A study of continuous vector representations for theorem proving

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