Equivalence issues in abduction and induction

This paper discusses several equivalence issues in abduction and induction. Three different problems: equivalence of theories, equivalence of explanations, and equivalence of observations are considered in the context of first-order logic and nonmonotonic logic programming. Necessary and sufficient conditions for those problems, and computational complexity results are provided. These equivalence measures provide methods for comparing different abductive or inductive theories, and also state conditions for optimizing those theories in program development.