Formalizing Confidence Propagation in Analogico-Inductive Reasoning

Although argument by analogy is studied and featured in many computational models, less appreciated is the ability to reason over analogies (RoA); i.e., not only being able to produce inferences in accordance with arguments by analogy, but having the ability to negate analogies, recognize and learn to avoid bad analogies, compare the relative strengths of analogies, reason about them nonmonotonically, evaluate hypothetical analogies, and so on. To do all of these things, one needs the ability to represent analogies (and not just the products of analogies) in such a way that the analogies themselves can be objects of reasoning processes (including analogy). We take a first step toward the full ability to reason over analogies by presenting a formalization, based on the cognitive event calculus, that treats analogical mappings and hypothetical inferences as objects between which confidence can be propagated. We will argue that computational models of analogy (both descriptive and normative) will need to use such a formalization, and then we show that our formalization provides a new way to evaluate analogical arguments