Deductive Reasoning Under Uncertainty: A Water Tank Analogy

摘要: This paper describes a cubic water tank equipped with movable partition receiving various amounts of liquid used to represent joint probability distributions. device is applied the investigation deductive inferences under uncertainty. The analogy exploited determine by qualitative reasoning limits in conclusion twenty basic arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often benchmark problems theoretical approaches bounds imposed premises on are derived basis few trivial principles such “a part cannot contain more than its capacity allows”, or “if empty, other contains all liquid”. stems from equivalence between physical constraints and subdivisions volumes liquid, axioms rules probability. materializes de Finetti’s coherence approach It also suggests counterpart Dutch book assess individuals’ rationality judgments sense that individuals whose degrees belief out intervals would commit themselves executing physically impossible tasks.