Year: 2024
Type: preprint
Abstract: An inductive proof can be represented as a proof schema, i.e. as a parameterized sequence of proofs defined in a primitive recursive way. A corresponding cut-elimination method, called schematic CERES, can be used to analyze these proofs, and to extract their (schematic) Herbrand sequents, even though Herbrand's theorem in general does not hold for proofs with induction inferences. This work focuses on the most crucial part of the schematic cut-elimination method, which is to construct a refutation of a schematic formula that represents the cut-structure of the original proof schema. We develop a new framework for schematic substitutions and define a unification algorithm for resolution schemata. Moreover, we show that this new formalism allows the extraction of a structure from the refutation schema, called a Herbrand schema, which represents its Herbrand sequent.
Source: arXiv (Cornell University)
Authors: Leitsch, Alexander, Lolic, Anela
Institutions: TU Wien, Kurt Gödel Society
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W4392118868