scholarly journals A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation

2019 ◽  
pp. 87-105 ◽  
Author(s):  
Sylvie Doutre ◽  
Mickaël Lafages ◽  
Marie-Christine Lagasquie-Schiex
Keyword(s):  
Abstract Argumentation ◽  
Enumeration Problem

scholarly journals On the Complexity of Enumerating the Extensions of Abstract Argumentation Frameworks

2017 ◽  
Author(s):  
Markus Kröll ◽  
Reinhard Pichler ◽  
Stefan Woltran
Keyword(s):  
Large Collection ◽  
Abstract Argumentation ◽  
Enumeration Problem ◽  
Credulous Reasoning

Several computational problems of abstract argumentation frameworks (AFs) such as skeptical and credulous reasoning, existence of a non-empty extension, verification, etc. have been thoroughly analyzed for various semantics. In contrast, the enumeration problem of AFs (i.e., the problem of computing all extensions according to some semantics) has been left unexplored so far. The goal of this paper is to fill this gap. We thus investigate the enumeration complexity of AFs for a large collection of semantics and, in addition, consider the most common structural restrictions on AFs.

scholarly journals Predictive models and abstract argumentation: the case of high-complexity semantics

2019 ◽  
Vol 34 ◽  
Author(s):  
Mauro Vallati ◽  
Federico Cerutti ◽  
Massimiliano Giacomin
Keyword(s):  
Predictive Models ◽  
Problem Instance ◽  
Sense Making ◽  
High Complexity ◽  
Algorithm Selection ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Complete Knowledge ◽  
Enumeration Problem ◽  
Human Sense

Abstract In this paper, we describe how predictive models can be positively exploited in abstract argumentation. In particular, we present two main sets of results. On one side, we show that predictive models are effective for performing algorithm selection in order to determine which approach is better to enumerate the preferred extensions of a given argumentation framework. On the other side, we show that predictive models predict significant aspects of the solution to the preferred extensions enumeration problem. By exploiting an extensive set of argumentation framework features—that is, values that summarize a potentially important property of a framework—the proposed approach is able to provide an accurate prediction about which algorithm would be faster on a given problem instance, as well as of the structure of the solution, where the complete knowledge of such structure would require a computationally hard problem to be solved. Improving the ability of existing argumentation-based systems to support human sense-making and decision processes is just one of the possible exploitations of such knowledge obtained in an inexpensive way.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

Complexity of fundamental problems in probabilistic abstract argumentation: Beyond independence

2019 ◽  
Vol 268 ◽  
pp. 1-29 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Abstract Argumentation

scholarly journals Towards fixed-parameter tractable algorithms for abstract argumentation

2012 ◽  
Vol 186 ◽  
pp. 1-37 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Reinhard Pichler ◽  
Stefan Woltran
Keyword(s):  
Fixed Parameter Tractable ◽  
Abstract Argumentation ◽  
Fixed Parameter

A Comparative Test on the Enumeration of Extensions in Abstract Argumentation*

2015 ◽  
Vol 140 (3-4) ◽  
pp. 263-278 ◽  
Author(s):  
Stefano Bistarelli ◽  
Fabio Rossi ◽  
Francesco Santini
Keyword(s):  
Comparative Test ◽  
Abstract Argumentation

scholarly journals Strong admissibility for abstract dialectical frameworks

2021 ◽  
pp. 1-41
Author(s):  
Atefeh Keshavarzi Zafarghandi ◽  
Rineke Verbrugge ◽  
Bart Verheij
Keyword(s):  
Maximal Element ◽  
Decision Problems ◽  
Current Work ◽  
Argument Evaluation ◽  
Abstract Argumentation ◽  
Proper Generalization

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: (1) whether a given interpretation is a strongly admissible interpretation of a given ADF, and (2) whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs.

scholarly journals Synthesizing Argumentation Frameworks from Examples

2019 ◽  
Vol 66 ◽  
pp. 503-554 ◽  
Author(s):  
Andreas Niskanen ◽  
Johannes Wallner ◽  
Matti Järvisalo
Keyword(s):  
Natural Extension ◽  
Research Abstract ◽  
Expressive Power ◽  
Synthesis Problem ◽  
Constraint Optimization ◽  
Abstract Argumentation ◽  
Central Notion ◽  
Definition Of ◽  
The Given ◽  
Representation Formalism

Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation---including revision and aggregation of AFs---non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.

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