On the equivalence between bipolar argumentation frameworks and frameworks with sets of attacking arguments (SETAFs)

Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung’s Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung’s AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension.

Bipolar Argumentation Frameworks (BAFs) are an important class of argumentation frameworks useful for capturing, reasoning with, and deriving conclusions from debates. They have the potential to make solid contributions to real-world multi-agent systems and human-agent interaction in domains such as legal reasoning, healthcare and politics. Despite this fact, practical systems implementing BAFs are largely lacking. In this demonstration, we provide a software system implementing novel algorithms for calculating extensions (winning sets of arguments) of BAFs. Participants in the demonstration will be able to input their own debates into our system, and watch a graphical representation of the algorithms as they process information and decide which sets of arguments are winners of the debate.

Bipolar Argumentation Frameworks (BAFs) encompass both attacks and supports among arguments. We study different semantic interpretations of support in BAFs, particularly necessary and deductive support, as well as argument coalitions and a recent proposal by Gabbay. We analyse the relationship of these different notions of support in BAFs with the semantics of a well established structured argumentation formalism, Assumption-Based Argumentation (ABA), which predates BAFs. We propose natural mappings from BAFs into a restricted class of (non-flat) ABA frameworks, which we call bipolar, and prove that the admissible and preferred semantics of these ABA frameworks correspond to the admissible and preferred semantics of the various approaches to BAFs. Motivated by the definition of stable semantics for BAFs, we introduce a novel set-stable semantics for ABA frameworks, and prove that it corresponds to the stable semantics of the various approaches to BAFs. Finally, as a by-product of modelling various approaches to BAFs in bipolar ABA, we identify precise semantic relationships amongst all approaches we consider.

Dung’s abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in artificial intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development of the Bipolar Argumentation Framework (BAF), and recursive attacks and supports, resulting in the Recursive BAF (Rec-BAF). Different interpretations of supports have been proposed, whereas for Rec-BAF (where the target of attacks and supports may also be attacks and supports) even different semantics for attacks have been defined. However, the semantics of these frameworks have either not been defined in the presence of support cycles or are often quite intricate in terms of the involved definitions. We encompass this limitation and present classical semantics for general BAF and Rec-BAF and show that the semantics for specific BAF and Rec-BAF frameworks can be defined by very simple and intuitive modifications of that defined for the case of AF. This is achieved by providing a modular definition of the sets of defeated and acceptable elements for each AF-based framework. We also characterize, in an elegant and uniform way, the semantics of general BAF and Rec-BAF in terms of logic programming and partial stable model semantics.

We introduce Incomplete Bipolar Argumentation Frameworks (iBAFs), the extension of Dung’s Abstract Argumentation Frameworks (AAFs) allowing the simultaneous presence of supports (borrowed from BAFs – Bipolar AAFs) and of uncertain elements of the argumentation graph (borrowed from iAAFs – incomplete AAFs). We investigate the computational complexity of verification problem (under the possible perspective) and the acceptance problem, by studying its sensitivity to the semantics of supports and the semantics of extensions. On the one hand, we show that adding supports on top of incompleteness does not affect the complexity of the acceptance. On the other hand, surprisingly, we show that the joint use of bipolarity and incompleteness has a deep impact on the complexity of the verification: for the semantics under which the verification over AAFs is polynomial-time solvable, although moving from AAFs to BAFs or to iAAFs does not change the complexity, the complexity of the verification over iBAFs may increase up to NP-complete.

The Bipolar Argumentation Framework approach is an extension of the Argumentation Framework. A Bipolar Argumentation Framework considers a support interaction between arguments, besides the attack interaction. As in the Argumentation Framework, some researches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a Bipolar Argumentation Framework under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real application domains there is a need for aggregating probability values from different sources so it is not suitable to aggregate such probability values in a unique probability distribution. To tackle this challenge, we use credal networks theory for modelling the uncertainty of the degree of belief of arguments in a BAF. We also propose an algorithm for calculating the degree of uncertainty of the extensions inferred by a given argumentation semantics. Moreover, we introduce the idea of modelling the support relation as a causal relation. We formally show that the introduced approach is sound and complete w.r.t the credal networks theory.

Bipolar Argumentation Frameworks (BAFs) are an important class of argumentation frameworks useful for capturing, reasoning with, and deriving conclusions from debates. They have the potential to make solid contributions to real-world multi-agent systems and human-agent interaction in domains such as legal reasoning, healthcare and politics. Despite this fact, practical systems implementing BAFs are largely lacking. In this demonstration, we provide a software system implementing novel algorithms for calculating extensions (winning sets of arguments) of BAFs. Participants in the demonstration will be able to input their own debates into our system, and watch a graphical representation of the algorithms as they process information and decide which sets of arguments are winners of the debate.

Argumentation Frameworks (AAFs) and Normal Logic Programs (NLPs) are closely related formalisms for which many equivalences have already been elicited. In this paper, we extend this line of research by considering Bipolar Argumentation Frameworks (BAFs), in which arguments have an explicit support relation, independent of the attack relation. We provide direct translations from BAFs to NLPs (and vice versa) in a one-to-one correspondence between several argumentation and 3-valued logic programming semantics. This includes the equivalence involving L-stable semantics. Besides, we deepen the connection between NLPs and BAFs by finding subsets of them for which the proposed translations are each other’s inverse up to isomorphism.

