2024/02/21 by Alexander Leitsch, Leitsch, Alexander, Anela Lolić +1
Engineering · Mathematics · Physics and Astronomy · #Aerospace Engineering and Control Systems #Electromagnetic Scattering and Analysis #FOS: Mathematics #Logic (math.LO) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2402.13905
openalex publication_date 2024/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.