Deciding the Winner of a Debate Using Bipolar Argumentation

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.

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.

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.

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.

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.

Much work using argumentation frameworks (AFs) treats arguments as entirely abstract, related by a uniform attack relation that always succeeds unless the attacker can itself be defeated. However, this does not seem adequate for legal argumentation. Some proposals have suggested regulating attack relations using preferences or values on arguments and that filter the attack relation, so that, depending on the audience addressed, some attacks fail and so can be removed from the framework. This does not, however, capture a central feature of legal reasoning: how a decision with respect to the same facts and legal reasoning varies as the judicial context varies. Nor does it capture related context-dependent features of legal reasoning, such as how an audience can prefer or value an argument, yet be constrained by precedent or authority not to accept it. Nor does it explain how certain types of attack may not be allowed in a particular procedural context. For this reason, evaluation of the status of arguments within a given framework must be allowed to depend not only on the attack relations along with the preference or value of arguments, but also on the nature of the attacks and the context in which they are made. We present a means to represent these features, enabling us to account for a number of factors currently considered to be beyond the remit of formal AFs. We give several examples of the use of approach including: appealing a case, overruling a precedent and rehearing of a case as a civil rather than criminal proceeding.

In this paper a new formal model of argument accrual is proposed as an adaptation of the ASPIC+ framework for structured argumentation. The new model aims to overcome several weaknesses of existing proposals. It is shown to have desirable formal properties that are in line with standard work on formal argumentation, and to be applicable to a range of situations in legal reasoning.

We introduce Forecasting Argumentation Frameworks (FAFs), a novel argumentation-based methodology for forecasting informed by recent judgmental forecasting research. FAFs comprise update frameworks which empower (human or artificial) agents to argue over time about the probability of outcomes, e.g. the winner of an election or a fluctuation in inflation rates, whilst flagging perceived irrationality in the agents' behaviour with a view to improving their forecasting accuracy. FAFs include five argument types, amounting to standard pro/con arguments, as in bipolar argumentation, as well as novel proposal arguments and increase/decrease amendment arguments. We adapt an existing gradual semantics for bipolar argumentation to determine the aggregated dialectical strength of proposal arguments and define irrational behaviour. We then give a simple aggregation function which produces a final group forecast from rational agents' individual forecasts. We identify and study properties of FAFs, and conduct an empirical evaluation which signals FAFs' potential to increase the forecasting accuracy of participants.

Different agents may have different points of view. This can be modelled using different abstract argumentation frameworks, each consisting of a set of arguments 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. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to come up in a multiagent system.

This paper investigates the practical reasoning involved in compliance-related decisions, distinguishing between two scenarios where a state of affairs is evaluated in the light of applicable norms: ex post compliance checking and ex ante compliance choices. While the literature in legal reasoning representation is exclusively focused on compliance checking scenarios, i.e., simulating a digital judge, different factors seem to play a role in the inner deliberation of compliance choices. In this paper we investigate how human agents are influenced in their compliance choices by their own value ranking and risk assessment and how, in turn, the choice affects their preference among alternative interpretations of the law. We contend that contributions from the literature such as the value-based argumentation framework, while focused on ex post judgments, may be able to provide a comprehensive framework for ex ante compliance decisions. The main goal of the research behind this work is to achieve a comprehensive representation of legal reasoning that can be used as a reference for the explanation of automated compliance decisions.

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.

In the last few years, argumentation frameworks have been successfully applied to multi agent systems. Recently, argumentation has been used to provide a framework for reasoning about coalition formation. At the same time alternating-time temporal logic has been used to reason about the behavior and abilities of coalitions of agents. However, ATL operators account only for the existence of successful strategies of coalitions. They do not consider whether coalitions can be actually formed.This paper is an attempt to combine both frameworks and to develop a logic through which we can reason at the same time (1) about abilities of coalitions of agents and (2) about the formation of coalitions. We provide a formal extension of ATL, ATLc, in which the actual computation of the coalition is modelled in terms of argumentation semantics. We show that ATLc's proof theory can be understood as a natural extension of the model checking procedure used in ATL.

Incorporating coalition formation algorithms into agent systems shall be advantageous due to the consequent increase in the overall quality of task performance. Coalition formation was addressed in game theory, however the game theoretic approach is centralized and computationally intractable. Recent work in DAI has resulted in distributed algorithms with computational tractability. This paper addresses the implementation of distributed coalition formation algorithms within a real-world multi-agent system. We present the problems that arise when attempting to utilize the theoretical coalition formation algorithms for a real-world system, demonstrate how some of their restrictive assumptions can be relaxed, and discuss the resulting benefits. In addition, we analyze the modifications, the complexity and the quality of the cooperation mechanisms. The task domain of our multi-agent system is information gathering, filtering and decision support within the WWW.

Since the seminal work of Dung, Argumentation Frameworks have been shown to find solutions to n-person cooperative games. In multi-agent systems, decentralised methods for multi-agent system coalition structure generation have been proposed. This paper offers the first dialogue game that utilises argumentation frameworks to find a coalition structure and a payoff vector in a decentralised manner. The payoff vector found is in the core set of stable solutions if the core is non-empty. This dialogue game also puts restrictions on the payoff vectors that can be proposed so that the most unfair ones are discarded. Lastly an algorithm is described that allows the agents to find out if the core is empty.