Valued Logic

Valued logic extends classical Boolean logic by allowing truth values beyond simple true/false, enabling the representation of uncertainty, vagueness, and inconsistency. Current research focuses on developing and applying valued logics (with varying numbers of truth values) to diverse areas, including decision-making under uncertainty (using models like seven-valued logics within rough set frameworks), formal verification (through automata generation for multi-valued temporal logics), and machine learning (by connecting deep neural networks to Lukasiewicz logic and extracting logical formulae from trained networks). This work has implications for improving the robustness and explainability of AI systems, enhancing the precision of decision support tools, and providing more nuanced modeling capabilities across various scientific domains.