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

TL;DR

This paper introduces a hierarchical abstraction method for grid-based problems in Answer Set Programming, enabling automatic identification of key problem elements and explaining unsolvability in a human-like manner.

Contribution

It extends abstraction in ASP to structural and hierarchical levels, facilitating automatic focus on relevant grid parts for unsolvability explanations.

Findings

Automatic abstractions align with human focus points.

Hierarchical abstraction improves understanding of problem unsolvability.

User study confirms similarity between machine and human explanations.

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.