  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.
