# Set of Support for Higher-Order Reasoning

@inproceedings{Bhayat2018SetOS, title={Set of Support for Higher-Order Reasoning}, author={Ahmed Bhayat and Giles Reger}, booktitle={PAAR@FLoC}, year={2018} }

Higher-order logic (HOL) is utilised in numerous domains from program verification to the formalisation of mathematics. However, automated reasoning in the higher-order domain lags behind first-order automation. Many higher-order automated provers translate portions of HOL problems to first-order logic (FOL) and pass them to FOL provers. However, FOL provers are not optimised for dealing with these translations. One of the reasons for this is that the axioms introduced during the translation (e…

## 15 Citations

Extensional Higher-Order Paramodulation in Leo-III

- Computer ScienceJ. Autom. Reason.
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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.

Extending SMT solvers to Higher-Order Logic ( Technical Report )

- Computer Science
- 2019

This work proposes a pragmatic extension of SMT solvers to natively support higher-order reasoning without compromising their performance on FOL problems, thus leveraging the extensive research and implementation efforts dedicated to efficient FOL solving.

Extending SMT Solvers to Higher-Order Logic

- Computer ScienceCADE
- 2019

This work proposes a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving.

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- 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.

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- 2019

A restricted version of Dougherty's algorithm that is incomplete, terminating and does not require polymorphism is presented, including a novel use of a substitution tree as a filtering index for higher-order unification.

Superposition for Full Higher-Order Logic (Technical Report)

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- 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.

Aiming for the Goal with SInE

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This paper implemented biasing clause selection to postpone introduction of input clauses further from the goal and goal sensitive simplification ordering in the automatic theorem prover Vampire and presented their experimental evaluation on the TPTP benchmark.

Some Thoughts About FOL-Translations in Vampire

- Computer ScienceARQNL@IJCAR
- 2018

This paper looks at translation activity from the perspective of a first-order ATP (mostly Vampire) and finds that not all translations are equal.

Superposition for Higher-Order Logic

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- 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.…

Superposition for Full Higher-order Logic

- PhilosophyCADE
- 2021

This work aims to reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics, and its implementation in Zipperposition outperforms all other higher- order theorem provers.

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