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The Higher-Order Prover Leo-III [chapter]

Alexander Steen, Christoph Benzmüller
2018 Lecture Notes in Computer Science  
In addition, the prover natively supports almost every normal higher-order modal logic.  ...  The automated theorem prover Leo-III for classical higherorder logic with Henkin semantics and choice is presented.  ...  Introduction Leo-III is an automated theorem prover (ATP) for classical higher-order logic (HOL) with Henkin semantics and choice. 3 It is the successor of the well-known LEO-II prover [1] , whose development  ... 
doi:10.1007/978-3-319-94205-6_8 fatcat:5qspukjutnemtglrulv6fp3gp4

The Higher-Order Prover Leo-III (Extended Version) [article]

Alexander Steen, Christoph Benzmüller
2018 arXiv   pre-print
The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented.  ...  In addition, the prover natively supports almost every normal higher-order modal logic.  ...  Summary Leo-III is a state-of-the-art higher-order reasoning system offering many relevant features and capabilities.  ... 
arXiv:1802.02732v2 fatcat:5mnhei5iarb7vgmy5dkuawthia

Is It Reasonable to Employ Agents in Automated Theorem Proving?

Max Wisniewski, Christoph Benzmüller
2016 Proceedings of the 8th International Conference on Agents and Artificial Intelligence  
This situation is motivating our ongoing work in the higher-order theorem prover Leo-III .  ...  In contrast to its predecessor -the well established prover LEO-II -and most other modern provers, Leo-III is designed from the very beginning for concurrent proof search.  ...  ACKNOWLEDGMENTS We would like to thank all members of the Leo-III project.  ... 
doi:10.5220/0005824702810286 dblp:conf/icaart/WisniewskiB16 fatcat:ppu6zkmyvbblvg6tqbzl67mpe4

Extensional Higher-Order Paramodulation in Leo-III [article]

Alexander Steen, Christoph Benzmüller
2021 arXiv   pre-print
Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.  ...  Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice.  ...  Introduction Leo-III is an automated theorem prover (ATP) for classical higher-order logic (HOL) with Henkin semantics and choice.  ... 
arXiv:1907.11501v2 fatcat:hv3uysew6fdrtixvtv5d7ydgb4

Agent-Based HOL Reasoning [chapter]

Alexander Steen, Max Wisniewski, Christoph Benzmüller
2016 Lecture Notes in Computer Science  
In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed.  ...  Leo-III combines its predecessor's concept of cooperating external specialist systems with a novel agent-based proof procedure.  ...  The Leo-III System In its core, Leo-III is a new higher-order automated theorem prover based on the associated system platform LeoPARD [WSB15] .  ... 
doi:10.1007/978-3-319-42432-3_10 fatcat:zh42ihlxzbgwxfj5idt7lvuin4

LeoPARD --- A Generic Platform for the Implementation of Higher-Order Reasoners [article]

Max Wisniewski and Alexander Steen and Christoph Benzmüller
2015 arXiv   pre-print
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s).  ...  parallelism at the term, clause, and search level).  ...  We thank the reviewers for their valuable feedback. Moreover, we thank Tomer Libal and the students of the Leo-III project for their contributions to LeoPARD.  ... 
arXiv:1505.01629v1 fatcat:4lv5zmy46bdr7feas2shqcxrvy

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

Alexander Steen
2019 Künstliche Intelligenz  
In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented.  ...  An evaluation on a heterogeneous set of benchmark problems confirms that Leo-III is one of the most effective and versatile higher-order automated reasoning systems to date. vii  ...  Alexander Steen, Christoph Benzmüller, The Higher-Order Prover Leo-III.  ... 
doi:10.1007/s13218-019-00628-8 fatcat:b6yfenxgxndb3myskqushsm6uy

Extending a Brainiac Prover to Lambda-Free Higher-Order Logic [chapter]

Petar Vukmirović, Jasmin Christian Blanchette, Simon Cruanes, Stephan Schulz
2019 Lecture Notes in Computer Science  
Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition-based prover E and gradually enrich it with higher-order features.  ...  Higher-order provers lag behind in terms of efficiency.  ...  We are grateful to the maintainers of StarExec for letting us use their service. We thank Ahmed Bhayat, Alexander Bentkamp  ... 
doi:10.1007/978-3-030-17462-0_11 fatcat:eg3yugmhdveqdgicjqxqtn2crm

