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 ...

Computational complexity and proof systems are fundamental areas in theoretical computer science that explore the limits of what can be computed and how efficiently problems can be solved. Recent ...

This is a preview. Log in through your library . Abstract We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n ...

Catalog description: Introduction to deductive logic. Topics include: basic concepts of deductive logic; techniques of formal proof in propositional and predicate logic. 3 units. Prerequisites: No ...

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 ...