Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

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 ...

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, ...

Solutions are available by request for course instructors and the self-taught. These documents are intended for the spring 2024 version of PHI 201, Introductory Logic. However, they will be fine-tuned ...

George Boole was a British mathematician whose work on logic laid many of the foundations for the digital revolution. The Lincolnshire-born academic is widely heralded as one of the most influential ...