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, ...

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 ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...