Complete and Efficient Higher-Order Reasoning via Lambda-Superposition-Reference-Cited by-同舟云学术

Complete and Efficient Higher-Order Reasoning via Lambda-Superposition

Published:2023-10 Issue:4 Volume:10 Page:25-40
ISSN:2372-3491
Container-title:ACM SIGLOG News
language:en
Short-container-title:ACM SIGLOG News

Author:

Bentkamp Alexander¹,Blanchette Jasmin²,Nummelin Visa³,Tourret Sophie⁴,Waldmann Uwe⁵

Affiliation:

1. Heinrich-Heine-Universität Düsseldorf, Germany

2. Ludwig-Maximilians-Universität München, Germany

3. Vrije Universiteit Amsterdam, the Netherlands

4. Université de Lorraine, CNRS, Inria, LORIA, Nancy, France

5. Max-Planck-Institut für Informatik, Germany

Abstract

Superposition is a highly successful proof calculus for reasoning about first-order logic with equality. We present λ-superposition, which extends superposition to higher-order logic. Its design goals include soundness, completeness, efficiency, and gracefulness with respect to standard first-order superposition. The calculus is implemented in two automatic theorem provers: E and Zipper position. These provers regularly win trophies at the CADE ATP System Competition, confirming the calculus's applicability. This paper is a summary of research that took place between 2017 and 2022.

Publisher

Association for Computing Machinery (ACM)

Subject

General Earth and Planetary Sciences,General Environmental Science

Link

https://dl.acm.org/doi/pdf/10.1145/3636362.3636367

Reference40 articles.

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