KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

Edited by

ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

Sponsored by
Published by

Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Treewidth-aware Reductions of Normal ASP to SAT - Is Normal ASP Harder than SAT after All?

  1. Markus Hecher(TU Wien, Vienna, Austria, University of Potsdam, Potsdam, Germany)


  1. Computational aspects of knowledge representation-General
  2. Logic programming, answer set programming, constraint logic programming-General
  3. Nonmonotonic logics, default logics, conditional logics-General


Answer Set Programming (ASP) is a paradigm and problem modeling/solving toolkit for KR that is often invoked. There are plenty of results dedicated to studying the hardness of (fragments of) ASP. So far, these studies resulted in characterizations in terms of computational complexity as well as in fine-grained insights presented in form of dichotomy-style results, lower bounds when translating to other formalisms like propositional satisfiability (SAT), and even detailed parameterized complexity landscapes. A quite generic and prominent parameter in parameterized complexity originating from graph

theory is the so-called treewidth, which in a sense captures structural density of a program. Recently, there was an increase in the number of treewidth-based solvers related to SAT. While there exist several translations from (normal) ASP to SAT, yet there is no reduction preserving treewidth or at least

being aware of the treewidth increase. This paper deals with a novel reduction from normal ASP to SAT that is aware of the treewidth, and guarantees that a slight increase of treewidth is indeed sufficient. Then, we also present a new result establishing that when considering treewidth, already the fragment

of normal ASP is slightly harder than SAT (under reasonable assumptions in computational complexity). This also confirms that our reduction probably cannot be significantly improved and that the slight increase of treewidth is unavoidable.