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 ...

MIT Press recently published Fundamental Proof Methods in Computer Science, a book by Konstantine Arkoudas and David Musser, a professor emeritus of computer science at the Rensselaer Polytechnic ...

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 ...

What seem to be Kurt Gödel's first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested ...

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, ...

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, ...

A computer-assisted proof of a 150-year-old mathematical conjecture can at last be checked by human mathematicians. The Four Colour Theorem, proposed by Francis Guthrie in 1852, states that any four ...

AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we ...