# The Higher-Order Prover Leo-III

@inproceedings{Steen2018TheHP,
title={The Higher-Order Prover Leo-III},
author={Alexander Steen and Christoph Benzm{\"u}ller},
booktitle={IJCAR},
year={2018}
}
• Published in IJCAR 8 February 2018
• Computer Science
The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF), including their recent extensions to rank-1 polymorphism (TF1, TH1). In addition, the prover natively supports almost every normal higher-order modal logic. Leo-III cooperates with first-order reasoning tools using translations to many-sorted first-order logic and…
Extensional Higher-Order Paramodulation in Leo-III
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Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.
Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III
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• 2019
In this dissertation, both the theoretical and the practical challenges of designing an effective higher-order reasoning system are studied and the resulting system, the automated theorem prover Leo-III, is one of the most effective and versatile systems, in terms of supported logical formalisms, to date.
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In this extended abstract, the features of Leo-III are surveyed and almost every normal higher-order modal logic is supported.
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• 2021
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## References

SHOWING 1-10 OF 28 REFERENCES
The Higher-Order Prover Leo-II
• Computer Science
Journal of Automated Reasoning
• 2015
It is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants.
Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III
• A. Steen
• Computer Science
KI - Künstliche Intelligenz
• 2019
In this dissertation, both the theoretical and the practical challenges of designing an effective higher-order reasoning system are studied and the resulting system, the automated theorem prover Leo-III, is one of the most effective and versatile systems, in terms of supported logical formalisms, to date.
MleanCoP: A Connection Prover for First-Order Modal Logic
MleanCoP is a fully automated theorem prover for first-order modal logic that supports heterogeneous multimodal logics and outputs a compact prefixed connection proof.
TFF1: The TPTP Typed First-Order Form with Rank-1 Polymorphism
• Computer Science
• 2013
The TFF1 format is introduced, an extension of TFF0 with rank-1 polymorphism, designed to be easy to process by existing reasoning tools that support ML-style polymorphism.
Implementing and Evaluating Provers for First-order Modal Logics
• Computer Science, Mathematics
ECAI
• 2012
This paper presents several implementations of fully automated theorem provers for first-order modal logics based on different proof calculi, among them the standard sequent calculus, a prefixed tableau calculus, an embedding into simple type theory, an instance-based method, and a Prefixed connection calculus.
Theorem Provers For Every Normal Modal Logic
• Computer Science, Philosophy
LPAR
• 2017
A procedure for algorithmically embedding problems formulated in higherorder modal logic into classical higher-order logic, and can be used as a preprocessor for turning TPTP THF-compliant theorem provers into provers for various modal logics.
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
• Computer Science
J. Formaliz. Reason.
• 2010
Key developments have been the specification of the THF language, the addition of higher-order problems to theTPTP, the development of the TPTP THF infrastructure, several ATP systems for higher- order logic, and the use of higher -order ATP in a range of domains.
LeoPARD - A Generic Platform for the Implementation of Higher-Order Reasoners
• Computer Science
CICM
• 2015
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s) with an ambitious multi-agent blackboard architecture supporting prover parallelism at the term, clause, and search level.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
• Computer Science
• 2002
This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.
The QMLTP Problem Library for First-Order Modal Logics
• Computer Science
IJCAR
• 2012
The Quantified Modal Logic Theorem Proving library provides a platform for testing and evaluating automated theorem proving systems for first-order modal logics and a small number of problems for multi-modal logic are included as well.