

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 ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...