On a Notion of Monotonic Support for 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.

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 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.

In this paper, we analyse properties of aggregation-based extensions of fuzzy measures depending on properties of aggregation functions which they are based on. We mainly focus on properties possessed by the well-known Lovász and Owen extensions. Moreover, we characterize aggregation functions suitable for extension of particular subclasses of fuzzy measures.

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.

This paper proposes a distributed coordination algorithm for robotic sensor networks to detect boundaries that separate areas of abrupt change of spatial phenomena. We consider an aggregate objective function, termed wombliness, that measures the change of the spatial field along the closed polygonal curve defined by the location of the sensors in the environment. We encode the network task as the optimization of the wombliness and characterize the smoothness properties of the objective function. In general, the complexity of the spatial phenomena makes the gradient flow cause self-intersections in the polygonal curve described by the network. Therefore, we design a distributed coordination algorithm that allows for network splitting and merging while guaranteeing the monotonic evolution of wombliness. The technical approach combines ideas from statistical estimation, dynamical systems, and hybrid modeling and design.

The field of explainable AI has grown exponentially in recent years. Within this landscape, argumentation frameworks have shown to be helpful abstractions of some AI models towards providing explanations thereof. While existing work on argumentative explanations and their properties has focused on static settings, we focus on dynamic settings whereby the (AI models underpinning the) argumentation frameworks need to change. Specifically, for a number of notions of explanations drawn from abstract argumentation frameworks under extension-based semantics, we address the following questions: (1) Are explanations robust to extension-preserving changes, in the sense that they are still valid when the changes do not modify the extensions? (2) If not, are these explanations pseudo-robust in that can be tractably updated? In this paper, we frame these questions formally. We consider robustness and pseudo-robustness w.r.t. ordinary and strong equivalence and provide several results for various extension-based semantics.

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.

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.

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.

Overlap function is a special type of aggregation function which measures the degree of overlapping between different classes. Recently, complex fuzzy sets have been successfully applied in many applications. In this paper, we extend the concept of overlap functions to the complex-valued setting. We introduce the notions of complex-valued overlap, complex-valued 0-overlap, complex-valued 1-overlap, and general complex-valued overlap functions, which can be regarded as the generalizations of the concepts of overlap, 0-overlap, 1-overlap, and general overlap functions, respectively. We study some properties of these complex-valued overlap functions and their construction methods.

In this paper, we present a construction method for fuzzy implication functions based on F-chains. Using this method, which comes from the theory of aggregation functions, one can construct from any given fuzzy implication function a new one. We discuss some properties of fuzzy implication functions which are preserved by this construction, and also provide several examples. Moreover, we introduce for fuzzy implication functions ordinal sums based on F-chains in the case of a single fuzzy implication function as well as in the case of n fuzzy implication functions.

The overlap function, a continuous aggregation function, is widely used in classification, decision-making, image processing, etc. Compared to applications, overlap functions have also achieved fruitful results in theory, such as studies on the fundamental properties of overlap functions, various generalizations of the concept of overlap functions, and the construction of additive and multiplicative generators based on overlap functions. However, most of the research studies on the overlap functions mentioned above contain commutativity and continuity, which can limit their practical applications. In this paper, we remove the symmetry and continuity from overlap functions and define discrete pseudo-quasi overlap functions on finite chains. Meanwhile, we also discuss their related properties. Then, we introduce pseudo-quasi overlap functions on sub-chains and construct discrete pseudo-quasi overlap functions on finite chains using pseudo-quasi overlap functions on these sub-chain functions. Unlike quasi-overlap functions on finite chains generated by the ordinal sum, discrete pseudo-quasi overlap functions on finite chains constructed through pseudo-quasi overlap functions on different sub-chains are dissimilar. Eventually, we remove the continuity from pseudo-automorphisms and propose the concept of pseudo-quasi-automorphisms. Based on this, we utilize pseudo-overlap functions, pseudo-quasi-automorphisms, and integral functions to obtain discrete pseudo-quasi overlap functions on finite chains, moreover, we apply them to fuzzy multi-attribute group decision-making. The results indicate that compared to overlap functions and pseudo-overlap functions, discrete pseudo-quasi overlap functions on finite chains have stronger flexibility and a wider range of practical applications.