Semantic Embeddings for Modal Logic

The concept of similarity between formulas in formal logic does not have a universally accepted interpretation; intuitively, two formulas should be considered similar if their behaviour is similar, that is, if they agree on most models. In this paper, we propose a novel framework to assess formula similarity inspired by word embeddings in natural language processing. To test the properties of our embedding, we choose modal logic, which provides a natural compromise between propositional and first-order logic. The results of our proof-of-concept implementation suggest that it is possible to represent the behaviour of logical formulas as numerical vectors, regardless of the properties of the underlying frame. Our technique is easily transferable to other logical frameworks, including temporal, spatial, description logics, and, possibly, even first-order frameworks, paving the way for various potential applications.

Recommended citation: Casavecchia, Pietro, Milella, Mauro, Monego, Riccardo, Paparella, Alberto, Sciavicco, Guido, and Serrentino, Leonardo (2026). "Semantic Embeddings for Modal Logic." 27th Italian Conference on Theoretical Computer Science, September 07-09, 2026, Udine. 1(1).
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