1. The premise behind mathematical induction is that a functional connection exists between x and y (i.e., y = f(x)), but in underdetermined problems there is at best a mapping to a distribution (i.e., P y = f(x)), and at worst a non-functional relationship between x and y. For example, the forward prediction problem of molecule to property is typically inductive, but the inverse problem of finding a molecule with a particular property is deductive and can be described as learning a mapping to a distribution of molecules shooting a reagent impurity, where input information (i.e., reagent and reaction conditions) has a non-functional relationship to the observed outcome (i.e., an unexpected product) due to hidden information.