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European Conference on Logics in Artificial Intelligence

JELIA 2019: Logics in Artificial Intelligence pp 58–68Cite as

A Possible World View and a Normal Form for the Constellation Semantics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11468))

Abstract

After Dung’s founding work in Abstract Argumentation Frameworks there has been a growing interest in extending the Dung’s semantics in order to describe more complex or real life situations. Several of these approaches take the direction of weighted or probabilistic extensions. One of the most prominent probabilistic approaches is that of constellation Probabilistic Abstract Argumentation Frameworks.

In this paper, we introduce the probabilistic attack normal form for the constellation semantics; and we prove that the probabilistic attack normal form is sufficient to represent any Probabilistic Abstract Argumentation Framework of the constellation semantics.

This work has been partially supported by: “Argumentation 360” and “RACRA18” (funded by Ricerca di Base 2017/2018).

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Notes

  1. 1.

    As we are going to present later in the paper, the structure of AAF might impose dependencies among otherwise assumed independent probabilistic elements.

  2. 2.

    For now we ask the reader to ignore the possible world column which is used later in the paper.

  3. 3.

    We refer to general PrAAFs, as any constellation PrAAF that uses a definition similar to Definition 1. With the term general PrAAFs we do not include any extra restrictions imposed to the PrAAF definition.

  4. 4.

    The \(\eta \) argument is only a construct we use in order to illustrate how Probabilistic Arguments can be transformed to Probabilistic Attacks and the PrAAF to retain the same probabilistic distribution.

  5. 5.

    Such transformation is categorized as a normal expansion [1] of the original PrAAF.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Member of the INdAM Research Group GNCS, University of Perugia, Perugia, Italy

    Stefano Bistarelli & Theofrastos Mantadelis

Authors
  1. Stefano Bistarelli
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  2. Theofrastos Mantadelis
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Correspondence to Theofrastos Mantadelis .

Editor information

Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Nicola Leone

  3. Mathematics and Computer Science, University of Calabria, Rende, Italy

    Marco Manna

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Bistarelli, S., Mantadelis, T. (2019). A Possible World View and a Normal Form for the Constellation Semantics. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-19570-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19569-4

  • Online ISBN: 978-3-030-19570-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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