Abduction, Induction, and the Logic of Scientific Knowledge Development

Abstract. In this paper we describe recent developments in the study of abduction and induction and their role in scientific modelling and knowledge formation. We present a central challenge that is emerging from this study, namely the problem of formulating and characterizing the boundaries of incompleteness for proving the “reverse truth ” that these two forms of reasoning provide. This challenge can have important implications in many fields, from the practice of Artificial intelligence and Machine Learning to scientific theory development in areas such as Systems Biology and Cognitive Science. Modelling a scientific domain is a continuous process of observing some phenomena, understanding these according to a currently chosen model, and using this understanding to improve the current general model of the domain. In this process one starts with a relatively simple model which gets further improved and expanded as the process is iterated. Any model of the phenomena at any stage of its development can be incomplete in its description. The task then is to use information given to us by experimental observations to improve and possibly complete this description. The development of our theories is driven by the observations and the need for these theories to conform to the observations. This point of view forms the basis of many formal theories of scientific discovery 3 in the sense that the development of a scientific theory is considered to be an incremental process of refinement strongly guided by the empirical observations. Considering a logical approach to this problem of incremental development of a scientific model, philosophers of science have recognized the need to introduce new synthetic forms of reasoning, alongside with the analytical reasoning form of deduction. Drawing on Aristotle’s syllogistic logic, Charles Sanders Peirce distinguished between abduction and induction, and studied their respective role in the development of scientific theories. More recently, several authors have studied abduction and inductio