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 ...

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of ...

God is by definition a perfect being. It is more perfect to exist than to not exist. Therefore, God exists. Just given these simple ideas, a few axioms, and a fondness for pushing around abstract ...

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 ...

WHEN the brilliant French mathematician Henri Poincaré was not actually doing maths, he liked to think about the nature of mathematical creativity. Logic, he felt, was important, but it was not enough ...

This course will discuss fundamental concepts and tools in discrete mathematics with emphasis on their applications to computer science. Example topics include logic and Boolean circuits; sets, ...