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A Hasse Diagram for Weighted Sceptical Semantics with a Unique-Status Grounded Semantics

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Book cover Logic Programming and Nonmonotonic Reasoning (LPNMR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10377))

Abstract

We provide an initial study on the Hasse diagram that represents the partial order -w.r.t. set inclusion- among weighted sceptical semantics in Argumentation: grounded, ideal, and eager. Being our framework based on a parametric structure of weights, we can directly compare weighted and classical approaches. We define a unique-status weighted grounded semantics, and we prove that the lattice of strongly-admissible extensions becomes a semi-lattice.

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Notes

  1. 1.

    The eager is a unique-status semantics only for finite AAFs [1], which we study in this paper.

  2. 2.

    Even if new and not in [3], we introduce this semantics in Definition 4 for the sake of presentation.

  3. 3.

    Since Dung’s definitions of semantics are directly encompassed by our framework (just by using the Boolean semiring), we do not introduce them in this paper for the sake of brevity.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

    Stefano Bistarelli & Francesco Santini

Authors
  1. Stefano Bistarelli
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  2. Francesco Santini
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Corresponding author

Correspondence to Francesco Santini .

Editor information

Editors and Affiliations

  1. Drexel University, Philadelphia, Pennsylvania, USA

    Marcello Balduccini

  2. Aalto University, Espoo, Finland

    Tomi Janhunen

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Bistarelli, S., Santini, F. (2017). A Hasse Diagram for Weighted Sceptical Semantics with a Unique-Status Grounded Semantics. In: Balduccini, M., Janhunen, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2017. Lecture Notes in Computer Science(), vol 10377. Springer, Cham. https://doi.org/10.1007/978-3-319-61660-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-61660-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61659-9

  • Online ISBN: 978-3-319-61660-5

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