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Omission-Based Abstraction for Answer Set Programs

Published online by Cambridge University Press:  09 June 2020

ZEYNEP G. SARIBATUR Open the ORCID record for ZEYNEP G. SARIBATUR [Opens in a new window]  and
THOMAS EITER Open the ORCID record for THOMAS EITER [Opens in a new window]
ZEYNEP G. SARIBATUR
Affiliation:
Institute of Logic and Computation, TU Wien, Vienna, Austria (e-mails: [email protected], [email protected])
THOMAS EITER
Affiliation:
Institute of Logic and Computation, TU Wien, Vienna, Austria (e-mails: [email protected], [email protected])
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Abstract

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Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original answer set maps to some abstract answer set). This allows for generating partial answer set candidates that can help with approximation of reasoning. Computing the abstract answer sets is intuitively easier due to a smaller search space, at the cost of encountering spurious answer sets. Faithful (non-spurious) abstractions may be used to represent projected answer sets and to guide solvers in answer set construction. For dealing with spurious answer sets, we employ an ASP debugging approach to help with abstraction refinement, which determines atoms as badly omitted and adds them back in the abstraction. As a show case, we apply abstraction to explain unsatisfiability of ASP programs in terms of blocker sets, which are the sets of atoms such that abstraction to them preserves unsatisfiability. Their usefulness is demonstrated by experimental results.

Keywords

knowledge representation and nonmonotonic reasoninganswer set programmingabstractioninconsistency explanation
Type
Rapid Communication
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 2 , March 2021 , pp. 145 - 195
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

*

This article is a revised and extended version of the paper presented at the 16th International Conference on Principles of Knowledge Representation and Reasoning (KR 2018), October 30–November 2, 2018, Tempe, Arizona, USA. This work has been supported by the Austrian Science Fund (FWF) project W1255-N23. The authors thank the reviewers for their constructive comments to improve this paper, and the authors are in particular grateful for the suggested correction of an error in the original proof of Theorem 14. The authors acknowledge TU Wien University Library for financial support through its Open Access Funding Programme.

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