Deep Reinforcement Learning for Synthesizing Functions in Higher-Order  Logic

Gauthier, Thibault

doi:10.29007/7jmg

Cited by 9 publications

(8 citation statements)

References 23 publications

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“…These estimates are to be used as rewards in our improved MCTS algorithm. We choose a TNN as our machine learning model because it performs well on arithmetic and propositional formulas [7] as well as on Diophantine equations and combinators [6]. In our TNN, each HOL4 operator of arity a has a neural network associated with it modeling a function from R a×d to R d , where d is a globally fixed embedding size.…”

Section: Learning Provabilitymentioning

confidence: 99%

Learned Provability Likelihood for Tactical Search

Gauthier¹

2021

Electron. Proc. Theor. Comput. Sci.

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We present a method to estimate the provability of a mathematical formula. We adapt the tactical theorem prover TacticToe to factor in these estimations. Experiments over the HOL4 library show an increase in the number of theorems re-proven by TacticToe thanks to this additional guidance. This amelioration in performance together with concurrent updates to the TacticToe framework lead to an improved user experience.

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Section: Learning Provabilitymentioning

confidence: 99%

Learned Provability Likelihood for Tactical Search

Gauthier¹

2021

Electron. Proc. Theor. Comput. Sci.

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“…Some efforts were however done to reconstruct a formula tree. Gauthier [Gau20] trained a tree network to construct a new tree, by choosing one symbol at a time, in a manner similar to sequence-to-sequence models. Here, the network was given the input tree, and the partially constructed output tree and tasked with predicting the next output symbol in a way similar to Tree2Tree models [CAR18].…”

Section: Related Workmentioning

confidence: 99%

A Study of Continuous Vector Representationsfor Theorem Proving

Purgał,

Parsert,

Kaliszyk

2021

Preprint

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Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is additionally reversible. This means that the tree shape of a formula including all symbols can be reconstructed from the dense vector representation. We do that by training two decoders: one that extracts the top symbol of the tree and one that extracts embedding vectors of subtrees. The syntactic and semantic logical properties that we aim to preserve include both structural formula properties, applicability of natural deduction steps, and even more complex operations like unifiability. We propose datasets that can be used to train these syntactic and semantic properties. We evaluate the viability of the developed encoding across the proposed datasets as well as for the practical theorem proving problem of premise selection in the Mizar corpus.

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“…The results are better than those we are able to get here, but no new logics or problems are tried and generalization and transfer have been very limited so far. The AlphaZero algorithm has also been applied in theorem proving to the synthesis of formulas (Brown and Gauthier 2019) and functions (Gauthier 2020).…”

Section: Introductionmentioning

confidence: 99%

Adversarial Learning to Reason in an Arbitrary Logic

Purgał

Kaliszyk²

2022

FLAIRS

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Existing approaches to learning to prove theorems focus on particular logics and datasets. In this work, we propose Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human knowledge or set of problems. Since the algorithm does not need any training dataset, it is able to learn to work with any logical foundation, even when there is no body of proofs or even conjectures available. We practically demonstrate the feasibility of the approach in multiple logical systems. The approach is stronger than training on randomly generated data but weaker than the approaches trained on tailored axiom and conjecture sets. It however allows us to apply machine learning to automated theorem proving for many logics, where no such attempts have been tried to date, such as intuitionistic logic or linear logic.

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Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic

Cited by 9 publications

References 23 publications

Learned Provability Likelihood for Tactical Search

Learned Provability Likelihood for Tactical Search

A Study of Continuous Vector Representationsfor Theorem Proving

Adversarial Learning to Reason in an Arbitrary Logic

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