Dung's Argumentation Framework Research Articles

Credulous acceptance in high-order argumentation frameworks with necessities: An incremental approach

Argumentation is an important research area in the field of AI. There is a substantial amount of work on different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are: i) extending the framework to account for recursive attacks and supports, and ii) considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on High-Order Argumentation Frameworks with Necessities (HOAFNs) which allow for attack and support relations (interpreted as necessity) not only between arguments but also targeting attacks and supports at any level. We propose an approach for the incremental evaluation of the credulous acceptance problem in HOAFNs, by “incrementally” computing an extension (a set of accepted arguments, attacks and supports), if it exists, containing a given goal element in an updated HOAFN. In particular, we are interested in monitoring the credulous acceptance of a given argument, attack or support (goal) in an evolving HOAFN. Thus, our approach assumes to have a HOAFN Δ, a goal ϱ occurring in Δ, an extension E for Δ containing ϱ, and an update u establishing some changes in the original HOAFN, and uses the extension for first checking whether the update is relevant; for relevant updates, an extension of the updated HOAFN containing the goal is computed by translating the problem to the AF domain and leveraging on AF solvers. We provide formal results for our incremental approach and empirically show that it outperforms the evaluation from scratch of the credulous acceptance problem for an updated HOAFN.

RAFDivider: a distributed algorithm for computing semantics in higher-order abstract argumentation frameworks

ABSTRACT This work is related to a computational issue concerning an enriched abstract argumentation framework called RAF (‘Recursive Argumentation Framework’). A RAF is composed of a set of arguments and of a binary relation which models the attacks as in Dung's seminal argumentation framework. The main difference between Dung's framework and a RAF is the fact that a RAF is able to take into account higher-order interactions (i.e. an attack can target an attack and not only an argument). This kind of framework is recent enough for an efficient computation of its main semantics to remain an open question. In this paper, we propose one of the first algorithms dedicated to this issue, RAFDivider. We prove its soundness and its completeness.

A claim-centric perspective on abstract argumentation semantics: Claim-defeat, principles, and expressiveness

Dung's abstract argumentation frameworks (AFs) are a key formalism in AI research nowadays. Claims are an inherent part of each argument; they substantially determine the structure of the abstract representation. Nevertheless, they are often not taken into account on the abstract level, which restricts the modeling capacities of AFs to problems that do not involve claims in the evaluation. In this work, we address this shortcoming and conduct a structural analysis of claim-based argumentation semantics utilizing claim-augmented argumentation frameworks (CAFs) which extend AFs by assigning a claim to each argument. Our main contributions are as follows: We first propose novel variants for preferred, naive, stable, semi-stable, and stage semantics based on claim-defeat and claim-set maximization, complementing existing CAF semantics. Among our findings is that for a certain subclass, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the other semantics. We then conduct a principle-based analysis of the semantics with respect to general and well-formed CAFs. Finally, we study the expressiveness of the semantics by characterizing their signatures. In summary, this paper provides a thorough analysis of fundamental properties of abstract argumentation semantics (along the lines of existing results for AFs) but from the perspective of the claims the arguments represent. This shift of perspective provides novel results which we deem relevant when abstract argumentation is used in an instantiation-based setting.

Explainable acceptance in probabilistic and incomplete abstract argumentation frameworks

Dung's Argumentation Framework (AF) has been extended in several directions, including the possibility of representing uncertainty about the existence of arguments and attacks. In this regard, two main proposals have been introduced in the literature: Probabilistic Argumentation Framework (PrAF) and Incomplete Argumentation Framework (iAF). PrAF is an extension of AF with probability theory, thus representing quantified uncertainty. In contrast, iAF represents unquantified uncertainty, that is it can be seen as a special case where we only know that some elements (arguments or attacks) are uncertain. In this paper, we first address the problem of computing the probability that a given argument is accepted in PrAF. This is carried out by introducing the concept of probabilistic explanation for any 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 PrAFs where odd-length cycles are forbidden. We investigate the approximate complexity of the related FP#P-hard problems of credulous and skeptical acceptance in PrAF, showing that they are generally harder than the problem of computing the probability that a given argument is accepted. Next we consider iAF and, after showing some equivalence properties among classes of iAFs, we study iAF as a special case of PrAF where uncertain elements have associated a probability equal to 1/2. Finally, given this result, we investigate the relationships between iAF acceptance problems and probabilistic acceptance in PrAF.

Abstract Argumentation Framework with Conditional Preferences

Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Preferences in AF allow to represent the comparative strength of arguments in a simple yet expressive way. Preference-based AF (PAF) has been proposed to extend AF with preferences of the form a > b, whose intuitive meaning is that argument a is better than b. In this paper we generalize PAF by introducing conditional preferences of the form a > b \leftarrow body that informally state that a is better than b whenever the condition expressed by body is true. The resulting framework, namely Conditional Preference-based AF (CPAF), extends the PAF semantics under three well-known preference criteria, i.e. democratic, elitist, and KTV. After introducing CPAF, we study the complexity of the verification problem (deciding whether a set of arguments is a ``best'' extension) as well as of the credulous and skeptical acceptance problems (deciding whether a given argument belongs to any or all ``best'' extensions, respectively) under multiple-status semantics (that is, complete, preferred, stable, and semi-stable semantics) for the above-mentioned preference criteria.

Argumentation frameworks with necessities and their relationship with logic programs

This paper presents a comprehensive study of argumentation frameworks with necessities (AFNs), a bipolar extension of Dung Abstract argumentation frameworks (AFs) where the support relation captures a positive interaction between arguments having the meaning of necessity: the acceptance of an argument may require the acceptance of other argument(s). The paper discusses new main acceptability semantics for AFNs and their characterization both by a direct approach and a labelling approach. It examines the relationship between AFNs and Dung AFs and shows the gain provided by the former in terms of concision. Finally, the paper shows how to represent an AFN as a normal logic program (LP) and vice versa and in both cases establishes a one-to-one correspondence between extensions under the main acceptability semantics (except for semi-stable semantics where the correspondence is not completely full) of an AFN and particular cases of 3-valued stable models of normal LPs.

An abstract, logical approach to characterizing strong equivalence in non-monotonic knowledge representation formalisms

Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism, since it allows to locally replace parts of a given theory without changing its meaning. In contrast to classical logic, where strong equivalence coincides with standard equivalence (having the same models), it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature. Consequently, much effort has been devoted to characterizing strong equivalence for knowledge representation formalisms such as logic programs under the stable model semantics, Reiter's default logic, or Dung's argumentation frameworks. For example, strong equivalence for logic programs under stable models can be characterized by so-called HT-models. More precisely, two logic programs are strongly equivalent if and only if they are standard equivalent in the logic of here and there. This means that the logic of here and there can be seen as a characterizing formalism for logic programs under stable model semantics.The aim of this article is to study whether the existence of such characterization logics can be guaranteed for any logic. One main result is that every knowledge representation formalism that allows for a notion of strong equivalence on its finite knowledge bases also possesses a canonical characterizing formalism. In particular, we argue that those characterizing formalisms can be seen as classical, monotonic logics. Moreover, we will not only show the existence of characterizing formalism, but even that the model theory of any characterizing logic is uniquely determined (up to isomorphism).

An interface between natural language and abstract argumentation frameworks for real-time debate analysis

Participatory approaches are increasingly being used to plan policies, usually involving stakeholders with conflicting interests, visions and objectives. Participants are often passionate about their cause, especially in sensitive contexts such as their health or the environment for example. Whether involved in, or observing a debate, more often than not, it is hard to follow its progress; positions are unclear and arguments are unstructured often resulting in circular discussions. This is true both for participants in an ongoing debate hoping to reach a consensus as well as for those who, a posteriori, wish to understand what was discussed and how. However, at the current time, there are to our knowledge no tools to support real-time debates by allowing participants to visualize arguments and identifying opposing points of view in order to resolve conflicts. In order to fill this gap, we developed a model based on Dung's argumentation framework that we implemented in a tool called AIPA, along with a web-application to facilitate user interaction. AIPA allows one to formalize and visualize, in real-time, the arguments of the participants, to conduct inferences in order to identify acceptable arguments and to highlight conflicting ones. Furthermore, AIPA can be used a posteriori to summarize a debate in an easy to follow argument representation. The main contribution of AIPA is its ability to structure the debate by making the arguments chain traceable and transparent, in real-time and a posteriori, and this, with users with no expertise in argumentation. In this paper, we present AIPA along with two applications to illustrate its workings and benefits.

Argumentation Frameworks with Strong and Weak Constraints: Semantics and Complexity

Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in formal argumentation. Key aspects of the success and popularity of Dung's framework include its simplicity and expressiveness. Integrity constraints help to express domain knowledge in a compact and natural way, thus keeping easy the modeling task even for problems that otherwise would be hard to encode within an AF. In this paper, after providing an intuitive semantics based on Lukasiewicz's logic for AFs with (strong) constraints, called Constrained AFs (CAFs), we propose Weak constrained AFs (WAFs) that enhance CAFs with weak constraints. Intuitively, these constraints can be used to find ``optimal'' solutions to problems defined through CAFs. We provide a detailed complexity analysis of CAFs and WAFs, showing that strong constraints do not increase the expressive power of AFs in most cases, while weak constraints systematically increase the expressive power of CAFs under several well-known argumentation semantics.

Investigating subclasses of abstract dialectical frameworks

Dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures.

On Three-Valued Acceptance Conditions of Abstract Dialectical Frameworks

Abstract Dialectical Frameworks (adfs) are generalizations of Dung's abstract argumentation frameworks (afs) where each argument has an associated acceptance condition expressed by a boolean formula. The resulting extension is robust enough not only to model the attack relation original to afs, but also others types of dependencies and interactions between arguments. A recent development in adfs proposed an alternative formalization involving three-valued acceptance conditions, connecting the original definitions of adfs to the concept of three-valued argument labellings, a core concept in computational argumentation literature. In this paper, we revise some of the main semantics defined under this three-valued approach and prove our definitions hold equivalence to well-known semantics of afs.

A comprehensive study of argumentation frameworks with sets of attacking arguments

It has been argued that Dung's classical Abstract Argumentation Framework (AAF) model is not appropriate for capturing “joint attacks”, a feature that is inherent in several contexts and applications. The model proposed by Nielsen and Parsons in [1], often referred to as “framework with sets of attacking arguments” (SETAF), fills this gap by introducing joint attacks as a generalisation of the standard attack relationship of AAFs, thus constituting a faithful generalization of Dung's model. Building on that work, we provide a more complete characterization of these frameworks, which includes the treatment of various semantics not considered in the original publication, a more fine-grained representation of all acceptability semantics using labellings, and two functions allowing the transition between extensions and labellings along with their properties. Moreover, we show that a variety of well-known results that apply to AAF can be migrated to the SETAF setting. To further associate the two frameworks, we provide a natural way to represent a SETAF as a Dung-style AAF, and show how the generated AAF behaves.

Characterizing acceptability semantics of argumentation frameworks with recursive attack and support relations

Over the last decade, several extensions of Dung's Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as necessity. Currently, to determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung's AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung's argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN).

Weighted Abstract Dialectical Frameworks

Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

An extension-based approach to belief revision in abstract argumentation

Argumentation is an inherently dynamic process, and recent years have witnessed tremendous research efforts towards an understanding of how the seminal AGM theory of belief change can be applied to argumentation, in particular to Dung's abstract argumentation frameworks (AFs). However, none of the attempts have yet succeeded in solving the natural situation where the revision of an AF is guaranteed to be representable by a single AF. Here we present a solution to this problem, which applies to many prominent argumentation semantics. To prove a full representation theorem, we make use of recent advances in both areas of argumentation and belief change. In particular, we use the concept of realizability in argumentation and the concept of compliance as introduced in Horn revision. We also present a family of concrete belief change operators tailored specifically for AFs and analyze their computational complexity.

