A New Framework for Formal Reasoning over Symbolic and Sub-Symbolic Knowledge

This discussion paper summarizes our work [1], recently accepted at the 40th International AAAI Conference on Artificial Intelligence (AAAI 2026). We propose a novel framework for combining symbolic and sub-symbolic knowledge. The framework is based on the notion of Hybrid Knowledge Base (HKB), a formalism that integrates ontologies with Machine Learning (ML) classifiers. In an HKB, an ontology provides a conceptual and logical description of the application domain, while ML classifiers operating over a feature space implicitly populate the instances of concepts and roles used in the ontology. We introduce a model-theoretic semantics for HKBs and study the computational complexity of query answering under two alternative semantics.