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Representing Abstract Dialectical Frameworks with Binary Decision Diagrams

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Logic Programming and Nonmonotonic Reasoning (LPNMR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13416))

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Abstract

Abstract dialectical frameworks (ADFs) are a well-studied generalisation of the prominent argumentation frameworks due to Phan Minh Dung. In this paper we propose to use reduced ordered binary decision diagrams (roBDDs) as a suitable representation of the acceptance conditions of arguments within ADFs. We first show that computational complexity of reasoning on ADFs represented by roBDDs is milder than in the general case, with a drop of one level in the polynomial hierarchy. Furthermore, we present a framework to systematically define heuristics for search space exploitation, based on easily retrievable properties of roBDDs and the recently proposed approach of weighted faceted navigation for answer set programming. Finally, we present preliminary experiments of an implementation of our approach showing promise both when compared to state-of-the-art solvers and when developing heuristics for reasoning.

This work is partly supported by the BMBF, Grant 01IS20056_NAVAS, by the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), and by the DFG through the Collaborative Research Center, Grant TRR 248 project ID 38 9792660.

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Notes

  1. 1.

    https://github.com/ellmau/adf-obdd/releases/tag/v0.2.4-beta.1 v0.2.4-beta.1.

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Author information

Authors and Affiliations

  1. Knowledge-Based Systems Group, cfaed, TU Dresden, Germany

    Stefan Ellmauthaler

  2. Logic Programming and Argumentation Group, TU Dresden, Germany

    Sarah Alice Gaggl & Dominik Rusovac

  3. Institute of Software Technology, TU Graz, Austria

    Johannes P. Wallner

Authors
  1. Stefan Ellmauthaler
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  2. Sarah Alice Gaggl
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  3. Dominik Rusovac
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  4. Johannes P. Wallner
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Corresponding author

Correspondence to Johannes P. Wallner .

Editor information

Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Georg Gottlob

  2. Miami University, Oxford, OH, USA

    Daniela Inclezan

  3. University of Genova, Genoa, Italy

    Marco Maratea

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Ellmauthaler, S., Gaggl, S.A., Rusovac, D., Wallner, J.P. (2022). Representing Abstract Dialectical Frameworks with Binary Decision Diagrams. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_14

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  • DOI: https://doi.org/10.1007/978-3-031-15707-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15706-6

  • Online ISBN: 978-3-031-15707-3

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