Vector space embeddings of modal logic formulas: theory and application

Reasoning tasks over modal logics are notoriously difficult, comprising problems which are often semi-decidable. Hence, it is not rare for applications leveraging such tasks to exploit heuristic approaches able to give results in an acceptable amount of time, at the cost of some inaccuracies. Some approaches may benefit from vector embeddings, allowing for instance to involve neural networks and machine learning models in the reasoning process. This work aims at providing a new way to provide such embeddings specifically for the modal case, allowing for faster reasoning through both mathematical and learning techniques.