Logic, Optimization, and Artificial Intelligence
Artificial Intelligence
Summary
The authors explain how combining logic with optimization techniques can improve rule-based AI systems, especially making them more transparent and trustworthy. They review different logical frameworks like probabilistic and many-valued logics and how optimization helps compute and explain logical conclusions. The paper also discusses advanced methods like decision diagrams and Benders decomposition to solve logic problems efficiently. Finally, the authors suggest future research paths to further integrate logic and optimization in AI.
Authors
J. N. Hooker
Abstract
Logic and optimization can, in combination, make valuable contributions to rule-based AI. Logic is the obvious medium for encoding a rule base and drawing inferences from it, while optimization provides a powerful technology for computing inferences. Their combination has taken on new relevance amid a growing concern for transparency in AI. which is important for reproducibility, explainability, trustworthiness, and fairness. Rule-based AI provides a natural solution to transparency that is becoming increasingly practical due to today's highly advanced optimization methods. This article surveys several areas of logic-optimization partnership, including probabilistic logic, Bayesian logic, belief logics and Dempster-Shafer theory, nonmonotonic (default) logic, many-valued logics, and inference of logical formulas from noisy data based on Boolean regression. It shows how to compute projections, the fundamental problem of both logic and optimization, using decision diagrams and logic-based Benders decomposition. It describes the use of postoptimality analysis to explain how conclusions are reached, further enhancing transparency, as well as the role of optimization in answer set programming modulo theories. The paper concludes by suggesting possible future research directions.