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An Abstract Argumentation and Logic Programming Comparison Based on 5-Valued Labellings

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12897))

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Abstract

Abstract argumentation and logic programming are two formalisms of non-monotonic reasoning that share many similarities. Previous studies contemplating connections between the two formalisms provided back and forth translations from one to the other and found they correspond in multiple different semantics, but not all. In this work, we propose a new set of five argument labels to revisit the semantic correspondences between abstract argumentation and logic programming. By doing so, we shed light on why the two formalisms are not absolutely equivalent. Our investigation lead to the specification of the novel least-stable semantics for abstract argumentation which corresponds to the L-stable semantics of logic programming.

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Notes

  1. 1.

    In graph theory, a sink node is one from which no edges emerge.

  2. 2.

    These are logic programs whose rules may contain weak but not strong negation and where the head of each rule is a single atom.

  3. 3.

    The above definition consists of a least fix-point of the immediate consequence operator \(\Psi \) defined in [13], which is guaranteed to exist and be unique for positive programs.

  4. 4.

    According to Definition 9.

  5. 5.

    In case there is no argument for a particular conclusion, it will be simply labelled \(\mathtt {out}\).

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Authors and Affiliations

  1. Universidade Federal do Ceará, Fortaleza, Brazil

    Samy Sá & João Alcântara

Authors
  1. Samy Sá
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  2. João Alcântara
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Correspondence to Samy Sá .

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Editors and Affiliations

  1. Institute of Information Theory and Automation, Prague, Czech Republic

    Jiřina Vejnarová

  2. Insight Centre for Data Analytics, School of Computer Science and IT University College Cork, Cork, Ireland

    Nic Wilson

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Sá, S., Alcântara, J. (2021). An Abstract Argumentation and Logic Programming Comparison Based on 5-Valued Labellings. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_12

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  • DOI: https://doi.org/10.1007/978-3-030-86772-0_12

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