A Case Study in Explanation and Implication

In this work we explore the problem of generating explanations for solutions obtained by consistency methods, either directly or via more sophisticated forms of inference. For this purpose, we employ a type of logic puzzle, called the 9-puzzle, that can be solved by inference alone. We show how one can generate explanations in the form of trees, guided by the sequence of inferences followed in obtaining a solution. Then we show how ordering heuristics and selection strategies allow us to obtain better explanations according to well-defined criteria. (Essentially, this amounts to finding smaller, more compact explanation trees.) Finally, we show how our testbed can be elaborated to support retraction of partial explanations, if the user wants to add values back to the present state of the puzzle. This allows the user to explore the implications of a given value selection. Together, these methods suggest some ways in which the process of solving combinatorial problems can be made more perspicuous and more interactive.