Kanger [4] gives a set of twelve axioms for the classical propositional Calculus which, together with modus ponens and substitution, have the following nice properties: (0.1) Each axiom contains ...

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 ...

This week we discuss the completeness theorem for the propositional calculus. Details can be found in this handout. You should also read Lemmon Chapter 4 during the next two weeks.