Propositional, probabilistic and evidential reasoning

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Drawing plausible conclusions from uncertain and conflicting evidence is a major challenge in Artificial Intelligence, essential for developing smart technologies to manage the modern information explosion. Additionally, computational modeling of uncertain reasoning is vital for understanding human rationality. Previous approaches have typically been divided into symbolic and numeric methods. This work presents a significant advancement by introducing a unifying framework that reconciles these two camps. The Incidence Calculus serves as both a symbolic and numeric mechanism, assigning numeric values to evidence indirectly through the possible worlds where that evidence holds true. This approach enables symbolic reasoning through possible worlds and numeric reasoning via their probabilities. Moreover, the indirect assignment addresses complex issues, such as combining dependent sources of evidence, which had previously challenged earlier methods. The author generalizes the Incidence Calculus and compares it to earlier computational mechanisms, including Dempster-Shafer Theory and Probabilistic Logic, illustrating how each is represented within this framework. The result is a unified mechanism that encompasses both symbolic and numeric methods, preserving their advantages while mitigating some of their limitations.