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it - Information Technology

Methods and Applications of Informatics and Information Technology

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Higher-order theorem proving and its applications

Alexander SteenORCID iD: https://orcid.org/0000-0001-8781-9462
Published Online: 2019-01-24 | DOI: https://doi.org/10.1515/itit-2019-0001

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.

Keywords: Theorem Proving; Automated Reasoning; Higher-Order Logic; Non-Classical Logics; Modal Logics

ACM CCS: Theory of computationLogicComputing methodologiesArtificial intelligenceKnowledge representation and reasoning

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About the article

Alexander Steen

Dr. Alexander Steen studied Computer Science and Mathematics at Freie Universität Berlin. During his undergraduate studies, he was awarded a scholarship of the German Academic Scholarship Foundation (Studienstiftung des Deutschen Volkes). Subsequently, Alexander joined the Dahlem Center for Robotics and Machine Learning at the Institute of Computer Science of FU Berlin as a research assistant, where he developed the higher-order automated theorem prover Leo-III (supported by the German Research Foundation DFG) as part of his doctoral studies. At FU Berlin, Alexander was strongly involved in administrative academic services and teaching, and was awarded the central teaching award (Zentraler Lehrpreis) of Freie Universität Berlin in 2015 for the conception of a novel, interdisciplinary lecture on Computational Metaphysics. Since August 2018, Alexander is a post-doctoral researcher at Luxembourg university focusing on applying computer-assisted reasoning technology to machine-ethics and normative reasoning in general. In the same year, he was awarded a GI Junior-Fellowship and elected Chair of the Special Interest Group for Deduction Systems (FG DedSys) of the Artificial Intelligence section (FB KI) of GI.


Received: 2019-01-11

Accepted: 2019-01-14

Published Online: 2019-01-24


Citation Information: it - Information Technology, ISSN (Online) 2196-7032, ISSN (Print) 1611-2776, DOI: https://doi.org/10.1515/itit-2019-0001.

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