Structured argumentation dynamics: Undermining attacks in default justification logic

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks

A logic of defeasible argumentation: Constructing arguments in justification logic

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t:F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as arguments and their acceptance semantics is given in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that (1) Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and (2) Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories

SCC-recursiveness: a general schema for argumentation semantics

AbstractIn argumentation theory, Dung's abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-recursiveness and we show that all Dung's admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dung's preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects

Evaluating the Impact of Defeasible Argumentation as a Modelling Technique for Reasoning under Uncertainty

Limited work exists for the comparison across distinct knowledge-based approaches in Artificial Intelligence (AI) for non-monotonic reasoning, and in particular for the examination of their inferential and explanatory capacity. Non-monotonicity, or defeasibility, allows the retraction of a conclusion in the light of new information. It is a similar pattern to human reasoning, which draws conclusions in the absence of information, but allows them to be corrected once new pieces of evidence arise. Thus, this thesis focuses on a comparison of three approaches in AI for implementation of non-monotonic reasoning models of inference, namely: expert systems, fuzzy reasoning and defeasible argumentation. Three applications from the fields of decision-making in healthcare and knowledge representation and reasoning were selected from real-world contexts for evaluation: human mental workload modelling, computational trust modelling, and mortality occurrence modelling with biomarkers. The link between these applications comes from their presumptively non-monotonic nature. They present incomplete, ambiguous and retractable pieces of evidence. Hence, reasoning applied to them is likely suitable for being modelled by non-monotonic reasoning systems. An experiment was performed by exploiting six deductive knowledge bases produced with the aid of domain experts. These were coded into models built upon the selected reasoning approaches and were subsequently elicited with real-world data. The numerical inferences produced by these models were analysed according to common metrics of evaluation for each field of application. For the examination of explanatory capacity, properties such as understandability, extensibility, and post-hoc interpretability were meticulously described and qualitatively compared. Findings suggest that the variance of the inferences produced by expert systems and fuzzy reasoning models was higher, highlighting poor stability. In contrast, the variance of argument-based models was lower, showing a superior stability of its inferences across different system configurations. In addition, when compared in a context with large amounts of conflicting information, defeasible argumentation exhibited a stronger potential for conflict resolution, while presenting robust inferences. An in-depth discussion of the explanatory capacity showed how defeasible argumentation can lead to the construction of non-monotonic models with appealing properties of explainability, compared to those built with expert systems and fuzzy reasoning. The originality of this research lies in the quantification of the impact of defeasible argumentation. It illustrates the construction of an extensive number of non-monotonic reasoning models through a modular design. In addition, it exemplifies how these models can be exploited for performing non-monotonic reasoning and producing quantitative inferences in real-world applications. It contributes to the field of non-monotonic reasoning by situating defeasible argumentation among similar approaches through a novel empirical comparison

