Logic and Optimization Enhance Transparent Rule-Based AI

The intersection of logic and optimization offers significant contributions to rule-based Artificial Intelligence, especially in an era where transparency in AI is increasingly critical. Logic provides a natural framework for encoding rule bases and deriving inferences, while optimization techniques offer powerful computational methods for these inferences. This synergy is vital for achieving AI systems that are reproducible, explainable, trustworthy, and fair. The article delves into several areas where logic and optimization collaborate, including probabilistic logic, Bayesian logic, belief logics, nonmonotonic logic, and many-valued logics. It also covers the inference of logical formulas from noisy data using Boolean regression. Key to this partnership is the computation of projections, a fundamental problem in both fields, which can be solved using decision diagrams and logic-based Benders decomposition. Furthermore, the paper highlights how post-optimality analysis can explain how conclusions are reached, thereby enhancing transparency, and discusses the role of optimization in answer set programming modulo theories. The survey concludes by suggesting future research directions for this powerful combination.