Towards a Process Algebra and Operator Theory for Learning System Objects

Recently, abstract systems theory has been used as a meta-theory for learning theory and machine learning in order to model learning systems directly as formal, mathematical objects. This effort was inspired by a desire to treat learning in terms of systems, as opposed to the more common practice of treating learning in terms of problems or problem-solving, by modeling learning as a relation on sets, that is, as an abstract system. Such a relational view of learning, however, is heavily structural. It neglects key behavioral aspects typically represented using operators and process algebra. This paper substantiates and motivates the development of a process algebra for learning systems in order to address this gap. In summary, this paper considers and distinguishes formal representations of learning as a problem, as a system, as an operator, and as a process.