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 ...

Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have ...

In the English as in most but not all languages (i.e. Chinese) number can be extracted from the noun leaving a lexical-propositional form of the noun. From book and books we get object predicate: 1.