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… 
Extending a High-Performance Prover to Higher-Order Logic
TLDR
This work extends E to full higher-order logic, and finds the resulting prover is the strongest one on benchmarks coming from a proof assistant, and the second strongest on TPTP benchmarks.
Automated Reasoning in Non-classical Logics in the TPTP World
TLDR
The latest extension of the TPTP World is described, which provides languages and infrastructure for reasoning in non-classical logics, and the extensions integrate seamlessly with the existing TP TP World.
Lash 1.0 (System Description)
TLDR
The ways in which Lash differs from Satallax are described and the performance improvement of Lash overSatallax when used with analogous flag settings are described.
Making Higher-Order Superposition Work
TLDR
Techniques that address issues such as infinitely branching inference rules, new possibilities such as reasoning about formulas, and the need to curb the explosion of specific higher-order rules are described and extensively evaluated in the Zipperposition theorem prover.
Seventeen Provers under the Hammer 1
TLDR
This paper uses Isabelle/HOL’s Sledgehammer tool to find out how useful modern provers 15 are at proving formulas in higher-order logic, and uses an alternative yardstick for comparing modern 18 provers next to the benchmarks and competitions emerging from the TPTP World and SMT-LIB.
A Formalisation of Abstract Argumentation in Higher-Order Logic
TLDR
This work presents an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic that enables the formal analysis and verification of meta-theoretical properties as well as the flexible generation of extensions and labellings with respect to well-known argumentation semantics.
Designing Normative Theories of Ethical Reasoning: Formal Framework, Methodology, and Tool Support
TLDR
Off-the-shelf theorem provers and model finders for higher-order logic are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples--all at the same time.
Local is Best: Efficient Reductions to Modal Logic K
<jats:p>We present novel reductions of extensions of the basic modal logic <jats:inline-formula><jats:alternatives><jats:tex-math>$${\textsf {K} }$$</jats:tex-math><mml:math
An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning
TLDR
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic and admits off-the-shelf automation for logics for which otherwise few to none provers are currently available.

References

SHOWING 1-10 OF 141 REFERENCES
The Higher-Order Prover Leo-III
TLDR
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
  • A. Steen
  • Computer Science
    KI - Künstliche Intelligenz
  • 2019
TLDR
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-II
TLDR
It is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants.
Extensional Higher-Order Paramodulation and RUE-Resolution
TLDR
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.
A Focused Sequent Calculus for Higher-Order Logic
TLDR
A focused intuitionistic sequent calculus for higher-order logic that has primitive support for equality and mixes λ-term conversion with equality reasoning and is proved sound with respect to Church's simple type theory.
Going Polymorphic - TH1 Reasoning for Leo-III
TLDR
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
TLDR
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)
TLDR
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
TLDR
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
TLDR
MleanCoP is a fully automated theorem prover for first-order modal logic that supports heterogeneous multimodal logics and outputs a compact prefixed connection proof.
...
...