Graph Models for Rational Social Interaction

A fundamental issue in multi-agent systems is to extract a consensus from a group of agents with different perspectives. Even if the bilateral relationships (reflecting the outcomes of disputes, product comparisons, or evaluation of political candidates) are rational, the collective output may be irrational (e.g., intransitivity of group preferences). This motivates AI’s research for devising social outcomes compatible with individual positions. Frequently, such situations are modeled as graphs. While the preponderance of formal theoretical studies of such graph based-models has addressed semantic concerns for defining a desirable output in order to formalize some high-level intuition, results relating to algorithmic and computational complexity are also of great significance from the computational point of view. The first Part of this thesis is devoted to combinatorial aspects of Argumentation Frameworks related to computational issues. These abstract frameworks, introduced by Dung in 1995, are directed graphs with nodes interpreted as arguments and the directed edges as attacks between the arguments. By designing a conflict-resolution formalism to make distinction among acceptable and unacceptable arguments, Dung initiated an important area of research in Artificial Intelligence. I prove that any argumentation framework can be syntactically augmented into a normal form preserving the semantic properties of the original arguments, by using a cubic time rewriting technique. I introduce polyhedral labellings for an argumentation frameworks, which is a polytope with the property that its integral points are exactly the incidence vectors of specific types of Dung’s outcome. Also, a new notion of acceptability of arguments is considered – deliberative acceptability – and I provide it’s time computational complexity analysis. This part extends and improves some of the results from the my Master thesis. In the second Part, I introduce a novel graph-based model for aggregating preferences. By using graph operations to describe properties of the aggregators, axiomatic characterizations of aggregators corresponding to usual majority or approval & disapproval rule are given. Integrating Dung’s semantics into our model provides a novel qualitative approach to classical social choice: argumentative aggregation of individual preferences. Also, a functional framework abstracting many-to-many two-sided markets is considered: the study of the existence of a Stable Choice Matching in a Bipartite Choice System is reduced to the study of the existence of Stable Common Fixed Points of two choice functions. A generalization of the Gale-Shapley algorithm is designed and, in order to prove its correctness, a new characterization of path independence choice functions is given. Finally, in the third Part, we extend Dung’s Argumentation Frameworks to Opposition Frameworks, reducing the gap between Structured and Abstract Argumentation. A guarded attack calculus is developed, giving proper generalizations of Dung’s extensions.Ein grundlegendes Problem von Multiagentensystemen ist, eine Gruppe von Agenten mit unterschiedlichen Perspektiven zum Konsens zu bringen.W¨ahrend die bilaterale Ergebnisse von Rechtsstreitigkeiten, Produktvergleichen sowie die Bewertung von politischen Kandidaten wiederspiegelnden Beziehungen rational sein sollten, k¨onnte der kollektive Ausgang irrational sein z.B. durch die Intransitivit¨at von Pr¨aferenzen der Gruppe. Das motiviert die KI-Forschung zur Entwicklung von sozialen Ergebnissen, welche mit individuellen Einstellungen kompatibel sind. H¨aufig werden solche Situationen als Graphen modelliert. W¨ahrend die meisten formalen theoretischen Studien von Graphmodellen sich mit semantischen Aspekten f¨ur die Definition eines w¨unschenswerten Ausgangs zur Formalisierung auf hohem Intuitionsniveau besch¨aftigen, ist es ebenfalls von großer Bedeutung, die Komplexit¨at von Algorithmen und Berechnungen zu verstehen. Der erste Teil der vorliegenden Arbeit widmet sich den kombinatorischen Aspekten von Argumentation Frameworks im Zusammenhang mit rechnerischen Fragen. Diese von Dung in 1995 eingef ¨uhrten abstrakten Frameworks sind gerichtete Graphen mit als Argumenten zu interpretierenden Knoten, wobei die gerichteten Kanten Angriffe zwischen den Argumenten sind. Somit hat Dung mit seiner Gestaltung eines Konfliktl¨osungsformalismus zur Unterscheidung zwischen akzeptablen und inakzeptablen Argumenten f¨ur einen wichtigen Bereich von Forschung in KI den Grundstein gelegt. Die Verfasserin hat bewiesen, dass jedes Argumentation Framework sich in einer die semantischen Eigenschaften der originalen Argumente bewahrenden normalen Form syntaktisch erweitern l¨asst, indem man eine mit kubischer Laufzeit umwandelnde Technik verwendet. Neu eingef¨urt werden hier Polyhedrische Etiketten f¨ur Argumentation Frameworks. Dabei handelt es sich um einen Polytop, wessen ganze Punkte genau die Inzidenzvektoren von bestimmten Arten von Dungs Ausgabe sind. Weiterhin wird ein neuer Begriff der Akzeptanz von Argumenten gepr¨agt, n¨amlich - deliberative Akzeptanz - und dessen Komplexit¨at analysiert. Dieser Teil erweitert und verfeinert einige ihrer Ergebnisse aus der Masterarbeit. Im zweiten Teil wurde ein neuartiges graphenbasiertes Modell f¨ur die Aggregation von Pr¨aferenzen erarbeitet. Hier werden axiomatische Charakterisierungen von Aggregatoren neu eingef¨uhrt, und zwar durch die Verwendung von Graphoperationen zur Beschreibung der Eigenschaften von Aggregatoren. Sie entsprechen dem ¨ublichen Mehrheitsprinzip bzw. der Genehmigungs- & Ablehnungsregel. Einen neuartigen, qualitativen Ansatz im Vergleich zu der klassischen Sozialwahltheorie bietet die Integration der Semantik von Dung in dem neuen Modell, und zwar argumentative Aggregation individueller Pr¨aferenzen. Desweiteren wird ein funktionales many to many zweiseitige M¨arkte abstrahierendes Framework untersucht, indem statt die Existenz einer Stabilen Wahl Matching in einem Bipartite Wahlsystem zu studieren, wird die Existenz von Stable Common Fixed Points auf zwei Wahlfunktionen erforscht. Im n¨achsten Schritt wird eine neue Verallgemeinerung des Gale-Shapley Algorithmus entworfen und eine neue Charakterisierung der Wegunabh¨angigkeitsfunktion gegeben, die einen Korrektheitsbeweis f¨ur den Algorithmus erm¨oglicht. Im dritten Teil werden schließlich Dungs Argumentation Frameworks auf Opposition Frameworks erweitert und dadurch die in der gegenw¨artigen Forschung bestehende L¨ucke zwischen strukturierter und abstrakter Argumentation verringert. Daf¨ur wird ein bewachter Angriffskalk¨ul entwickelt, welches strikten Verallgemeinerungen von Dungs echten Erweiterungen f¨uhrt