(Neural-Symbolic) Machine Learning for Inconsistency Measurement

TL;DR

This paper introduces machine learning models to predict inconsistency degrees in propositional logic knowledge bases, combining neural predictions with symbolic constraints to improve accuracy and address computational complexity.

Contribution

It presents a novel hybrid approach that integrates neural regression models with symbolic rules derived from inconsistency measure postulates.

Findings

Predicting inconsistency degrees is feasible in many cases.

Incorporating symbolic constraints improves prediction accuracy.

The approach addresses computational challenges in inconsistency measurement.

Abstract

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.