We develop a method of reasoning using an incrementally constructed bipolar argumentation framework (BAF) aiming to apply computational argumentation to legal reasoning. A BAF that explains the judgment of a certain case is constructed based on the user’s knowledge and recognition. More specifically, a set of effective laws are derived as the conclusions from evidential facts recognized by the user, in a bottom-up manner; conversely, the evidences required to derive a new conclusion are identified if certain conditions are added, in a top-down manner. The BAF is incrementally constructed by repeated exercise of this bidirectional reasoning. The method provides support for those who are not familiar with the law, so that they can understand the judgment process and identify strategies that might allow them to win their case.

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat ABA. We make use of a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). By utilizing compilability theory, we establish that the constructed BAFs will in general be of exponential size. To keep the number of arguments and computational cost low, we present three ways of identifying redundant arguments. Moreover, we identify fragments of ABA which admit a poly-sized instantiation. We propose two algorithmic approaches for reasoning in non-flat ABA; the first utilizes the BAF instantiation while the second works directly without constructing arguments. An empirical evaluation shows that the former outperforms the latter on many instances, reflecting the lower complexity of BAF reasoning. This result is in contrast to flat ABA, where direct approaches dominate instantiation-based solvers.

We develop a system allowing lawyers and law school students to analyze court judgments. We describe a transformation from the logic programming language PROLEG to a bipolar argumentation framework (BAF) and the legal reasoning involved. Legal knowledge written in a PROLEG program is transformed into a BAF, in which the structure of argumentation in a judgment is clear. We describe two types of reasoning by the BAF: clarification of the entire structure and causality of arguments, and identification of the required evidence, and we show its applications on legal reasoning.

In Chap. 4, we proposed a new method of analyzing precedents by introducing the concept of legal topoi to the description of precedents based on factors, and at the same time, we conducted an analysis of 21 precedents on tax law intending to investigate the possibility of predicting judgments and showed that it is possible to observe the trend of judgments in tax law. However, the method in Chap. 4 could not sufficiently verify the logic of the precedents because the relationship between the claims of plaintiffs and defendants and the judgments of judges in the precedents depended on the hierarchical relationship of factors and legal topoi. Therefore, in this chapter, we will use computational argumentation theory to describe the claims of plaintiffs and defendants and the judgments of judges in an argumentation framework for further analysis and logical verification of precedents. Specifically, the bipolar argumentation framework (BAF), which is an extension of the argumentation framework (AF), and the extended argumentation framework (EAF) will be used together to look at the plaintiff and defendant from both sides, and at the same time, the court’s decision will be described and discussed in the form of an EAF.

Bipolar Argumentation Frameworks ($\textit{BAF}$s) extend Dung’s Abstract Argumentation Frameworks ($\textit{AAF}$s) by incorporating an explicit notion of support between arguments. However, there is a price to pay: the semantics for $\textit{BAF}$s often involve more intricate definitions and computational procedures than those for $\textit{AAF}$s. In this paper, we establish a dual relation between defeat and defence. Taking profit from this dual perspective, we define conflict-free sets, acceptability, extension-based and labelling-based semantics as in $\textit{AAF}$s. We also show that our definitions collapse into the corresponding concepts proposed for $\textit{AAF}$s when the support relation is ignored. In particular, we prove the semantics $\beta $-admissible, $\beta $-complete, $\beta $-grounded, $\beta $-preferred, $\beta $-stable and $\beta $-semi-stable defined here for $\textit{BAF}$s are generalisations of the corresponding semantics for $\textit{AAF}$s. Besides generalising $\textit{AAF}$s semantics to $\textit{BAF}$s, our approach also preserves some of their most remarkable results, including Dung’s Fundamental Lemma.

In this thesis, we have introduced new techniques for the problems of open-ended learning, online incremental learning, and explainable learning. These methods have applications in the classification of tabular data, 3D object category recognition, and 3D object parts segmentation. We have utilized argumentation theory and probability theory to develop these methods. The first proposed open-ended online incremental learning approach is Argumentation-Based online incremental Learning (ABL). ABL works with tabular data and can learn with a small number of learning instances using an abstract argumentation framework and bipolar argumentation framework. It has a higher learning speed than state-of-the-art online incremental techniques. However, it has high computational complexity. We have addressed this problem by introducing Accelerated Argumentation-Based Learning (AABL). AABL uses only an abstract argumentation framework and uses two strategies to accelerate the learning process and reduce the complexity. The second proposed open-ended online incremental learning approach is the Local Hierarchical Dirichlet Process (Local-HDP). Local-HDP aims at addressing two problems of open-ended category recognition of 3D objects and segmenting 3D object parts. We have utilized Local-HDP for the task of object part segmentation in combination with AABL to achieve an interpretable model to explain why a certain 3D object belongs to a certain category. The explanations of this model tell a user that a certain object has specific object parts that look like a set of the typical parts of certain categories. Moreover, integrating AABL and Local-HDP leads to a model that can handle a high degree of occlusion.

Bipolar Argumentation Frameworks (BAFs) admit several interpretations of the support relation and diverging definitions of semantics. Recently, several classes of BAFs have been captured as instances of bipolar Assumption-Based Argumentation, a class of Assumption-Based Argumentation (ABA). In this paper, we establish the complexity of bipolar ABA, and consequently of several classes of BAFs. In addition to the standard five complexity problems, we analyse the rarely-addressed extension enumeration problem too. We also advance backtracking-driven algorithms for enumerating extensions of bipolar ABA frameworks, and consequently of BAFs under several interpretations. We prove soundness and completeness of our algorithms, describe their implementation and provide a scalability evaluation. We thus contribute to the study of the as yet uninvestigated complexity problems of (variously interpreted) BAFs as well as of bipolar ABA, and provide the lacking implementations thereof.