Abstract
We propose a new internal guidance method for automated theorem provers based on the given-clause algorithm. Our method influences the choice of unprocessed clauses using positive and negative examples from previous proofs. To this end, we present an efficient scheme for Naive Bayesian classification by generalising label occurrences to types with monoid structure. This makes it possible to extend existing fast classifiers, which consider only positive examples, with negative ones. We implement the method in the higher-order logic prover Satallax, where we modify the delay with which propositions are processed. We evaluated our method on a simply-typed higher-order logic version of the Flyspeck project, where it solves 26 % more problems than Satallax without internal guidance.
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- 1.
We omitted several constant factors. Furthermore, FEMaLeCoP considers also features of training examples that are not part of the features \(F\), albeit this is a further derivation of the theoretical model.
- 2.
Technically, our reference prover Satallax does not implement a given-clause algorithm, as Satallax treats terms instead of clauses, and it interleaves the choice of unprocessed terms with other commands. However, for the sake of internal guidance, we can consider Satallax to implement a version of the given-clause algorithm. We describe the differences in more detail in Sect. 6.
- 3.
The test set, as well as our modified version of Satallax and instructions to recreate our evaluation, can be found under: http://cl-informatik.uibk.ac.at/~mfaerber/satallax.html.
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Acknowledgements
We would like to thank Sebastian Joosten and Cezary Kaliszyk for reading initial drafts of the paper, and especially Josef Urban for inspiring discussions and inviting the authors to Prague. Furthermore, we would like to thank the anonymous IJCAR referees for their valuable comments.
This work has been supported by the Austrian Science Fund (FWF) grant P26201 as well as by the European Research Council (ERC) grant AI4REASON.
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Färber, M., Brown, C. (2016). Internal Guidance for Satallax. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_24
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