Control Structures in Hypothesis Spaces: The Influence on Learning

In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the influence on learnability of the presence or absence of certain control structures in the hypothesis space. First presented are control structure characterizations of some rather specific but illustrative learnability results. The presence of these control structures is thereby shown essential to maintain full learning power. Then presented are the main theorems. Each of these non-trivially characterizes the invariance of a learning class over hypothesis space V and the presence of a particular projection control structure, called proj, in V as: V has suitable instances of all denotational control structures. In a sense, then, proj epitomizes the control structures whose presence needn’t help and whose absence needn’t hinder learning power.