Probable implication, the contrapositive, and contingency tables

In everyday life, the deductive logic of mathematical reasoning is generally replaced by inductive logic, which usually derives uncertain conclusions from a body of observed facts. The authors examine this distinction using probabilities based on 2×2 contingency tables. Some anomalies are discussed, such as the difference between the empirical probability of the implication A=>B and that of the logically equivalent contrapositive implication not-B=> not-A, although they are almost equal under near-certainty. Other classical examples are also discussed quantitatively, such as modus ponens and transitivity of implication