Project Presentation: Algorithmic Structuring and Compression of Proofs (ASCOP)

Abstract

Computer-generated proofs are typically analytic, i.e. they essentially consist only of formulas which are present in the theorem that is shown. In contrast, mathematical proofs written by humans almost never are: they are highly structured due to the use of lemmas. The ASCOP-project aims at developing algorithms and software which structure and abbreviate analytic proofs by computing useful lemmas. These algorithms will be based on recent groundbreaking results establishing a new connection between proof theory and formal language theory. This connection allows the application of efficient algorithms based on formal grammars to structure and compress proofs.

Understanding Resolution Proofs through Herbrand’s Theorem

“…Herbrand's theorem and methods based on it have furthermore also been used in a number of smaller case studies such as [9] by Baaz et al or [10] by Urban. In the context of the GAPT-system, Herbrand's theorem also plays a central role for the development of techniques for lemma generation, see Hetzl et al [11,12], and the tool described in this paper is routinely used there.…”