Formal learning

Formal learning, normally delivered by trained teachers in a systematic intentional way within a school, academy/college/institute or university, is one of three forms of learning as defined by the OECD, the others being informal learning, which typically takes place naturally as part of some other activity, and non-formal learning, which includes everything else, such as sports instruction provided by non-trained educators without a formal curriculum.

Formal learning theory is the formal study of inductive problems and their intrinsic solvability for both ideal and computable agents. Modal operator theory has very little to do with formal learning theory especially with respects to

Research on logical reliability theory was first pursued under the name formal learning theory, given to the discipline by (Osherson et al. 1986). This name is somewhat misleading, as it suggests a study of how cognizers learn. With this in mind, Kevin Kelly renamed the approach computational epistemology (1991, 1996), which reflects its historical roots in computability theory while avoiding misinterpretation.

Computer scientists are in the business of recommending and providing programs and algorithms for various empirical purposes. From this perspective learning is about reliable convergence to correct answers on various empirical questions. Thus learning theory is the formal study of inductive problems and their complexity and solvability for both ideal and Turing-computable agents.

In the middle of 1960s, (Gold 1967) applied formal learning theory to theories of language acquisition in which a child is asked to reliably converge to a grammar for its natural language. Very briefly, languages are modeled as recursive enumerable sets (or r.e sets) and a child is conceived as a function required to converge to a correct r.e index for a given set over all possible enumerations of the set. About the same time H.Reicherbanch's students, Hilary Putnam (Putnam 1963) applied learning theory to criticize Carnap's confirmation theory. Putnam at tempted to show Carnap's justification standards for a probabilistic theory of confirmation, there exists a hypothesis the Carnapian extrapolation algorithm cannot learn even given every possible instance of the hypothesis. Further mathematical treatments of the problems of induction were provided by (Blum and Blum 1975) and (Angluin 1980).

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