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Solving Advanced Argumentation Problems with Answer Set Programming

Published online by Cambridge University Press:  15 January 2020

GERHARD BREWKA ,
MARTIN DILLER Open the ORCID record for MARTIN DILLER [Opens in a new window] ,
GEORG HEISSENBERGER ,
THOMAS LINSBICHLER  and
STEFAN WOLTRAN
GERHARD BREWKA
Affiliation:
Universität Leipzig, Leipzig, Germany
MARTIN DILLER
Affiliation:
TU Dresden, Dresden, Germany
GEORG HEISSENBERGER
Affiliation:
TU Wien, Vienna, Austria
THOMAS LINSBICHLER
Affiliation:
TU Wien, Vienna, Austria
STEFAN WOLTRAN
Affiliation:
TU Wien, Vienna, Austria
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Abstract

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Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.

Keywords

ADFsGRAPPAencodingsASP
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 3 , May 2020 , pp. 391 - 431
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
Copyright © Cambridge University Press 2020

Footnotes

*

This research has been supported by DFG (projects BR 1817/7-2 as well as 389792660 – TRR 248) and FWF (projects I2854, Y698, P32830, S11409-N23, and W1255-N23). The authors also thank Jörg Pührer for his helpful observations regarding the encodings. Also thanks to Wolfgang Dvořák and Ringo Baumann for guiding the paper through the editing process.

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