Argumentation Frameworks Induced by Assumption-based Argumentation: Relating Size and Complexity

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.

Computational argumentation is primed to strengthen the current hot research field of Explainable Artificial Intelligence (XAI), e.g., by dialectical approaches. In this paper, we extend and discuss a recently proposed approach of so-called strong acceptance on abstract argumentation that aims to support explaining argumentative acceptance. Our goal is to push these results into the realm of structured argumentation. In this setting, a knowledge base induces an abstract argumentation framework (AF) via instantiation. We investigate how and under which conditions it is possible to transfer results regarding strong acceptance between the given knowledge base and the induced AF. To this end we consider generic functions formalizing the interaction of the AF and the knowledge base. This approach helps us to infer rather general results making basic assumptions rather than dealing with the technical details of several structured argumentation formalisms. Along the way, we apply our techniques to the concrete approach of assumption-based argumentation (ABA) which constitutes one of the primal structured argumentation formalisms.

Assumption-based argumentation can serve as an effective computational tool for argumentation-based epistemic and practical reasoning, as required in a number of applications. In this paper we substantiate this claim by presenting formal mappings from frameworks for epistemic and practical reasoning onto assumption-based argumentation frameworks. We also correlate these mappings to formulations of epistemic and practical reasoning in abstract argumentation terms.KeywordsPractical ReasoningInference RuleLogic ProgrammingDeductive SystemStrict RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Conflicts exist in multi-agent systems for a number of reasons: agents have different interests and desires; agents hold different beliefs; agents make different assumptions. To resolve conflicts, agents need to better convey information to each other and facilitate fair negotiations yielding jointly agreeable outcomes. We present a two-agent, dialogical conflict resolution scheme developed with the Assumption-Based Argumentation (ABA) framework.

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 has gained traction as a formalism to make more transparent decisions and provide formal explanations recently. In this paper, we present an argumentation-based approach to decision making that can support modelling and automated reasoning about complex qualitative preferences and offer dialogical explanations for the decisions made. We first propose Qualitative Preference Decision Frameworks (QPDFs). In a QPDF, we use contextual priority to represent the relative importance of combinations of goals in different contexts and define associated strategies for deriving decision preferences based on prioritized goal combinations. To automate the decision computation, we map QPDFs to Assumption-based Argumentation (ABA) frameworks so that we can utilize existing ABA argumentative engines for our implementation. We implemented our approach for two tasks, diagnostics and prognostics of Alzheimer's Disease (AD), and evaluated it with real-world datasets. For each task, one of our models achieves the highest accuracy and good precision and recall for all classes compared to common machine learning models. Moreover, we study how to formalize argumentation dialogues that give contrastive, focused and selected explanations for the most preferred decisions selected in given contexts.

The existing approaches which map the given explicit preferences into standard assumption-based argumentation frameworks (ABAs) reveal some difficulties such as generating a huge number of rules and so on. To overcome them, we present an assumption-based argumentation framework equipped with preferences (p_ABA). It increases the expressive power of ABA by incorporating preferences between sentences into the framework. The semantics of p_ABAs is given by \(\mathcal{P}\) extensions selected from extensions of ABAs based on the given sentence ordering. The advantages of our approach are that not only it enables us to express different kinds of preferences such as preferences over rules, over goals, over decisions by means of sentence orderings in p_ABAs but we also successfully obtain solutions from \(\mathcal{P}\) extensions of the p_ABAs expressing the respective knowledge for various applications such as epistemic reasoning, practical reasoning, decision-making with preferences and so on in a uniform way without suffering from difficulties of existing ones.

We give some design guidelines for argumentation systems. These guidelines are meant to indicate essential features of argumentation when used to support “practical reasoning”. We express the guidelines in terms of postulates. We use a notion of redundancy to provide a formal counterpart of these postulates. We study the satisfaction of these postulates in two existing argumentation frameworks: assumption-based argumentation and argumentation in classical logic.

Home networks are a fast growing market but managing them is a difficult task, and diagnosing faults is even more challenging. Current fault management tools provide comprehensive information about the network and the devices but it is left to the user to interpret and reason about the data and experiment in order to find the cause of a problem. Home users may not have motivation or time to learn the required skills. Furthermore current tools adopt a closed approach which hardcodes a knowledge base, making them hard to update and extend. This paper proposes an open fault management framework for home networks, whose goal is to simplify network troubleshooting for non-expert users. The framework is based on assumption-based argumentation that is an AI technique for knowledge representation and reasoning. With the underlying argumentation theory, we can easily capture and model the diagnosis procedures of network administrators. The framework is rule-based and extensible, allowing new rules to be added into the knowledge base and diagnostic strategies to be updated on the fly.The framework can also utilise external knowledge and make distributed diagnosis.

We briefly discuss and compare two frameworks for reasoning with inconsistent belief bases: argumentation systems, based on the construction and selection of acceptable arguments in favor of a conclusion, and syntax-based approaches to non-monotonic entailment, based on the selection of preferred consistent subbases. In the case of a flat belief base (i.e. without any priority between its elements), we show that most of the argument-based inference relations can be exactly restated in the framework of syntax-based entailment. Then, taking advantage of the modelling of prioritized syntax-based entailment, we propose a methodological approach to the integration of preference orderings in argumentation frameworks.

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

Argumentative reasoning and taxonomic analysis for the identification of medical errors

An abstract framework for structured arguments is presented, which instantiates Dung's (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games’, Artificial Intelligence, 77, 321–357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog.

This study highlights the computer-mediated discursive activity of two dyads of first year educational sciences students, each collaboratively exploring several options for increasing the equilibrium size of a fish population in a lake. Our focus is on peers' attempts to come up with justified predictions about the adequacy of several options for maintaining a larger fish population, as well as on their attempts to refine or radically reconsider these theoretical predictions in the light of empirical data provided by software simulations. Thus, this paper is particularly concerned with the construction of arguments on the level of the argumentative (i.e. claims, justifications, challenges) and epistemic operations (i.e. recognising assumptions, appealing to limiting factors) and the contribution of the software simulations in this process. According to the analysis of peers' discourse, both dyads seem to be engaged in the construction of directly justified theoretical predictions by activating several epistemic tools, while only one seems to reach the target concept of carrying capacity. Significant differences may be identified in regard with the two dyads' interest as well as capability in using the simula-tions as a meaningful feedback upon their initial arguments. Implications of students' tendency to transfer the sterile culture of ‘doing school’ into problem-based collaborative learning environments, as well as of their difficulties on both the conceptual level and the level of meaningfully integrating the software simulations in their argumentative reasoning, are discussed.

The field of Computational Argumentation is well-tailored to approach commonsense reasoning, due to its ability to model contradictory information. In this paper, we present preliminary work on how an argumentation framework can explicitly model commonsense knowledge, both at a logically structured and at an abstract level. We discuss the correlation with current research and present interesting future directions.