A QBF-based Formalization of Abstract Argumentation Semantics

Ofer Arieli; Martin W.A. Caminada

doi:10.1016/j.jal.2013.03.009

A QBF-based Formalization of Abstract Argumentation Semantics

Ofer Arieli, Martin W.A. Caminada

Computing Science

The Academic College of Tel-Aviv

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

9 Downloads (Pure)

Abstract

We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Further more, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.

Original language	English
Pages (from-to)	229-252
Number of pages	24
Journal	Journal of Applied Logic
Volume	11
Issue number	2
Early online date	21 Mar 2013
DOIs	https://doi.org/10.1016/j.jal.2013.03.009
Publication status	Published - Jun 2013

Bibliographical note

Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).

Keywords

semantics for abstract argumentation
frameworks
quantified Boolean formulas
signed theories

Access to Document

10.1016/j.jal.2013.03.009Licence: Other

Accepted Manuscript
© 2013. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Applied Logic. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF APPLIED LOGIC, VOL 11, ISSUE 2, (2013) DOI: 10.1016/j.jal.2013.03.009
Accepted author manuscript, 237 KBLicence: CC BY-NC-ND

Cite this

@article{d461f9cc14164fb2bad2df65724c7c40,

title = "A QBF-based Formalization of Abstract Argumentation Semantics",

abstract = "We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Further more, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.",

keywords = "semantics for abstract argumentation, frameworks, quantified Boolean formulas, signed theories",

author = "Ofer Arieli and Caminada, {Martin W.A.}",

note = "Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).",

year = "2013",

month = jun,

doi = "10.1016/j.jal.2013.03.009",

language = "English",

volume = "11",

pages = "229--252",

journal = "Journal of Applied Logic",

number = "2",

}

TY - JOUR

T1 - A QBF-based Formalization of Abstract Argumentation Semantics

AU - Arieli, Ofer

AU - Caminada, Martin W.A.

N1 - Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).

PY - 2013/6

Y1 - 2013/6

N2 - We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Further more, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.

AB - We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Further more, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.

KW - semantics for abstract argumentation

KW - frameworks

KW - quantified Boolean formulas

KW - signed theories

U2 - 10.1016/j.jal.2013.03.009

DO - 10.1016/j.jal.2013.03.009

M3 - Article

VL - 11

SP - 229

EP - 252

JO - Journal of Applied Logic

JF - Journal of Applied Logic

IS - 2

ER -

A QBF-based Formalization of Abstract Argumentation Semantics

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this