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 ...

This paper investigates the "general" semantics for first-order logic introduced to Antonelli (Review of Symbolic Logic 6 (4), 637-58, 2013): a sound and complete axiom system is given, and the ...