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 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.

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 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 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.

The Orchestra as Acting Area in Greek Tragedy

Ramus ◽  
1985 ◽  
Vol 14 (2) ◽  
pp. 75-84 ◽  
Author(s):  
Graham Ley ◽  
Michael Ewans
Keyword(s):  
Greek Tragedy ◽  
Close Relation ◽  
Central Problem ◽  
Classical Drama ◽  
Considerable Experience

For some years past there has been a welcome change of emphasis towards the consideration of staging in books published on Greek tragedy; and yet with that change also a curious failure to be explicit about the central problem connected with all stagecraft, namely that of the acting-area. In this study two scholars with considerable experience of teaching classical drama in performance consider this problem of the acting-area in close relation to major scenes from two Greek tragedies, and suggest some general conclusions. The article must stand to some extent as a critique of the succession of books that has followed the apparently pioneering study of Oliver Taplin, none of which has made any substantial or sustained attempt to indicate where actors might have acted in the performance of Greek tragedy, though most, if not all, have been prepared to discard the concept of a raised ‘stage’ behind the orchestra. Hippolytus (428 BC) is the earliest of the surviving plays of Euripides to involve three speaking actors in one scene. Both Alcestis (438 BC and Medea (431 BC almost certainly require three actors to be performed with any fluency, but surprisingly present their action largely through dialogue and confrontation — surprisingly, perhaps, because at least since 458 BC and the performance of the Oresteia it is clear that three actors were available to any playwright.

When Is True Belief Knowledge?

2012 ◽  
Author(s):  
Richard Foley
Keyword(s):  
True Belief ◽  
Theory Of Knowledge ◽  
Central Problem ◽  
Significant Aspect ◽  
Coming To Know ◽  
Contemporary Epistemology ◽  
What Matters

A woman glances at a broken clock and comes to believe it is a quarter past seven. Yet, despite the broken clock, it really does happen to be a quarter past seven. Her belief is true, but it isn't knowledge. This is a classic illustration of a central problem in epistemology: determining what knowledge requires in addition to true belief. This book finds a new solution to the problem in the observation that whenever someone has a true belief but not knowledge, there is some significant aspect of the situation about which she lacks true beliefs—something important that she doesn't quite “get.” This may seem a modest point but, as the book shows, it has the potential to reorient the theory of knowledge. Whether a true belief counts as knowledge depends on the importance of the information one does or doesn't have. This means that questions of knowledge cannot be separated from questions about human concerns and values. It also means that, contrary to what is often thought, there is no privileged way of coming to know. Knowledge is a mutt. Proper pedigree is not required. What matters is that one doesn't lack important nearby information. Challenging some of the central assumptions of contemporary epistemology, this is an original and important account of knowledge.

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