https://github.com/leoprover/leo-iii
An Automated Theorem Prover for Classical Higher-Order Logic with Henkin Semantics
https://github.com/leoprover/leo-iii
atp deduction-system higher-order-logic logic reasoning theorem-proving
Last synced: 10 months ago
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An Automated Theorem Prover for Classical Higher-Order Logic with Henkin Semantics
- Host: GitHub
- URL: https://github.com/leoprover/leo-iii
- Owner: leoprover
- License: bsd-3-clause
- Created: 2014-03-19T14:21:36.000Z (about 12 years ago)
- Default Branch: master
- Last Pushed: 2025-06-19T12:24:18.000Z (12 months ago)
- Last Synced: 2025-08-16T03:11:25.549Z (10 months ago)
- Topics: atp, deduction-system, higher-order-logic, logic, reasoning, theorem-proving
- Language: Scala
- Homepage:
- Size: 34 MB
- Stars: 49
- Watchers: 17
- Forks: 10
- Open Issues: 11
-
Metadata Files:
- Readme: README.md
- License: LICENSE
- Authors: AUTHORS
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README
Leo-III
========
*An automated theorem prover for classical higher-order logic with choice*
Leo-III [SB19,S18,SB18] is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives [Sut08,SWB17].
It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II [BP15], heavily relies on cooperation with external (mostly first-order) theorem provers for increased performance. Nevertheless, Leo-III can also be used as a stand-alone prover without employing any external cooperation.
In addition for its HOL reasoning capabilities, Leo-III supports reasoning in many higher-order quantified modal logics [GS18,GSB17].
Leo-III was initially developed at Freie Universität Berlin, and then at University of Luxembourg (until 2021). From 2014 - 2018, it was supported by the German National Research Foundation (DFG) under project BE 2501/11-1 (Leo-III). Since 2022, Leo-III is maintained and developed at the University of Greifswald, Germany. The main contributors are (sorted alphabetically): Christoph Benzmüller, Alexander Steen and Max Wisniewski. For a full list of contributors to the project and used and third-party libraries, please refer to the `AUTHORS` file in the source distribution.
Leo-III may be cited as [](https://doi.org/10.5281/zenodo.4435994)
## Install
Leo-III is written in the Scala programming language. It can be installed quite simply using the sbt build tool. Please refer to [INSTALL.md](INSTALL.md) to details.
## Usage
Leo-III runs on the JVM and accepts pretty much every [TPTP input dialect](http://www.cs.miami.edu/~tptp/TPTP/TR/TPTPTR.shtml) (e.g. FOF, TFF, THF) but it's mainly focused on reasoning in classical higher-order logic represented as THF. See [USAGE.md](USAGE.md) for details for its usage.
## License
Leo-III is licensed under the BSD 3-clause "New" or "Revised" License. See [LICENSE](LICENSE).
## Contributing
We are always greateful to hear feedback from our users:
- If you are using Leo-III for any project yourself, we would be happy to hear about it!
- If you encounter problems using Leo-III, feel tree to open a bug report (or simply a question) on the GitHub page.
- If you are interested to contribute to the project, simply fork the GitHub repository and open pull requests!
## Further information
Further information including related projects can be found on the [Leo-III project GitHub page](https://github.com/leoprover/), and for details on the Leo-III system (implementation), we refer to the system description [BSW17] and Steen's dissertation [S18].
## References
[SB21] Alexander Steen, Christoph Benzmüller, *Extensional Higher-Order Paramodulation in Leo-III*. Journal of Automated Reasoning 65, pp. 775-807, 2021. Preprint available at [arXiv:1907.11501](https://arxiv.org/abs/1907.11501).
[S18] Alexander Steen, [*Extensional Paramodulation for Higher-Order Logic and its Effective Implementation Leo-III*](http://www.aka-verlag.de/index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=701&virtuemart_category_id=4&Itemid=482&lang=en). Dissertation, Freie Universität Berlin. Published in Dissertations in Artificial Intelligence (DISKI), volume 345, EAN/ISBN 978-3-89838-739-2, AKA-Verlag, 2018. Preprint available [here](https://www.alexandersteen.de/phd/thesis-steen.pdf).
[GS18] Tobias Gleißner, Alexander Steen, [*The MET: The Art of Flexible Reasoning with Modalities*](https://doi.org/10.1007/978-3-319-99906-7_19). In Christoph Benzmüller, Francesco Ricca (Eds.), 2nd International Joint Conference on Rules and Reasoning (RuleML+RR 2018), Proceedings, Springer, LNCS, 2018.
[SB18] Alexander Steen, Christoph Benzmüller, [*The Higher-Order Prover Leo-III*](https://doi.org/10.1007/978-3-319-94205-6_8). In Didier Galmiche, Stephan Schulz, Roberto Sebastiani (Eds.), Automated Reasoning --- 9th International Joint Conference, IJCAR 2018, Oxford, UK, July 14-17, 2018, Proceedings , Springer, LNCS, Volume 10900, pp. 108-116, 2018. Preprint available [here](http://christoph-benzmueller.de/papers/C70.pdf).
[GSB17] Tobias Gleißner, Alexander Steen, Christoph Benzmüller, [*Theorem Provers for Every Normal Modal Logic*](https://doi.org/10.29007/jsb9). In LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning (Thomas Eiter, David Sands, eds.), EasyChair, EPiC Series in Computing, volume 46, pp. 14-30, 2017.
[BSW17] Christoph Benzmüller, Alexander Steen, Max Wisniewski, [*Leo-III Version 1.1 (System description)*](https://doi.org/10.29007/grmx), In Thomas Eiter, David Sands, Geoff Sutcliffe and Andrei Voronkov (Eds.), IWIL Workshop and LPAR Short Presentations, EasyChair, Kalpa Publications in Computing, Volume 1, pp. 11-26, 2017.
[SWB16] Alexander Steen, Max Wisniewski, Christoph Benzmüller, [*Agent-Based HOL Reasoning*](http://dx.doi.org/10.1007/978-3-319-42432-3_10). In 5th International Congress on Mathematical Software, ICMS 2016, Berlin, Germany, July 2016, Proceedings, Springer, LNCS, volume 9725. 2016.
[SWB17] Alexander Steen, Max Wisniewski, Christoph Benzmüller, [*Going Polymorphic - TH1 Reasoning for Leo-III*](https://doi.org/10.29007/jgkw). In IWIL@LPAR 2017 Workshop and LPAR-21 Short Presentations, Maun, Botswana, May 7-12, 2017 (Thomas Eiter, David Sands, Geoff Sutcliffe, Andrei Voronkov, eds.), EasyChair, Kalpa Publications in Computing, volume 1, 2017.
[BP15] Christoph Benzmüller, Lawrence C. Paulson, Nik Sultana, Frank Theiß, [*The Higher-Order Prover LEO-II*](http://dx.doi.org/10.1007/s10817-015-9348-y), In Journal of Automated Reasoning, volume 55, number 4, pp. 389-404, 2015.
[Sut08] Sutcliffe G. (2008), [*The SZS Ontologies for Automated Reasoning Software*](http://www.cs.miami.edu/home/geoff/Papers/Conference/2008_Sut08_KEAPPA-38-49.pdf),
Rudnicki P., Sutcliffe G., Proceedings of the LPAR Workshops: Knowledge
Exchange: Automated Provers and Proof Assistants, and The 7th International
Workshop on the Implementation of Logics (Doha, Qattar), CEUR Workshop
Proceedings 418, 38-49.