Property Invariant Embedding for Automated Reasoning

Miroslav Olšák, Cezary Kaliszyk, Josef Urban

24th European Conference on Artificial Intelligence (ECAI 2020), Frontiers in Artificial Intelligence and Applications 325, pp. 1395 – 1402, 2020.


Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and rotations in vision, are becoming more common. Standard methods of embedding mathematical formulas for learning theorem proving are however yet unable to handle many important transformations. In particular, embedding previously unseen labels, that often arise in definitional encodings and in Skolemization, has been very weak so far. Similar problems appear when transferring knowledge between known symbols. We propose a novel encoding of formulas that extends existing graph neural network models. This encoding represents symbols only by nodes in the graph, without giving the network any knowledge of the original labels. We provide additional links between such nodes that allow the network to recover the meaning and therefore correctly embed such nodes irrespective of the given labels. We test the proposed encoding in an automated theorem prover based on the tableaux connection calculus, and show that it improves on the best characterizations used so far. The encoding is further evaluated on the premise selection task and a newly introduced symbol guessing task, and shown to correctly predict 65% of the symbol names.


  PDF |    doi:10.3233/FAIA200244  


author = {Miroslav Ols{\'{a}}k and Cezary Kaliszyk and
Josef Urban},
editor = {Giuseppe De Giacomo and
Alejandro Catal{\'{a}} and
Bistra Dilkina and
Michela Milano and
Sen{\'{e}}n Barro and
Alberto Bugar{\'{\i}}n and
J{\'{e}}r{\^{o}}me Lang},
title = {Property Invariant Embedding for Automated Reasoning},
booktitle = {{ECAI} 2020 - 24th European Conference on Artificial Intelligence},
series = {Frontiers in Artificial Intelligence and Applications},
volume = {325},
pages = {1395--1402},
publisher = {{IOS} Press},
year = {2020},
url = {},
doi = {10.3233/FAIA200244},
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