Predicate credibility logic for artificial intelligence

In artificial intelligence (AI) and machine learning (ML), decision-making frequently involves uncertainty. However, existing logical frameworks often fall short when dealing with the vagueness and randomness inherent in real-world data. This paper introduces Predicate Credibility Logic (PCL), a novel reasoning framework designed to improve decision-making in AI and ML. PCL goes beyond classical logic, probability theory, multi-valued logic, and fuzzy logic by more closely aligning with human reasoning across the dimensions of certainty, vagueness, and randomness. Grounded in benchmarks of truth and falsehood, PCL is built on a rigorous mathematical foundation that defines its core concepts, principles, and semantics. At the heart of the framework is predicate algebra, a formal structure that underpins its logic. PCL also features rigorously developed deduction principles that support precise uncertainty management while ensuring both soundness and completeness. It can be seamlessly integrated into neurosymbolic AI systems and Bayesian networks, enhancing AI’s reasoning capabilities and contributing to progress toward artificial general intelligence.