Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction problem and investigate under which conditions concept mappings are uniquely determined by the constraints. We prove that a discrimination property (requiring that no valid concept mapping can be transformed into another valid mapping by swapping two concept values) is necessary for shortcut-freeness under bijective mappings, but demonstrate via a counterexample that it is insufficient even when the constraint graph is connected. We develop an ASP-based algorithm that verifies whether a given constraint set uniquely determines the intended concept mapping, with proven soundness and completeness. When shortcuts are detected, a greedy repair algorithm eliminates them by augmenting the constraint set, converging in at most k iterations, where k is the number of alternative valid mappings. We further provide a complexity classification: deciding shortcut-freeness is coNP-complete, counting shortcuts is #P-complete, and finding minimal repairs is NP-hard. We also establish sample complexity bounds showing that logarithmically many label queries suffice for disambiguation in favorable cases, while querying all ambiguous positions suffices in the worst case. Experiments across eight benchmark domains validate our approach.

We introduce a new method for integrating neural networks with logic programming in Neural-Symbolic AI (NeSy), aimed at learning with distant supervision, in which direct labels are unavailable. Unlike prior methods, our approach does not depend on symbolic solvers for reasoning about missing labels. Instead, it evaluates logical implications and constraints in a differentiable manner by embedding both neural network outputs and logic programs into matrices. This method facilitates more efficient learning under distant supervision. We evaluated our approach against existing methods while maintaining a constant volume of training data. The findings indicate that our method not only matches or exceeds the accuracy of other methods across various tasks but also speeds up the learning process. These results highlight the potential of our approach to enhance both accuracy and learning efficiency in NeSy applications.

Abstract We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using answer set programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract explanatory rules. For global explanations, candidate rules are chosen from the entire trained tree-ensemble models, whereas for local explanations, candidate rules are selected by only considering rules that are relevant to the particular predicted instance. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks.