Distinguishability in Abstract Argumentation

2021 ◽  
Author(s):  
Isabelle Kuhlmann ◽  
Tjitze Rienstra ◽  
Lars Bengel ◽  
Kenneth Skiba ◽  
Matthias Thimm
Keyword(s):  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Exhaustive Study

In abstract argumentation, the admissible semantics can be said to distinguish the preferred semantics in the sense that argumentation frameworks with the same admissible extensions also have the same preferred extensions. In this paper we present an exhaustive study of such distinguishability relationships, including those between sets of semantics. We further examine restricted classes of argumentation frameworks, such as self-attack-free and acyclic frameworks. We discuss the relevance of our results in the context of the argumentation framework elicitation problem.

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.

scholarly journals Paracoherent Answer Set Semantics meets Argumentation Frameworks

2019 ◽  
Vol 19 (5-6) ◽  
pp. 688-704
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Great Success ◽  
Argumentation Framework ◽  
Computational Costs ◽  
Abstract Argumentation ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractIn the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

scholarly journals Reasoning with Inconsistent Possibilistic Ontologies by Applying Argument Accrual

2017 ◽  
Vol 17 (02) ◽  
pp. e16
Author(s):  
Sergio Alejandro Gómez
Keyword(s):  
Logic Programming ◽  
Description Logic ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Possibilistic Logic ◽  
Grounded Semantics

We present an approach for performing instance checking in possibilistic description logic programming ontologies by accruing arguments that support the membership of individuals to concepts. Ontologies are interpreted as possibilistic logic programs where accruals of arguments as regarded as vertexes in an abstract argumentation framework. A suitable attack relation between accruals is defined. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach that is capable of reasoning under Dung’s grounded semantics.

scholarly journals Defining the Semantics of Abstract Argumentation Frameworks through Logic Programs and Partial Stable Models (Extended Abstract)

2021 ◽  
Author(s):  
Gianvincenzo Alfano ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Stable Models

Extensions of Dung’s Argumentation Framework (AF) include the class of Recursive Bipolar AFs (Rec-BAFs), i.e. AFs with recursive attacks and supports. We show that a Rec-BAF \Delta can be translated into a logic program P_\Delta so that the extensions of \Delta under different semantics coincide with subsets of the partial stable models of P_\Delta.

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.

Independence and D-separation in Abstract Argumentation

2020 ◽  
Author(s):  
Tjitze Rienstra ◽  
Matthias Thimm ◽  
Kristian Kersting ◽  
Xiaoting Shao
Keyword(s):  
Markov Property ◽  
Argumentation Framework ◽  
Separation Criterion ◽  
Abstract Argumentation ◽  
The Status ◽  
Definition Of ◽  
Semantic Definition

We investigate the notion of independence in abstract argumentation, i.e., the question of whether the evaluation of one set of arguments is independent of the evaluation of another set of arguments, given that we already know the status of a third set of arguments. We provide a semantic definition of this notion and develop a method to discover independencies based on transforming an argumentation framework into a DAG on which we then apply the well-known d-separation criterion. We also introduce the SCC Markov property for argumentation semantics, which generalises the Markov property from the classical acyclic case and guarantees the soundness of our approach.

Computing Grounded Extensions Of Abstract Argumentation Frameworks

2019 ◽  
Author(s):  
Samer Nofal ◽  
Katie Atkinson ◽  
Paul E Dunne
Keyword(s):  
Directed Graph ◽  
Ad Hoc ◽  
State Of The Art ◽  
Input Graph ◽  
Argumentation Framework ◽  
Abstract Argumentation

Abstract An abstract argumentation framework is a directed graph $(V,E)$ such that the vertices of $V$ denote abstract arguments and $E \subseteq V \times V$ represents the attack relation between them. We present a new ad hoc algorithm for computing the grounded extension of an abstract argumentation framework. We show that the new algorithm runs in $\mathcal{O}(|V|+|E|)$ time. In contrast, the existing state-of-the-art algorithm runs in $\mathcal{O}(|V|+|S||E|)$ time where $S$ is the grounded extension of the input graph.

scholarly journals Rationalisation of Profiles of Abstract Argumentation Frameworks: Characterisation and Complexity

2017 ◽  
Vol 60 ◽  
pp. 149-177 ◽  
Author(s):  
Stéphane Airiau ◽  
Elise Bonzon ◽  
Ulle Endriss ◽  
Nicolas Maudet ◽  
Julien Rossit
Keyword(s):  
Artificial Intelligence ◽  
Social Choice ◽  
Research Agenda ◽  
Multiagent System ◽  
Social Values ◽  
Algorithmic Problem ◽  
Argumentation Framework ◽  
Popular Approach ◽  
Abstract Argumentation ◽  
Points Of View

Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modeled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Explainable Acceptance in Probabilistic Abstract Argumentation: Complexity and Approximation

2020 ◽  
Author(s):  
Gianvincenzo Alfano ◽  
Marco Calautti ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Probability Theory ◽  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Polynomial Approximation ◽  
Special Class ◽  
Hard Problem ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Additive Error ◽  
Probabilistic Argumentation

Recently there has been an increasing interest in probabilistic abstract argumentation, an extension of Dung's abstract argumentation framework with probability theory. In this setting, we address the problem of computing the probability that a given argument is accepted. This is carried out by introducing the concept of probabilistic explanation for a given (probabilistic) extension. We show that the complexity of the problem is FP^#P-hard and propose polynomial approximation algorithms with bounded additive error for probabilistic argumentation frameworks where odd-length cycles are forbidden. This is quite surprising since, as we show, such kind of approximation algorithm does not exist for the related FP^#P-hard problem of computing the probability of the credulous acceptance of an argument, even for the special class of argumentation frameworks considered in the paper.

Sign in / Sign up

Export Citation Format

Share Document