AI Chat AI Image Generator AI Video Text to Speech

Axioms vs. rewrite rules: from completeness to cut elimination

06/01/2023

∙

by Gilles Dowek, et al.

∙

∙

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may require in particular to prove cut elimination for an extended notion of proof that combines deductions and computations. This suggests new interactions between automated theorem proving and proof theory.

page 1

page 2

page 3

page 4

research

∙ 04/21/2023

A Simple Proof That Super-Consistency Implies Cut Elimination

We give a simple and direct proof that super-consistency implies the cut...

0 Gilles Dowek, et al. ∙

research

∙ 06/25/2021

A Curiously Effective Backtracking Strategy for Connection Tableaux

Automated proof search with connection tableaux, such as implemented by ...

0 Michael Färber, et al. ∙

research

∙ 05/27/2011

Cooperation between Top-Down and Bottom-Up Theorem Provers

Top-down and bottom-up theorem proving approaches each have specific adv...

0 M. Fuchs, et al. ∙

research

∙ 05/02/2023

On the convergence of reduction-based and model-based methods in proof theory

In the recent past, the reduction-based and the model-based methods to p...

0 Gilles Dowek, et al. ∙

research

∙ 01/27/2020

Layered Clause Selection for Theory Reasoning

Explicit theory axioms are added by a saturation-based theorem prover as...

0 Bernhard Gleiss, et al. ∙

research

∙ 04/17/2019

Towards Evolutionary Theorem Proving for Isabelle/HOL

Mechanized theorem proving is becoming the basis of reliable systems pro...

0 Yutaka Nagashima, et al. ∙

research

∙ 03/10/2023

Lemmas: Generation, Selection, Application

Noting that lemmas are a key feature of mathematics, we engage in an inv...

0 Michael Rawson, et al. ∙