Abstraction: A Historical and Interdisciplinary Perspective

Abstraction is a pervasive activity in human perception, conceptualization and reasoning; it enters the vocabulary of almost all disciplines, both scientific and humanistic, as well as everyday life. No wonder, then, that providing a definition of abstraction, at the same time precise and general, has been, up to now, unsuccessful. The complexity of abstraction can be clearly understood by comparing the (formal or informal) alternative notions proposed along the centuries in many disciplines, such as Philosophy, Computer Science, Cognition, Perception, Art, and Mathematics. Formal models of abstraction have been proposed as well, mostly in Artificial Intelligence. An overview and comparison of those models let a characterization of abstraction emerge, allowing precise boundaries to be set between abstraction and cognate notions, such as generalization, approximation and reformulation. To this aim we exploit an approach based on the notions of information and information state space, where abstraction corresponds to a process of information reduction. Abstraction is not only a conceptually interesting notion, but it has also universal applicability. We concentrate, for the purpose of illustrating its power, on the fields of Complex Systems and Machine Learning. We conclude with the description of some novel problems, where abstraction has not yet played a role, but it will.