Deep Network Guided Proof Search

Sarah Loos, Geoffrey Irving, Christian Szegedy, Cezary Kaliszyk.

21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, EPiC 46, pp. 85-105, 2017.


Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go. Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification. Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of
proof search steps while increasing the number of theorems proved.
Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that didnot previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.




author = {Sarah Loos and Geoffrey Irving and Christian Szegedy and Cezary Kaliszyk},
title = {Deep Network Guided Proof Search},
booktitle = {LPAR-21. 21st International Conference on Logic for Programming,
Artificial Intelligence and Reasoning},
editor = {Thomas Eiter and David Sands},
series = {EPiC Series in Computing},
volume = {46},
pages = {85--105},
year = {2017},
publisher = {EasyChair},
bibsource = {EasyChair,},
issn = {2398-7340}
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