  Inductive inference in supervised classification context constitutes to
methods and approaches to assign some objects or items into different
predefined classes using a formal rule that is derived from training data and
possibly some additional auxiliary information. The optimality of such an
assignment varies under different conditions due to intrinsic attributes of the
objects being considered for such a task. One of these cases is when all the
objects' features are discrete variables with a priori known categories. As
another example, one can consider a modification of this case with a priori
unknown categories. These two cases are the main focus of this thesis and based
on Bayesian inductive theories, de Finetti type exchangeability is a suitable
assumption that facilitates the derivation of classifiers in the former
scenario. On the contrary, this type of exchangeability is not applicable in
the latter case, instead, it is possible to utilise the partition
exchangeability due to John Kingman. These two types of exchangeabilities are
discussed and furthermore here I investigate inductive supervised classifiers
based on both types of exchangeabilities. I further demonstrate that the
classifiers based on de Finetti type exchangeability can optimally handle test
items independently of each other in the presence of infinite amounts of
training data while on the other hand, classifiers based on partition
exchangeability still continue to benefit from joint labelling of all the test
items. Additionally, it is shown that the inductive learning process for the
simultaneous classifier saturates when the amount of test data tends to
infinity.
