From Common Sense Reasonig to Neural Network Models: a Conditional and Multi-preferential Approach for Explainability and Neuro-Symbolic Integration

This short paper reports about a line of research exploiting a conditional logic of commonsense reasoning to provide a semantic interpretation to neural network models. A “concept-wise" multi-preferential semantics for conditionals is exploited to build a preferential interpretation of a trained neural network starting from its input-output behavior. The approach is general (model agnostic): it is based on a notion of metric distance to define preferences and has been first proposed for Self-Organising Maps (SOMs). For MultiLayer Perceptrons (MLPs), a deep network can as well be regarded as a (fuzzy) conditional knowledge base (KB), in which the synaptic connections correspond to weighted conditionals. This opens to the possibility of adopting conditional description logics as a basis for neuro-symbolic integration. Proof methods for many-valued weighted conditional KBs have been developed, based on Answer Set Programming and Datalog encodings to deal with the entailment and model-checking problems.