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Higher-order theorem proving and its applications

Alexander Steen ORCID logo

Abstract

Automated theorem proving systems validate or refute whether a conjecture is a logical consequence of a given set of assumptions. Higher-order provers have been successfully applied in academic and industrial applications, such as planning, software and hardware verification, or knowledge-based systems. Recent studies moreover suggest that automation of higher-order logic, in particular, yields effective means for reasoning within expressive non-classical logics, enabling a whole new range of applications, including computer-assisted formal analysis of arguments in metaphysics. My work focuses on the theoretical foundations, effective implementation and practical application of higher-order theorem proving systems.

This article briefly introduces higher-order reasoning in general and presents an overview of the design and implementation of the higher-order theorem prover Leo-III. In the second part, some example applications of Leo-III are discussed.

ACM CCS:

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Received: 2019-01-11
Accepted: 2019-01-14
Published Online: 2019-01-24
Published in Print: 2019-08-27

© 2019 Walter de Gruyter GmbH, Berlin/Boston