(Neural-Symbolic) Machine Learning for Inconsistency Measurement
This work addresses a computational bottleneck in automated reasoning for AI systems that handle inconsistent logical knowledge bases, though it is incremental in combining existing learning methods with symbolic constraints.
The paper tackles the problem of efficiently computing numerical inconsistency degrees for propositional logic knowledge bases, which is computationally hard using conventional methods. It shows that machine learning models can predict these values effectively, with symbolic constraints derived from rationality postulates improving prediction quality.
We present machine-learning-based approaches for determining the \emph{degree} of inconsistency -- which is a numerical value -- for propositional logic knowledge bases. Specifically, we present regression- and neural-based models that learn to predict the values that the inconsistency measures $\incmi$ and $\incat$ would assign to propositional logic knowledge bases. Our main motivation is that computing these values conventionally can be hard complexity-wise. As an important addition, we use specific postulates, that is, properties, of the underlying inconsistency measures to infer symbolic rules, which we combine with the learning-based models in the form of constraints. We perform various experiments and show that a) predicting the degree values is feasible in many situations, and b) including the symbolic constraints deduced from the rationality postulates increases the prediction quality.