Learning from Multiple Proofs: First Experiments

Kühlwein, Daniel; Urban, Josef

doi:10.29007/nb2g

Cited by 10 publications

(14 citation statements)

References 6 publications

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“…Additional dependency data are obtained by running ATPs on the ATP problems created from the HOL Light proof dependencies, i.e., the ATPs are run in the re-proving mode. Such data are often smaller and preferable [48]. These data are again exported using the same format as in (1).…”

Section: Total 855mentioning

confidence: 99%

“…No "software engineering" or other approach can prevent new shortcuts to be found in mathematics, unless an exhaustive (and infeasible) proof minimization is applied. 48 An interesting case is McAllester's Ontic [52]. The whole library is searched automatically, but the automation is fast and intentionally incomplete.…”

Section: Related Work and Contributionsmentioning

confidence: 99%

“…Automated theorem proving over large theories goes back at least to Quaife's large developments [66] with Otter [55] 48 (continued to some extent by Belinfante [9]). Most of the ATP/ITP combinations developed in 1990s used ATPs on user-restricted search space.…”

Section: Related Work and Contributionsmentioning

confidence: 99%

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Learning-Assisted Automated Reasoning with Flyspeck

2014

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The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

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Section: Total 855mentioning

confidence: 99%

Section: Related Work and Contributionsmentioning

confidence: 99%

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Learning-Assisted Automated Reasoning with Flyspeck

2014

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“…They tend to involve more, different facts than Sledgehammer proofs. Sometimes they rely on induction, which is beyond the scope of first-order provers; but even excluding induction, there is evidence that the provers work better if the proofs used for learning were produced by similar provers [18,38]. A special mode of Sledgehammer runs an automatic prover on all available facts to learn from machine-generated proofs.…”

Section: Learning From and For Isabellementioning

confidence: 99%

A Learning-Based Fact Selector for Isabelle/HOL

et al. 2016

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Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the fact selector, heuristically ranks the thousands of facts (lemmas, definitions, or axioms) available and selects a subset, based on syntactic similarity to the current proof goal. We introduce MaSh, an alternative that learns from successful proofs. New challenges arose from our "zero click" vision: MaSh integrates seamlessly with the users' workflow, so that they benefit from machine learning without having to install software, set up servers, or guide the learning. MaSh outperforms the old fact selector on large formalizations.

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“…It is also worth mentioning that even in the ITP setting, ATP proofs are typically a valuable source of training data for learning premise selection [11,6]. This means that the ATP and ITP lemma extraction could likely be fruitfully combined in the various strong [AI]TP "hammer" systems.…”

Section: Related Workmentioning

confidence: 99%

Lemmatization for Stronger Reasoning in Large Theories

Kaliszyk¹,

Urban²,

VyskoăźIl³

2015

Frontiers of Combining Systems

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Abstract. In this work we improve ATP performance in large theories by the reuse of lemmas derived in previous related problems. Given a large set of related problems to solve, we run automated theorem provers on them, extract a large number of lemmas from the proofs found and post-process the lemmas to make them usable in the remaining problems. Then we filter the lemmas by several tools and extract their proof dependencies, and use machine learning on such proof dependencies to add the most promising generated lemmas to the remaining problems.On such enriched problems we run the automated provers again, solving more problems. We describe this method and the techniques we used, and measure the improvement obtained. On the MPTP2078 large-theory benchmark the method yields 6.6% and 6.2% more problems proved in two different evaluation modes.

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Learning from Multiple Proofs: First Experiments

Cited by 10 publications

References 6 publications

Learning-Assisted Automated Reasoning with Flyspeck

Learning-Assisted Automated Reasoning with Flyspeck

A Learning-Based Fact Selector for Isabelle/HOL

Lemmatization for Stronger Reasoning in Large Theories

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