
Towards Proof Synthesis Guided by Neural Machine Translation for Intuitionistic Propositional Logic
Inspired by the recent evolution of deep neural networks (DNNs) in machi...
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Automated Theorem Proving in Intuitionistic Propositional Logic by Deep Reinforcement Learning
The problemsolving in automated theorem proving (ATP) can be interprete...
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Learning to Reason
Automated theorem proving has long been a key task of artificial intelli...
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Residual Network Based Direct Synthesis of EM Structures: A Study on OnetoOne Transformers
We propose using machine learning models for the direct synthesis of on...
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Tree Neural Networks in HOL4
We present an implementation of tree neural networks within the proof as...
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ENIGMA: Efficient Learningbased Inference Guiding Machine
ENIGMA is a learningbased method for guiding given clause selection in ...
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ProofBased Synthesis of Sorting Algorithms Using Multisets in Theorema
Using multisets, we develop novel techniques for mechanizing the proofs ...
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Automated proof synthesis for propositional logic with deep neural networks
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which quantifies the likelihood that a proof is indeed a correct one of a given proposition. Based on this model, we give a proofsynthesis procedure that searches for a proof in the order of the likelihood. This procedure uses an estimator of the likelihood of an inference rule being applied at each step of a proof. As an implementation of the estimator, we propose a propositiontoproof architecture, which is a DNN tailored to the automated proof synthesis problem. To empirically demonstrate its usefulness, we apply our model to synthesize proofs of propositional logic. We train the propositiontoproof model using a training dataset of propositionproof pairs. The evaluation against a benchmark set shows the very high accuracy and an improvement to the recent work of neural proof synthesis.
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