Incomplete Bipolar Argumentation Frameworks

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.

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.

The bipolar argumentation framework (BAF) setting is an extension of Dung’s setting for abstract argumentation, that considers an additional relation, called support relation. Several interpretations of such a support relation have been pointed out so far, including deductive, necessity, general and backing supports. These notions of support capture different kinds of interactions between arguments, that do not primarily correspond to attacks. In this paper, we propose a new notion of support, called monotonic support. Our approach is axiomatic: two postulates are introduced for capturing the intuition that underlies this notion of support in formal terms. The first postulate, monotony, prevents the support relation from downgrading the acceptance status of the supported argument. The second postulate, non-triviality, requires the existence of BAFs for which supporting an argument leads to increase its acceptance status. We present a general family of extension-based semantics for BAFs, called support score-based (SSB) semantics, that satisfy the two postulates and are parameterized by some aggregation functions. We prove a characterisation result linking the postulates that a SBB semantics satisfies with the properties of the aggregation functions used to define it. We also show that none of the previously introduced semantics for BAFs satisfies the monotony postulate.

We introduce a novel method to aggregate Bipolar Argumentation (BA) Frameworks expressing opinions by different parties in debates. We use Bipolar Assumption-based Argumentation (ABA) as an all-encompassing formalism for BA under different semantics. By leveraging on recent results on judgement aggregation in Social Choice Theory, we prove several preservation results, both positive and negative, for relevant properties of Bipolar ABA.

Argumentation frameworks have been widely studied both in terms of formal properties they exhibit under different semantics and in terms of applications they can support. But where are argumentation frameworks coming from, and how can argumentation, a model-based approach to AI, beneficially integrate with the nowadays-much-widespread data-centric AI perspective? In this talk I will overview applications empowered by a variety of (extension-based and gradual) semantics for abstract and bipolar argumentation frameworks automatically obtained from data (including but not limited to text) and from logical rules. Some of these applications require the integration of argumentation and machine learning, and result in a mixed model-based and data-centric pipeline. For some applications, the semantics informs the definition of the frameworks rather than, as is conventionally the case, being enforced on frameworks a posteriori.

In this paper, we extend the abstract argumentation framework proposed by [1] in order to take into account two kinds of interaction between arguments: a positive interaction (an argument can help, support another argument) and a negative interaction (an argument can attack another argument). In this new abstract argumentation framework, called a bipolar argumentation framework, we propose a gradual interaction-based valuation process. With this process, the value of each argument A only depends on the value of the arguments which are directly interacting with A in the argumentation system.

argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.

Verification in incomplete argumentation frameworks

In the symbolic artificial intelligence community, abstract argumentation with its semantics, i.e. approaches for defining sets of valid conclusions (extensions) that can be derived from argumentation graphs, is considered a promising method for non-monotonic reasoning. However, from a sequential perspective, abstract argumentation-based decision-making processes typically do not guarantee an alignment with common formal notions to assess consistency; in particular, abstract argumentation can, in itself, not enforce the satisfaction of relational principles such as reference independence (based on a key principle of microeconomic theory) and cautious monotony. In this paper, we address this issue by introducing different approaches to ensuring reference independence and cautious monotony in sequential argumentation: a reductionist, an expansionist, and an extension-selecting approach. The first two approaches are generically applicable, but may require comprehensive changes to the corresponding argumentation framework. In contrast, the latter approach guarantees that an extension of the corresponding argumentation framework can be selected to satisfy the relational principle by requiring that the used argumentation semantics is weakly reference independent or weakly cautiously monotonous, respectively, and also satisfies some additional straightforward principles. To highlight the relevance of the approach, we illustrate how the extension-selecting approach to reference independent argumentation can be applied to model (boundedly) rational economic decision-making.

Control argumentation frameworks (CAFs) [4] extend the standard model of argumentation framework (AF) due to Dung [6] in a way that takes unquantified uncertainty regarding arguments and attacks into account. Complementing recent work by Skiba et al. [21] for incomplete argumentation frameworks, we study the (nonempty) existence problem for CAFs and fully analyze its computational complexity for the most common semantics.

We propose natural generalizations of the credulous and skeptical acceptance problems in abstract argumentation for incomplete argumentation frameworks [3]. This continues earlier work on a similar generalization of the verification problem. We provide a full analysis of the computational complexity of the generalized problems for all original semantics, showing that, in almost all cases, acceptance problems for incomplete argumentation frameworks are significantly harder than the respective problems for argumentation frameworks without uncertainty. All our hardness results for the classes NP, coNP, Πp2, and Σp2

A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted conditional knowledge base. This semantics, in its different variants, suggests some gradual argumentation semantics, which are related to the family of the gradual semantics studied by Amgoud and Doder. The relationships between weighted conditional knowledge bases and MLPs extend to the proposed gradual semantics to capture the stationary states of MPs, in agreement with previous results on the relationship between argumentation frameworks and neural networks. The paper also suggests a simple way to extend the proposed semantics to deal attacks/supports by a boolean combination of arguments, based on the fuzzy semantics of weighted conditionals, as well as an approach for defeasible reasoning over a weighted argumentation graph, building on the proposed gradual semantics.

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

This chapter discusses the nuclear arms race in terms of its technological aspects and its political implications. It explains biological and chemical weapons, theory of conflict and some regional case studies. Weapons and strategy interact because it is the quality of nuclear weapons that determines their strategic uses, while at the same time strategic thinking may be an important factor in weapon developments. There is ample evidence that at present the nuclear arms race is strongly technologically determined. The general problems of nuclear armament and arms control were introduced from different perspectives of academic disciplines and diplomatic practice. But most participants were agreed that nuclear weapons have had a deep impact on the practice and theory of international politics. An issue that come up in most discussions on conventional, biological, chemical, and nuclear disarmament is the problem of verification. International politics being basically anarchic, planned general and complete disarmament is impossible.

This paper presents a formal approach to explaining change of inference in Quantitative Bipolar Argumentation Frameworks (QBAFs). When drawing conclusions from a QBAF and updating the QBAF to then again draw conclusions (and so on), our approach traces changes – which we call strength inconsistencies – in the partial order over argument strengths that a semantics establishes on some arguments of interest, called topic arguments. We trace the causes of strength inconsistencies to specific arguments, which then serve as explanations. We identify sufficient, necessary, and counterfactual explanations for strength inconsistencies and show that strength inconsistency explanations exist if and only if an update leads to strength inconsistency. We define a heuristic-based approach to facilitate the search for strength inconsistency explanations, for which we also provide an implementation.