First Order Theory

First-order logic (FOL) provides a foundational framework for representing knowledge and reasoning, with current research focusing on extending its applicability to diverse domains. Active areas include developing efficient algorithms for deciding satisfiability and containment problems within FOL, particularly within the context of constraint languages like SHACL and temporal logics (LTLfMT). These advancements are improving the explainability and verification of complex systems, such as machine learning models and logic programs, by leveraging FOL's expressive power to analyze their behavior and ensure correctness. The resulting tools and techniques are impacting fields ranging from knowledge representation and reasoning to the development of more robust and trustworthy AI systems.