# Extensional Higher-Order Paramodulation in Leo-III

@article{Steen2021ExtensionalHP, title={Extensional Higher-Order Paramodulation in Leo-III}, author={Alexander Steen and Christoph Benzm{\"u}ller}, journal={J. Autom. Reason.}, year={2021}, volume={65}, pages={775-807} }

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems…

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## References

SHOWING 1-10 OF 141 REFERENCES

The Higher-Order Prover Leo-III

- Computer ScienceIJCAR
- 2018

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented and natively supports almost every normal higher- order modal logic.

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

- Computer ScienceKI - 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.

Extensional Higher-Order Paramodulation and RUE-Resolution

- Computer ScienceCADE
- 1999

Two approaches to primitive equality treatment in higher-order (HO) automated theorem proving are presented: a calculus EP adapting traditional first-orders paramodulation, and a calculus ERUE adapting FO RUE-Resolution to classical type theory, i.e., HO logic based on Church's simply typed λ-calculus.

Going Polymorphic - TH1 Reasoning for Leo-III

- Computer ScienceIWIL@LPAR
- 2017

Modifications to the higher-order automated theorem prover Leo-III are presented for turning it into a reasoning system for rank-1 polymorphic HOL and a suitable paramodulation-based calculus are sketched.

HOL Based First-Order Modal Logic Provers

- Computer ScienceLPAR
- 2013

The FMLtoHOL tool enables the application of off-the-shelf HOL provers and model finders for reasoning within first-order modal logics and sequentially schedules various HOL reasoners.

Leo-III Version 1.1 (System description)

- Computer ScienceLPAR
- 2017

This paper sketches Leo-III’s underlying calculus, survey implementation details and give examples of use, and sketches the role of asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme.

System Description: LEO - A Higher-Order Theorem Prover

- Computer ScienceCADE
- 1998

Leo uses a higher-order Logic based upon Church's simply typed λ-calculus, so that the comprehension axioms are implicitly handled by αβη-equality, and extensionality principles are build in into Leo’s unification, and hence do not have to be axiomatized in order to achieve Henkin completeness.

MleanCoP: A Connection Prover for First-Order Modal Logic

- Computer ScienceIJCAR
- 2014

MleanCoP is a fully automated theorem prover for first-order modal logic that supports heterogeneous multimodal logics and outputs a compact prefixed connection proof.

Set of Support for Higher-Order Reasoning

- Computer SciencePAAR@FLoC
- 2018

Limiting how axioms introduced during translation can improve proof search with higher-order problems is shown and heuristics based on the set-of-support strategy for minimising the effects are introduced.

Equality and extensionality in automated higher order theorem proving

- Computer Science
- 1999

The three new calculi ER, ERUE, EP and ERUE which improve the mechanisation of defined and primitvie equality in classical type theory and these calculi reach Henkin completeness without requiring additional extensionality axioms are introduced.