LeoPARD — A Generic Platform for the Implementation of Higher-Order Reasoners [chapter]

Max Wisniewski, Alexander Steen, Christoph Benzmüller
2015 Lecture Notes in Computer Science  
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s).  ...  parallelism at the term, clause and search level).  ...  In particular, LeoPARD provides the base layer of the new HO automated theorem prover (ATP) Leo-III, the successor of the well known provers LEO-I [3] and LEO-II [6] .  ... 
doi:10.1007/978-3-319-20615-8_22 fatcat:sgmw6ajnfvh5xh53lmkembpiim

Effective Normalization Techniques for HOL [chapter]

Max Wisniewski, Alexander Steen, Kim Kern, Christoph Benzmüller
2016 Lecture Notes in Computer Science  
It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers.  ...  In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool.  ...  These procedures are intended as preprocessing routines for the new Leo-III theorem prover [17] .  ... 
doi:10.1007/978-3-319-40229-1_25 fatcat:c46ta7reevguxabjqq5ljle5wm

Combined reasoning by automated cooperation

Christoph Benzmüller, Volker Sorge, Mateja Jamnik, Manfred Kerber
2008 Journal of Applied Logic  
In particular, in Section 4 we present this specialist integration for first-order and higher-order theorem provers.  ...  Of particular interest is the integration of first-order and higher-order techniques.  ...  In our architecture the problems are tackled by a collaboration of the higher-order theorem prover LEO, the first-order theorem prover OTTER, and the computer algebra system MAPLE.  ... 
doi:10.1016/j.jal.2007.06.003 fatcat:5wlvkzittjbkplgwkpx4qsqyya

Making Higher-Order Superposition Work [chapter]

Petar Vukmirović, Alexander Bentkamp, Jasmin Blanchette, Simon Cruanes, Visa Nummelin, Sophie Tourret
2021 Lecture Notes in Computer Science  
higher-order rules.  ...  Largely thanks to their use, Zipperposition won the higher-order division of the CASC-J10 competition.  ...  We are grateful to the maintainers of StarExec for letting us use their service. Ahmed Bhayat and Giles Reger guided us through details of Vampire 4.5.  ... 
doi:10.1007/978-3-030-79876-5_24 fatcat:equtnqydmvbmrexuw2eqjr7muq

An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning [article]

Alexander Steen
2022 arXiv   pre-print
When used as a pre-processor or library for higher-order theorem provers, the tool admits off-the-shelf automation for logics for which otherwise few to none provers are currently available.  ...  The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic.  ...  Exemplary ATP system results are produced by the higher-order prover Leo-III [35] , version 1.6.8, in which LET is integrated as a library and accessed via its API.  ... 
arXiv:2203.12352v1 fatcat:jfvsgqst5nbc7iunaozx7ucn5q

Superposition with Lambdas [chapter]

Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vukmirović, Uwe Waldmann
2019 Lecture Notes in Computer Science  
We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning.  ...  The inference rules work on βη-equivalence classes of λ-terms and rely on higher-order unification to achieve refutational completeness.  ...  LEO [13] and Leo-II [16] implement variants of RUE resolution. Leo-III [58] is based on higher-order paramodulation.  ... 
doi:10.1007/978-3-030-29436-6_4 fatcat:4gdwlahzjrhjljglvsqlinkhpa

Combining and automating classical and non-classical logics in classical higher-order logics

Christoph Benzmüller
2011 Annals of Mathematics and Artificial Intelligence  
We present illustrating example problems and report on experiments with off-the-shelf higher-order automated theorem provers.  ...  Numerous classical and non-classical logics can be elegantly embedded in Church's simple type theory, also known as classical higher-order logic.  ...  Geoff Sutcliffe, in collaboration with the author and supported by several further contributors, developed the new higher-order TPTP THF infrastructure (EU FP7 grant THFTPTP PIIF-GA-2008-219982).  ... 
doi:10.1007/s10472-011-9249-7 fatcat:4ppv6v36njcshd327mvguuj52a
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