leanCoP 2.0 and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions)

Otten, Jens

doi:10.1007/978-3-540-71070-7_23

Cited by 47 publications

(66 citation statements)

References 22 publications

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“…The results for HOL-P are presented in Table 1. Moreover, in Table 1 the performance of HOL-P is compared to corresponding results as reported on the QMLTP-website 7 for the provers f2p-MSPASS-3.0 (an instance-based prover which employs MSPASS [8] to prove or refute the propositional formulas it generates), MleanSeP-1.2 (a sequent prover; its calculus extends the classical sequent calculus with specific rules for 2 and 3), MleanTAP-1.3 (a tableaux prover; a classical tableaux calculus is extended by adding and employing prefixes to each formula), and MleanCoP-1.2 (a connection prover based on leanCoP [12,11]; again formula prefixes are employed). Previous results on the HOL provers LEO-II and Satallax (cf.…”

Section: The Prover Hol-pmentioning

confidence: 99%

HOL Based First-Order Modal Logic Provers

Benzmüller

Raths

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. First-order modal logics (FMLs) can be modeled as natural fragments of classical higher-order logic (HOL). The FMLtoHOL tool exploits this fact and it enables the application of off-the-shelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf-syntax for FML and the TPTP thf0-syntax for HOL. It currently supports logics K, K4, D, D4, T, S4, and S5 with respect to constant, varying and cumulative domain semantics. The approach is evaluated in combination with a meta-prover for HOL, which sequentially schedules various HOL reasoners. The resulting system is very competitive.

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Section: The Prover Hol-pmentioning

confidence: 99%

HOL Based First-Order Modal Logic Provers

Benzmüller

Raths

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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“…The standard translation into clausal form as well as the definitional translation [Plaisted and Greenbaum, 1986;Eder, 1992], which introduces definitions for subformulae, cause a significant overhead for the proof search [Otten, 2010]. For example, the disjunctive normal form of F # , in which some parts of the formula are copied, has more than twice the size of the original formula.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, proof search with more "natural" non-clausal calculi, such as sequent or standard tableau calculi [Gentzen, 1935;Hähnle, 2001] is less efficient. This paper describes the non-clausal prover nanoCoP for classical first-order logic [Otten, 2016]. By performing the proof search on the original structure of the input formula, it combines the advantages of more natural non-clausal calculi with the efficiency of a goal-oriented connection-based proof search.…”

Section: Introductionmentioning

confidence: 99%

nanoCoP: Natural Non-clausal Theorem Proving

Otten

2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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Most efficient fully automated theorem provers implement proof search calculi that require the input formula to be in a clausal form, i.e. disjunctive or conjunctive normal form. The translation into clausal form introduces a significant overhead to the proof search and modifies the structure of the original formula. Translating a proof in clausal form back into a more readable non-clausal proof of the original formula is not straightforward. This paper presents a non-clausal automated theorem prover for classical first-order logic. It is based on a non-clausal connection calculus and implemented with a few lines of Prolog code. Working entirely on the original structure of the input formula yields not only a speed up of the proof search, but the resulting non-clausal proofs are also shorter.

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“…Furthermore, it is a proof search method that is frequently used in HOL4 and Isabelle/HOL [NPW02,PS07]. As shown by the second author [KUV15], Metis can solve many problems that tableaux-based methods included in HOL Light, such as MESON [Har96b] and leanCoP [Ott08], cannot solve. However, up to now, Metis was not available as proof search method in HOL Light.…”

Section: Related Workmentioning

confidence: 99%

Metis-based Paramodulation Tactic for HOL Light

Färber¹,

Kaliszyk²

EPiC Series in Computing

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Metis is an automated theorem prover based on ordered paramodulation. It is widely employed in the interactive theorem provers Isabelle/HOL and HOL4 to automate proofs as well as reconstruct proofs found by automated provers. For both these purposes, the tableaux-based MESON tactic is frequently used in HOL Light. However, paramodulation-based provers such as Metis perform better on many problems involving equality. We created a Metis-based tactic in HOL Light which translates HOL problems to Metis, runs an OCaml version of Metis, and reconstructs proofs in Metis' paramodulation calculus as HOL proofs. We evaluate the performance of Metis as proof reconstruction method in HOL Light.

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leanCoP 2.0 and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions)

Cited by 47 publications

References 22 publications

HOL Based First-Order Modal Logic Provers

HOL Based First-Order Modal Logic Provers

nanoCoP: Natural Non-clausal Theorem Proving

Metis-based Paramodulation Tactic for HOL Light

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