Abduction and induction are reasoning forms for drawing conclusions from incomplete information. Induction, i.e. inferring properties of sets of individuals from properties of individuals, was already distinguished by Aristotle, while the term �abduction� was introduced much later by Peirce for inference of explanations for observed phenomena. Both reasoning forms are presently being studied and applied by researchers in artificial intelligence and logic programming. However, the current views of abduction and induction and their interrelation are problematic, which is mainly caused by the fact that Peirce developed two perspectives on abduction, one based on syllogisms, the other on the underlying inferential pattern. In this paper I argue that both perspectives have their merits but need further formalisation. Furthermore, I propose a formalisation of the inferential perspective.