摘要：Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Pi_1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The key to treating non-prenex cuts lies in using a new class of tree grammars, constraint grammars, which describe the relationship of the applicability of its productions by a propositional formula.
关键词：proof theory; cut-elimination; Herbrand's theorem; tree grammars
