Abstraction for Zooming-In to Unsolvability Reasons of Grid-Cell Problems

Abstract: Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important for the problem. Recently, the notion of abstraction has been introduced for Answer Set Programming (ASP), a knowledge representation and reasoning paradigm widely used in problem solving, with the potential to understand the key elements of a program that play a role in finding a solution. The present paper takes this further and empowers abstraction to deal with structural aspects, and in particular with hierarchical abstraction over the domain. We focus on obtaining the reasons for unsolvability of problems on grids, and show the possibility to automatically achieve human-like abstractions that distinguish only the relevant part of the grid. A user study on abstract explanations confirms the similarity of the focus points in machine vs. human explanations and reaffirms the challenge of employing abstraction to obtain machine explanations.