In this paper, we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying TaitGirard's saturated sets method. Next, we prove the completeness ...

In propositional logic, an atomic sentence is simple in the sense that it is not the result of composition from simpler sentences using the propositional connectives.

We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using ...