  The topic of comprehensibility of machine-learned theories has recently drawn
increasing attention. Inductive Logic Programming (ILP) uses logic programming
to derive logic theories from small data based on abduction and induction
techniques. Learned theories are represented in the form of rules as
declarative descriptions of obtained knowledge. In earlier work, the authors
provided the first evidence of a measurable increase in human comprehension
based on machine-learned logic rules for simple classification tasks. In a
later study, it was found that the presentation of machine-learned explanations
to humans can produce both beneficial and harmful effects in the context of
game learning. We continue our investigation of comprehensibility by examining
the effects of the ordering of concept presentations on human comprehension. In
this work, we examine the explanatory effects of curriculum order and the
presence of machine-learned explanations for sequential problem-solving. We
show that 1) there exist tasks A and B such that learning A before B has a
better human comprehension with respect to learning B before A and 2) there
exist tasks A and B such that the presence of explanations when learning A
contributes to improved human comprehension when subsequently learning B. We
propose a framework for the effects of sequential teaching on comprehension
based on an existing definition of comprehensibility and provide evidence for
support from data collected in human trials. Empirical results show that
sequential teaching of concepts with increasing complexity a) has a beneficial
effect on human comprehension and b) leads to human re-discovery of
divide-and-conquer problem-solving strategies, and c) studying machine-learned
explanations allows adaptations of human problem-solving strategy with better
performance.
