Credulous and skeptical acceptability in probabilistic abstract argumentation: complexity results

2019 ◽  
Vol 12 (2) ◽  
pp. 181-191
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Abstract Argumentation ◽  
Complexity Results

scholarly journals Complexity of Abstract Argumentation under a Claim-Centric View

2019 ◽  
Vol 33 ◽  
pp. 2801-2808 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Stefan Woltran
Keyword(s):  
Knowledge Base ◽  
Complexity Analysis ◽  
Decision Problems ◽  
Fixed Parameter Tractability ◽  
Abstract Argumentation ◽  
Complexity Results ◽  
Fixed Parameter

Abstract argumentation frameworks have been introduced by Dung as part of an argumentation process, where arguments and conflicts are derived from a given knowledge base. It is solely this relation between arguments that is then used in order to identify acceptable sets of arguments. A final step concerns the acceptance status of particular statements by reviewing the actual contents of the acceptable arguments. Complexity analysis of abstract argumentation so far has neglected this final step and is concerned with argument names instead of their contents, i.e. their claims. As we outline in this paper, this is not only a slight deviation but can lead to different complexity results. We, therefore, give a comprehensive complexity analysis of abstract argumentation under a claim-centric view and analyse the four main decision problems under seven popular semantics. In addition, we also address the complexity of common sub-classes and introduce novel parameterisations – which exploit the nature of claims explicitly – along with fixed-parameter tractability results.

scholarly journals On the Intertranslatability of Argumentation Semantics

2011 ◽  
Vol 41 ◽  
pp. 445-475 ◽  
Author(s):  
W. Dvořák ◽  
S. Woltran
Keyword(s):  
Knowledge Representation ◽  
Abstract Argumentation ◽  
Negative Results ◽  
Complexity Results ◽  
Simple Formalism

Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms of different semantics proposed for abstract argumentation frameworks, a nonmonotonic yet simple formalism which received increasing interest within the last decade. Although the properties of these different semantics are nowadays well understood, there are no explicit results about intertranslatability. We provide such translations wrt. different properties and also give a few novel complexity results which underlie some negative results.

scholarly journals Probabilistic bipolar abstract argumentation frameworks: complexity results

2018 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Probabilistic Modeling ◽  
Deterministic Case ◽  
Abstract Argumentation ◽  
Complexity Results

Probabilistic Bipolar Abstract Argumentation Frameworks (prBAFs), combining the possibility of specifying supports between arguments with a probabilistic modeling of the uncertainty, are considered, and the complexity of the fundamentalproblem of computing extensions' probabilities is addressed.The most popular semantics of supports and extensions are considered, as well as different paradigms for defining the probabilistic encoding of the uncertainty.Interestingly, the presence of supports, which does not alter the complexity of verifying extensions in the deterministic case, is shown to introduce a new source of complexity in some probabilistic settings, for which tractable cases are also identified.

scholarly journals A General Notion of Equivalence for Abstract Argumentation

2017 ◽  
Author(s):  
Ringo Baumann ◽  
Wolfgang Dvořák ◽  
Thomas Linsbichler ◽  
Stefan Woltran
Keyword(s):  
General Notion ◽  
Abstract Argumentation ◽  
Complexity Results

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this notion of equivalence nicely captures the concept of local simplifications. We provide exact characterizations and complexity results for deciding our new notion of equivalence.

scholarly journals Counting Complexity for Reasoning in Abstract Argumentation

2019 ◽  
Vol 33 ◽  
pp. 2827-2834 ◽  
Author(s):  
Johannes K. Fichte ◽  
Markus Hecher ◽  
Arne Meier
Keyword(s):  
Parameterized Complexity ◽  
Upper Bounds ◽  
Argumentation Framework ◽  
Bounded Treewidth ◽  
Abstract Argumentation ◽  
Counting Complexity ◽  
Complexity Results ◽  
Model Counting ◽  
Novel Algorithms ◽  
Input Instance

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.

scholarly journals Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

2017 ◽  
Vol 60 ◽  
pp. 1-40 ◽  
Author(s):  
Johannes P. Wallner ◽  
Andreas Niskanen ◽  
Matti Järvisalo
Keyword(s):  
Computational Complexity ◽  
Formal Model ◽  
Legal Reasoning ◽  
Knowledge Representation And Reasoning ◽  
Polynomial Hierarchy ◽  
Prototype System ◽  
Multi Agent Systems ◽  
Abstract Argumentation ◽  
Complexity Results ◽  
Complete Problems

