A Sequent-Calculus Based Formulation of the Extended First Epsilon Theorem
The optimal calculation of Herbrand disjunctions from unformalized or formalized mathematical proofs is one of the most prominent problems of computational proof theory. The up-to-date most direct approach to calculate Herbrand disjunctions is based on Hilbert’s epsilon formalism (which is in fact also the oldest framework for proof theory). The algorithm to calculate Herbrand disjunctions is an integral part of the proof of the extended first epsilon theorem. This paper connects epsilon proofs and sequent calculus derivations with cuts. This leads to an improved notation for the epsilon formalism and a computationally improved version of the extended first epsilon theorem, which allows a nonelementary speed-up of the computation of Herbrand disjunctions.
KeywordsExtended first epsilon theorem Herbrand disjunctions Epsilon calculus
Partially supported by FWF grants P-26976-N25, I-2671-N35 and the Czech-Austrian project MOBILITY No. 7AMB17AT054.