Computational Complexity of Semi-stable Semantics in Abstract Argumentation Frameworks

2008 ◽  
pp. 153-165 ◽  
Author(s):  
Paul E. Dunne ◽  
Martin Caminada
Keyword(s):  
Computational Complexity ◽  
Abstract Argumentation ◽  
Stable Semantics

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.

Reasoning over Attack-incomplete AAFs in the Presence of Correlations

2021 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Computational Complexity ◽  
Logical Operators ◽  
Abstract Argumentation ◽  
Precise Representation ◽  
User Friendly

Attack-Incomplete Abstract Argumentation Frameworks (att- iAAFs) are a popular extension of AAFs where attacks are marked as uncertain when they are not unanimously per- ceived by different agents reasoning on the same arguments. We here extend att-iAAFs with the possibility of specifying correlations involving the uncertain attacks. This feature sup- ports a unified and more precise representation of the differ- ent scenarios for the argumentation, where, for instance, it can be stated that an attack α has to be considered only if an attack β is considered, or that α and β are alternative, and so on. In order to provide a user-friendly language for spec- ifying the correlations, we allow the argumentation analyst to express them in terms of a set of elementary dependen- cies, using common logical operators (namely, OR , NAND , CHOICE , ⇒). In this context, we focus on the problem of verifying extensions under the possible perspective, and study the sensitivity of its computational complexity to the forms of correlations expressed and the semantics of the extensions.

Choices and their Consequences - Explaining Acceptable Sets in Abstract Argumentation Frameworks

2021 ◽  
Author(s):  
Ringo Baumann ◽  
Markus Ulbricht
Keyword(s):  
Computational Complexity ◽  
Characteristic Function ◽  
Decision Problems ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Exhaustive Study ◽  
The Given ◽  
Made In

We develop a notion of explanations for acceptance of arguments in an abstract argumentation framework. To this end we show that extensions returned by Dung's standard semantics can be decomposed into i) non-deterministic choices made on even cycles of the given argumentation graph and then ii) deterministic iteration of the so-called characteristic function. Naturally, the choice made in i) can be viewed as an explanation for the corresponding extension and thus the arguments it contains. We proceed to propose desirable criteria a reasonable notion of an explanation should satisfy. We present an exhaustive study of the newly introduced notion w.r.t. these criteria. Finally some interesting decision problems arise from our analysis and we examine their computational complexity, obtaining some surprising tractability results.

Semi-Stable Semantics for Abstract Dialectical Frameworks

2021 ◽  
Author(s):  
Atefeh Keshavarzi Zafarghandi ◽  
Rineke Verbrugge ◽  
Bart Verheij
Keyword(s):  
Current Work ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Proper Generalization ◽  
Stable Models

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria that have been used to settle the acceptance of arguments are called semantics. However, the notion of semi-stable semantics as studied for abstract argumentation frameworks has received little attention for ADFs. In the current work, we present the concepts of semi-two-valued models and semi-stable models for ADFs. We show that these two notions satisfy a set of plausible properties required for semi-stable semantics of ADFs. Moreover, we show that semi-two-valued and semi-stable semantics of ADFs form a proper generalization of the semi-stable semantics of AFs, just like two-valued model and stable semantics for ADFs are generalizations of stable semantics for AFs.

An introduction to argumentation semantics

2011 ◽  
Vol 26 (4) ◽  
pp. 365-410 ◽  
Author(s):  
Pietro Baroni ◽  
Martin Caminada ◽  
Massimiliano Giacomin
Keyword(s):  
State Of The Art ◽  
The State ◽  
Final Part ◽  
Domain Specific ◽  
Abstract Argumentation ◽  
General Properties ◽  
Stable Ideal ◽  
Stable Semantics

AbstractThis paper presents an overview on the state of the art of semantics for abstract argumentation, covering both some of the most influential literature proposals and some general issues concerning semantics definition and evaluation. As to the former point, the paper reviews Dung's original notions of complete, grounded, preferred, and stable semantics, as well as subsequently proposed notions like semi-stable, ideal, stage, and CF2 semantics, considering both the extension-based and the labelling-based approaches with respect to their definitions. As to the latter point, the paper presents an extensive set of general properties for semantics evaluation and analyzes the notions of argument justification and skepticism. The final part of the paper is focused on the discussion of some relationships between semantics properties and domain-specific requirements.

scholarly journals Novel Algorithms for Abstract Dialectical Frameworks based on Complexity Analysis of Subclasses and SAT Solving

2018 ◽  
Author(s):  
Thomas Linsbichler ◽  
Marco Maratea ◽  
Andreas Niskanen ◽  
Johannes P. Wallner ◽  
Stefan Woltran
Keyword(s):  
Computational Complexity ◽  
Complexity Analysis ◽  
Sat Solving ◽  
Sat Solvers ◽  
Abstract Argumentation ◽  
Novel Algorithms ◽  
High Computational Complexity

