The Higher-Order Prover Leo-III

Steen, Alexander; Benzmüller, Christoph

doi:10.1007/978-3-319-94205-6_8

Cited by 43 publications

(63 citation statements)

References 15 publications

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“…Because it is based on Bachmair and Ganzinger's framework, our approach generally applies to all saturation-based provers, with or without redundancy. This includes resolution, paramodulation, ordered rewriting, superposition, and variants thereof, covering many of the most successful provers for equational [8,12], first-order [21,42,53], and higher-order logic [45].…”

Section: Resultsmentioning

confidence: 99%

A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness. Methodologically, we apply stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for first-order logic. CCS Concepts • Theory of computation → Logic and verification; Automated reasoning;

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Section: Resultsmentioning

confidence: 99%

A verified prover based on ordered resolution

Schlichtkrull¹,

Blanchette

Traytel

2019

Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs

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show abstract

“…The practical evidence that quantified modal logics can effectively be modeled as a fragment of classical higher-order logic furthermore suggests that higherorder logic can serve as an universal meta-logic [Ben17b]. This claim is further substantiated by more recent evaluations [BOR12,GSB17,SB18] and the observation that there exist analogous reductions for numerous further non-classical logics [BS16,SB16,Ben17a,Ben17c,BFP18], for many of which there exist none or only few specialized reasoning systems. A strong foundation for the automation of higher-order logic and an effective implementation of a corresponding deduction system thus enables computer-assisted reasoning in even more, practically relevant, logical systems and application areas.…”

Section: Motivationmentioning

confidence: 90%

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

Steen

2019

Künstl Intell

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In this thesis the theoretical foundations and the practical components for implementing an effective automated theorem proving system for higher-order logic are presented. A primary focus of this thesis is the provision of evidence that a paramodulation-based proof calculus can effectively be employed for performant equational reasoning in Extensional Type Theory (higher-order logic). To that end, a sound and complete paramodulation calculus for extensional higherorder logic with Henkin semantics is presented. The completeness proof hereby unifies and simplifies existing abstract consistency techniques for a formulation of higher-order logic that is based on primitive equality as sole logical connective. In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented. Leo-III is based on the above paramodulation calculus and implements additional practically motivated inference rules including equational simplification routines such as heuristic rewriting and support for reasoning with choice. The system encompasses a flexible mechanism for asynchronous cooperation with first-order reasoning systems, a powerful proof search procedure and a sophisticated and efficient set of underlying data structures. Pragmatic and practically significant features of Leo-III are discussed, including its native support for polymorphic higher-order logic and reasoning in higher-order quantified modal logics. An evaluation on a heterogeneous set of benchmark problems confirms that Leo-III is one of the most effective and versatile higher-order automated reasoning systems to date. vii The dissertation project was conducted within the "Leo-III" project funded by the German Research Foundation (DFG) under grant BE 2501/11-1, and the project "Consistent Rational Argumentation in Politics" funded by the Volkswagenstiftung. All source code related to work presented in this thesis is publicly available (under BSD-3 license) at https://github.com/leoprover/Leo-III.

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“…67 These systems, in turn, make calls to specialist tools such as Kodkod, Paradox, smbc, and the SMT solvers CVC4 68 and Z3. 69 Other systems integrated with Sledgehammer include the first-order ATPs E, 70 Spass, 71 Vampire, 72 and the higher-order ATPs Leo-II, 73 Leo-III, 74 and Satallax. 75 If one downloads Isabelle/HOL, all of these systems are bundled with it, except for the higher order provers like Leo-II, Leo-III and Satallax, which can be accessed via the TPTP infrastructure using remote calls.…”

Section: Generalizing the Cross-fertilizationmentioning

confidence: 99%

Computer Science and Metaphysics: A Cross-Fertilization

2019

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Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that led to these results may be more broadly applicable within computer science. The paper includes a description of our background methodology and how it evolved, and a discussion of our new results.

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The Higher-Order Prover Leo-III

Cited by 43 publications

References 15 publications

A verified prover based on ordered resolution

A verified prover based on ordered resolution

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

Computer Science and Metaphysics: A Cross-Fertilization

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