Herbrand Disjunctions, Cut Elimination and Context-Free Tree Grammars
نویسندگان
چکیده
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
منابع مشابه
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 o...
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