13th International Conference on Typed Lambda Calculi and Applications (TLCA'15)

Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs in first-order predicate logic involving Π1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Π2-cuts. Given a proof π of a Σ1 formula with cuts only on Π2 formulæ, we show there is associated to π a natural context-free tree grammar whose language is finite and yields a Herbrand disjunction for π. 1998 ACM Subject Classification F.4.1 Mathematical Logic, F.4.2 Grammars and Other Rewriting Systems, F.4.3 Formal Languages