Looking-ahead in backtracking algorithms for abstract argumentation

We refine implemented backtracking algorithms for a number of problems related to Dung's argumentation frameworks. Under admissible, preferred, complete, stable, semi stable, and ideal semantics we add enhancements, what are so-called global looking-ahead pruning strategies, to the-state-of-the-art implementations of two problems. First, we tackle the extension enumeration problem: constructing some/all set(s) of acceptable arguments of a given argumentation framework. Second, we address the acceptance decision problem: deciding whether an argument is in some/all set(s) of accepted arguments of a given argumentation framework. The experiments that we report show that the speedup gain of the new enhancements is quite significant.

Comparing the expressiveness of argumentation semantics

Understanding the expressiveness of a formalism is undoubtedly an important part of understanding its possibilities and limitations. Translations between different formalisms have proven to be valuable tools for understanding this very expressiveness. In this work we complement recent investigations of the intertranslatability of argumen- tation semantics for Dung's abstract argumentation frameworks. As our focus is on the expressiveness of argumentation semantics we expand the area of interest beyond efficiently computable translations and also consider translations that might not (always) be efficiently computable. This allows us to provide translations between certain semantics, where under established complexity assumptions no efficiently computable translation exists. However, for some semantics we give strong translational impossibility results stating that even with arbitrary computational power we can not in all situations translate one to the other. Finally, this allows us to draw a hierarchy for the expressiveness of argumentation semantics.

On efficiently estimating the probability of extensions in abstract argumentation frameworks

Probabilistic abstract argumentation is an extension of Dung's abstract argumentation framework with probability theory. In this setting, we address the problem of computing the probability Pr sem ( S ) that a set S of arguments is an extension according to a semantics sem . We focus on four popular semantics (i.e., complete , grounded , preferred and ideal-set ) for which the state-of-the-art approach is that of estimating Pr sem ( S ) by using a Monte-Carlo simulation technique, as computing Pr sem ( S ) has been proved to be intractable. In this paper, we propose a new Monte-Carlo simulation approach which exploits some properties of the above-mentioned semantics for estimating Pr sem ( S ) using much fewer samples than the state-of-the-art approach, resulting in a significantly more efficient estimation technique. • A new Monte-Carlo-based technique for estimating the probability that a set of arguments is an extension is proposed. • The performances of the proposed technique are thoroughly analyzed both experimentally and theoretically. • The proposed technique outperforms the state of the art.

Argumentative reasoning and taxonomic analysis for the identification of medical errors

Telemedicine consists of the use of information and communication technologies (ICTs) in the practice of medicine. The massive digitalisation of the society is changing the behaviour of ordinary people even in medical sectors. The impact of digitisation is also having impacts on teleexpertise, where a medical professional can remotely ask some advices through the use of ICTs to provide treatment to a patient in critical conditions in remote environment. However, sometimes the outcome of such advice obtained remotely can lead to medical errors. In these situations, it is important to determine whether the causes of the errors could have been avoidable or not for the purposes of establishing the truth and assuring justice for the victims of medical errors. The proposed work fits this perspective with the objective to formalise elements of argumentation in collaborative medical organisations using telemedicine. In other words, a technique that extends the Dung's argumentation framework in order to bring out the errors committed following a remote medical procedure has been proposed. The proposed technique is underpinned by graphical reasoning. The reasoning is represented through a directed graph in which the extended nodes specify the arguments with their source(s) and the identification of errors is done according to the Makeham's and Tempos taxonomies. To illustrate the functioning of the proposed technique or solution, an example of the practice of teleexpertise (between two French hospitals) that leads to litigation is presented.

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Abstract dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.