Abduction and deduction play a fundamental role in problem solving. The paper extends abduction and deduction to abductive CBR (case-based reasoning) and deductive CBR and shows that abductive CBR and deductive CBR can be integrated in problem solving. Then it provides a unified formalization for integration of abduction, abductive CBR, deduction and deductive CBR. The paper also investigates abductive case retrieval and deductive case retrieval using similarity relations, fuzzy similarity relations and similarity metrics. The proposed approach demonstrates that the integration of abductive CBR and deductive CBR is of practical significance in problem solving such as system diagnosis and analysis.