probabilistic-logic

This paper introduces MT-PDCL, a measure-theoretic probabilistic definite clause logic framework that generalizes probabilistic logic programming to continuous domains by using Lebesgue integration over standard Borel σ-algebras instead of discrete grounding. It replaces combinatorial grounding bottlenecks with exact algebraic and differentiable inference while preserving declarative definite clause syntax.

This paper surveys the historical and ongoing synergy between logic and optimization in AI, arguing that rule-based approaches enhanced by optimization solvers can provide transparency, explainability, and trustworthiness in contrast to purely connectionist methods.