Abstract dialectical frameworks (ADFs) constitute one of the most powerful formalisms in abstract argumentation. Their high computational complexity poses, however, certain challenges when designing efficient systems. In this paper, we tackle this issue by (i) analyzing the complexity of ADFs under structural restrictions, (ii) presenting novel algorithms which make use of these insights, and (iii) empirically evaluating a resulting implementation which relies on calls to SAT solvers.

scholarly journals Decomposition-Guided Reductions for Argumentation and Treewidth

2021 ◽  
Author(s):  
Johannes Fichte ◽  
Markus Hecher ◽  
Yasir Mahmood ◽  
Arne Meier
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Complexity Analysis ◽  
Upper Bounds ◽  
Abstract Argumentation

Argumentation is a widely applied framework for modeling and evaluating arguments and its reasoning with various applications. Popular frameworks are abstract argumentation (Dung’s framework) or logic-based argumentation (Besnard-Hunter’s framework). Their computational complexity has been studied quite in-depth. Incorporating treewidth into the complexity analysis is particularly interesting, as solvers oftentimes employ SAT-based solvers, which can solve instances of low treewidth fast. In this paper, we address whether one can design reductions from argumentation problems to SAT-problems while linearly preserving the treewidth, which results in decomposition-guided (DG) reductions. It turns out that the linear treewidth overhead caused by our DG reductions, cannot be significantly improved under reasonable assumptions. Finally, we consider logic-based argumentation and establish new upper bounds using DG reductions and lower bounds.

scholarly journals On the Responsibility for Undecisiveness in Preferred and Stable Labellings in Abstract Argumentation (Extended Abstract)

2019 ◽  
Author(s):  
Claudia Schulz ◽  
Francesca Toni
Keyword(s):  
General Question ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
High Level ◽  
The Given ◽  
Different Levels

Different semantics of abstract Argumentation Frameworks (AFs) provide different levels of decisiveness for reasoning about the acceptability of conflicting arguments.The stable semantics is useful for applications requiring a high level of decisiveness, as it assigns to each argument the label "accepted" or the label "rejected". Unfortunately, stable labellings are not guaranteed to exist, thus raising the question as to which parts of AFs are responsible for the non-existence. In this paper, we address this question by investigating a more general question concerning preferred labellings (which may be less decisive than stable labellings but are always guaranteed to exist), namely why a given preferred labelling may not be stable and thus undecided on some arguments. In particular, (1) we give various characterisations of parts of an AF, based on the given preferred labelling, and (2) we show that these parts are indeed responsible for the undecisiveness if the preferred labelling is not stable. We then use these characterisations to explain the non-existence of stable labellings.

scholarly journals An Efficient Java-Based Solver for Abstract Argumentation Frameworks: jArgSemSAT

2017 ◽  
Vol 26 (02) ◽  
pp. 1750002 ◽  
Author(s):  
Federico Cerutti ◽  
Mauro Vallati ◽  
Massimiliano Giacomin
Keyword(s):  
Computational Complexity ◽  
Web Service ◽  
Computational Models ◽  
State Of The Art ◽  
Legal Reasoning ◽  
Intelligence Analysis ◽  
Abstract Argumentation ◽  
Current State ◽  
In Virtue Of ◽  
Argumentation Systems

Dung’s argumentation frameworks are adopted in a variety of applications, from argument-mining, to intelligence analysis and legal reasoning. Despite this broad spectrum of already existing applications, the mostly adopted solver—in virtue of its simplicity—is far from being comparable to the current state-of-the-art solvers. On the other hand, most of the current state-of-the-art solvers are far too complicated to be deployed in real-world settings. In this paper we provide and extensive description of jArgSemSAT, a Java re-implementation of ArgSemSAT. ArgSemSAT represents the best single solver for argumentation semantics with the highest level of computational complexity. We show that jArgSemSAT can be easily integrated in existing argumentation systems (1) as an off-the-shelf, standalone, library; (2) as a Tweety compatible library; and (3) as a fast and robust web service freely available on the Web. Our large experimental analysis shows that despite being written in Java, jArgSemSAT would have scored in most of the cases among the three bests solvers for the two semantics with highest computational complexity “Stable and Preferred” in the last competition on computational models of argumentation.

scholarly journals Expressiveness of Two-Valued Semantics for Abstract Dialectical Frameworks

2015 ◽  
Vol 54 ◽  
pp. 193-231 ◽  
Author(s):  
Hannes Strass
Keyword(s):  
Computational Complexity ◽  
Propositional Logic ◽  
Existence Problem ◽  
Logic Programs ◽  
Efficient Manner ◽  
Abstract Argumentation ◽  
Normal Logic ◽  
Model Existence

We analyse the expressiveness of Brewka and Woltran's abstract dialectical frameworks for two-valued semantics. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. We also compare ADFs' expressiveness with that of (the two-valued semantics of) abstract argumentation frameworks, normal logic programs and propositional logic. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements. We finally also analyse and compare the representational succinctness of ADFs (for two-valued model semantics), that is, their capability to represent two-valued interpretation sets in a space-efficient manner.

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