Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration
This work addresses the challenge of combining neural and symbolic methods in AI, offering a novel framework that bridges two major strands in neurosymbolic integration, though it is incremental in building on existing fuzzy logic techniques.
The paper tackles the problem of unifying rule injection and rule induction in neurosymbolic integration by introducing Logic of Hypotheses (LoH), a language that enables flexible integration of data-driven learning with symbolic priors, resulting in strong performance on tasks like Visual Tic-Tac-Toe while producing interpretable rules.
Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of Goedel fuzzy logic and the recently developed Goedel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on the Visual Tic-Tac-Toe NeSy task, while producing interpretable decision rules.