Argumentation is an active area of modern artificial intelligence (AI) research, with connections to a range of fields, from computational complexity theory and knowledge representation and reasoning to philosophy and social sciences, as well as application-oriented work in domains such as legal reasoning, multi-agent systems, and decision support. Argumentation frameworks (AFs) of abstract argumentation have become the graph-based formal model of choice for many approaches to argumentation in AI, with semantics defining sets of jointly acceptable arguments, i.e., extensions. Understanding the dynamics of AFs has been recently recognized as an important topic in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation as a recently proposed form of argumentation dynamics. We provide a nearly complete computational complexity map of argument-fixed extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constraint optimization under the maximum satisfiability (MaxSAT) paradigm. Going beyond NP, we propose novel MaxSAT-based counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

scholarly journals Smallest Explanations and Diagnoses of Rejection in Abstract Argumentation

2020 ◽  
Author(s):  
Andreas Niskanen ◽  
Matti Järvisalo
Keyword(s):  
Central Problem ◽  
Maximum Satisfiability ◽  
Satisfiability Solvers ◽  
Abstract Argumentation ◽  
Complexity Results

Deciding acceptance of arguments is a central problem in the realm of abstract argumentation. Beyond mere acceptance status, when an argument is rejected it would be informative to analyze reasons for the rejection. Recently, two complementary notions---explanations and diagnoses---were proposed for capturing underlying reasons for rejection in terms of (small) subsets of arguments or attacks. We provide tight complexity results for deciding and computing argument-based explanations and diagnoses. Computationally, we identify that smallest explanations and diagnoses for argumentation frameworks can be computed as so-called smallest unsatisfiable subsets (SMUSes) and smallest correction sets of propositional formulas. Empirically, we show that SMUS extractors and maximum satisfiability solvers (computing smallest correction sets) offer effective ways of computing smallest explanations and diagnoses.

scholarly journals Reasoning over Assumption-Based Argumentation Frameworks via Direct Answer Set Programming Encodings

2019 ◽  
Vol 33 ◽  
pp. 2938-2945 ◽  
Author(s):  
Tuomo Lehtonen ◽  
Johannes P. Wallner ◽  
Matti Järvisalo
Keyword(s):  
Answer Set Programming ◽  
Direct Approach ◽  
Problem Complexity ◽  
New Approach ◽  
Abstract Argumentation ◽  
Reasoning Systems ◽  
Complexity Results ◽  
Empirical Performance ◽  
Direct Answer ◽  
Answer Set

Focusing on assumption-based argumentation (ABA) as a central structured formalism to AI argumentation, we propose a new approach to reasoning in ABA with and without preferences. While previous approaches apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct approach by encoding ABA reasoning tasks in answer set programming. This significantly improves on the empirical performance of current ABA reasoning systems. We also give new complexity results for reasoning in ABA+, suggesting that the integration of preferential information into ABA results in increased problem complexity for several central argumentation 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.

Concern, Respect, and Cooperation

2018 ◽  
Author(s):  
Garrett Cullity
Keyword(s):  
Moral Theory ◽  
Fundamental Principle ◽  
Simple Set ◽  
Collective Activity ◽  
Complexity Results ◽  
Concern For Others ◽  
Moral Theories ◽  
Moral Responsibilities

Three things often recognized as central to morality are concern for others’ welfare, respect for their self-expression, and cooperation in worthwhile collective activity. When philosophers have proposed theories of the substance of morality, they have typically looked to one of these three sources to provide a single, fundamental principle of morality—or they have tried to formulate a master-principle for morality that combines these three ideas in some way. This book views them instead as three independently important foundations of morality. It sets out a plural-foundation moral theory with affinities to that of W. D. Ross. There are major differences: the account of the foundations of morality differs from Ross’s, and there is a more elaborate explanation of how the rest of morality derives from them. However, the overall aim is similar. This is to illuminate the structure of morality by showing how its complex content is generated from a relatively simple set of underlying elements—the complexity results from the various ways in which one part of morality can derive from another, and the various ways in which the derived parts of morality can interact. Plural-foundation moral theories are sometimes criticized for having nothing helpful to say about cases in which their fundamental norms conflict. Responding to this, the book concludes with three detailed applications of the theory: to the questions surrounding paternalism, the use of others as means, and our moral responsibilities as consumers.

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