Abduction: A Categorical Characterization

Abstract

Scientific knowledge is gained by the informed (on the basis of theoretic ideas and criteria) examination of data. This can be easily seen in the context of quantitative data, handled with statistical methods. Here we are interested in other forms of data analysis, although with the same goal of extracting meaningful information. The idea is that data should guide the construction of suitable models, which later may lead to the development of new theories. This kind of inference is called abduction and constitutes a central procedure called Peircean qualitative induction. In this paper we will present a category-theoretic representation of abduction based on the notion of adjunction, which highlights the fundamental fact that an abduction is the most efficient way of capturing the information obtained from a large body of evidence.