# 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} }

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…

## 50 Citations

Extensional Higher-Order Paramodulation in Leo-III

- Computer ScienceJ. Autom. Reason.
- 2021

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

- 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.

The Higher-Order Prover Leo-III (Extended Abstract)

- Computer Science, MathematicsKI
- 2019

In this extended abstract, the features of Leo-III are surveyed and almost every normal higher-order modal logic is supported.

System Demonstration: The Higher-Order Prover Leo-III

- Computer ScienceARQNL@IJCAR
- 2018

The Leo-III prover is presented, an automated theorem prover for classical higher-order logic (HOL) with Henkin semantics and choice, which supports flexible and effective reasoning in every common semantical variation of normal modal logics.

Superposition for Lambda-Free Higher-Order Logic ( Technical Report )

- Computer Science
- 2018

Refutationally complete superposition calculi for intentional and extensional λ-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.

A verified prover based on ordered resolution

- Computer Science, MathematicsCPP
- 2019

This work specifies, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establishes its soundness and refutational completeness, and applies stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program.

Superposition for Lambda-Free Higher-Order Logic

- Computer ScienceIJCAR
- 2018

Refutationally complete superposition calculi for intentional and extensional \(\lambda \)-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.

Extending a brainiac prover to lambda-free higher-order logic

- Computer ScienceTACAS
- 2019

This work proposes to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to higher- order logic, a formalism that supports partial application and applied variables.

Superposition for Full Higher-Order Logic (Technical Report)

- Computer Science
- 2021

This work designs a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics, and implements its implementation in Zipperposition on a par with an earlier, pragmatic prototype of Booleans.

Superposition for Higher-Order Logic

- Philosophy
- 2021

We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free λ-superposition and superposition for first-order logic with interpreted Booleans.…

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

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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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