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Argumentation-Based Semantics for Logic Programs with First-Order Formulae

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PRIMA 2016: Principles and Practice of Multi-Agent Systems (PRIMA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9862))

Abstract

This paper studies different semantics of logic programs with first order formulae under the lens of argumentation framework. It defines the notion of an argumentation-based answer set and the notion of an argumentation-based well-founded model for programs with first order formulae. The main ideas underlying the new approach lie in the notion of a proof tree supporting a conclusion given a program and the observation that proof trees can be naturally employed as arguments in an argumentation framework whose stable extensions capture the program’s well-justified answer semantics recently introduced in [23]. The paper shows that the proposed approach to dealing with programs with first order formulae can be easily extended to a generalized class of logic programs, called programs with FOL-representable atoms, that covers various types of extensions of logic programming proposed in the literature such as weight constraint atoms, aggregates, and abstract constraint atoms. For example, it shows that argumentation-based well-founded model is equivalent to the well-founded model in [27] for programs with abstract constraint atoms. Finally, the paper relates the proposed approach to others and discusses possible extensions.

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Notes

  1. 1.

    SLD stands for “selective linear definite” (see, e.g., [15]).

  2. 2.

    Intuitively, a tree T belongs to the kernel of S if T belongs to S and the level of T is minimal wrt trees in S supporting the same conclusion.

  3. 3.

    Precise formula for computing W(C) is not really important for the discussion. It can be found in [19].

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Author information

Authors and Affiliations

  1. Department of Computer Science, Asian Institute of Technology, Klong Luang, Thailand

    Phan Minh Dung

  2. Department of Computer Science, New Mexico State University, Las Cruces, NM, USA

    Tran Cao Son

  3. Department of Computer Science, Burapha University International College, Bangsaen, Thailand

    Phan Minh Thang

Authors
  1. Phan Minh Dung
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  2. Tran Cao Son
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  3. Phan Minh Thang
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Corresponding author

Correspondence to Phan Minh Dung .

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Torino , Torino, Italy

    Matteo Baldoni

  2. Computing and Communications, Lancaster University, Lancaster, United Kingdom

    Amit K. Chopra

  3. Department of Computer Science, New Mexico State University, Las Cruces, New Mexico, USA

    Tran Cao Son

  4. Graduate School of Maritime Sciences, Kobe University, Kobe, Japan

    Katsutoshi Hirayama

  5. Dept. di Informatica: Sci. e Ingegneria, Universitá di Bologna, Bologna, Italy

    Paolo Torroni

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Dung, P.M., Son, T.C., Thang, P.M. (2016). Argumentation-Based Semantics for Logic Programs with First-Order Formulae. In: Baldoni, M., Chopra, A., Son, T., Hirayama, K., Torroni, P. (eds) PRIMA 2016: Principles and Practice of Multi-Agent Systems. PRIMA 2016. Lecture Notes in Computer Science(), vol 9862. Springer, Cham. https://doi.org/10.1007/978-3-319-44832-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-44832-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44831-2

  • Online ISBN: 978-3-319-44832-9

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