In lecture 7, we have seen how axiomatics and semantics of modal logic fit together in soundness proofs and correspondence proofs. We have seen several examples of classes of Kripke frames that are characterized by formulas of propositional modal logic. These were several special cases. But we are looking for a general correspondence result. Can we find a full correspondence result? For any for...

This paper is an exercise in formal and philosophical logic. I will show how intuitionistic propositional logic can be extended with a new two-place connective, not expressible in the traditional language of intuitionistic logic (the language of conjunction, disjunction, negation and implication). The new system will be shown to be a conservative extension of intuitionistic logic. After examini...