Embeddings as Probabilistic Equivalence in Logic Programs
Jaron Maene, Efthymia Tsamoura
Logic programs have been combined with embeddings to enable differentiable reasoning over the representation space, giving rise to neurosymbolic models that can jointly learn symbolic rules and train neural networks. The key idea behind this composition is to replace unification in logic programming with soft unification. Unlike unification, its soft counterpart exploits the similarity between symbols in the representation space to decide when two symbols are equivalent. However, the semantics of similarity violate the transitive law of equivalence. We prove this has undesirable consequences during learning. To alleviate the above shortcomings, we introduce a probability distribution on equivalences in logic programs. Embeddings in this context can be understood as a factorization of the probabilistic equivalence. Finally, we introduce an exact probabilistic inference method that can exploit the symmetries between equivalent symbols.