Modelling Accrual of Arguments in ASPIC+

We endow Brewka's prioritised default logic (PDL) with argumentation semantics using the ASPIC+M framework for structured argumentation. We prove that the conclusions of the justified arguments correspond to the prioritised default extensions in a normatively rational manner. Argumentation semantics for PDL will allow for the application of argument game proof theories to the process of inference in PDL, making the reasons for accepting a conclusion transparent and the inference process more intuitive. This also opens up the possibility for argumentation-based distributed reasoning and communication amongst agents with PDL representations of mental attitudes.

Scientific research in the formal sciences comes in multiple degrees of formality: fully formal work; rigorous proofs that practitioners know to be formalizable in principle; and informal work like rough proof sketches and considerations about the advantages and disadvantages of various formal systems. This informal work includes informal and semi-formal debates between formal scientists, e.g. about the acceptability of foundational principles and proposed axiomatizations. In this paper, we propose to use the methodology of structured argumentation theory to produce a formal model of such informal and semi-formal debates in the formal sciences. For this purpose, we propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate natural deduction style arguments and explanations. We illustrate the applicability of the framework to debates in the formal sciences by presenting a simple model of some arguments about proposed solutions to the Liar paradox, and by discussing a more extensive—but still preliminary—model of parts of the debate that mathematicians had about the Axiom of Choice in the early twentieth century.

Explainable Artificial Intelligence (XAI) is a research area that clarifies AI decision-making processes to build user trust and promote responsible AI. Hence, a key scientific challenge in XAI is the development of methods that generate transparent and interpretable explanations while maintaining scalability and effectiveness in complex scenarios. Rule-based methods in XAI generate rules that can potentially explain AI inferences, yet they can also become convoluted in large scenarios, hindering their readability and scalability. Moreover, they often lack contrastive explanations, leaving users uncertain why specific predictions are preferred. To address this scientific problem, we explore the integration of computational argumentation—a sub-field of AI that models reasoning processes through defeasibility—into rule-based XAI systems. Computational argumentation enables arguments modelled from rules to be retracted based on new evidence. This makes it a promising approach to enhancing rule-based methods for creating more explainable AI systems. Nonetheless, research on their integration remains limited despite the appealing properties of rule-based systems and computational argumentation. Therefore, this study also addresses the applied challenge of implementing such an integration within practical AI tools. The study employs the Logic Learning Machine (LLM), a specific rule-extraction technique, and presents a modular design that integrates input rules into a structured argumentation framework using state-of-the-art computational argumentation methods. Experiments conducted on binary classification problems using various datasets from the UCI Machine Learning Repository demonstrate the effectiveness of this integration. The LLM technique excelled in producing a manageable number of if-then rules with a small number of premises while maintaining high inferential capacity for all datasets. In turn, argument-based models achieved comparable results to those derived directly from if-then rules, leveraging a concise set of rules and excelling in explainability. In summary, this paper introduces a novel approach for efficiently and automatically generating arguments and their interactions from data, addressing both scientific and applied challenges in advancing the application and deployment of argumentation systems in XAI.

This article deals with general problem of connection between legal reasoning, legal argumentation and, on the other hand, logic. Although this connection seems obvious since ancient times, its nature is still the subject of non-trivial discussions. The purpose of my study is to explore one important aspect of this connection, namely, is general, or formal, logic necessary and sufficient to determine relevant form of legal reasoning and argumentation? To reach this purpose, method of comparative analysis is employed both synchronically and diachronically. First, in order to prove importance of the issue, a diachronic comparison of several basic approaches is carried out (G.W. von Leibniz, O.W. Holmes, Jr., etc.). Then a comparative analysis of the views of some contemporary experts is carried out, especially Ilmar Tammelo and Stephen Toulmin. It is argued, in the field of law there is a special legal validity that differs significantly from the formal-logical validity. The legal validity is determined directly and mainly by the value of the right not by the value of formal or material truth. It is not the subject of formal logic, but of a special legal logic and, more broadly, informal logic. Therefore, formal logic does not determine relevant form of legal reasoning and argumentation, since, first of all, there is the essential difference between the formal-logical validity and the legal validity. It is argued, formal logic is neither sufficient nor necessary to think like a jurist. In this regard, it is shown that the formal-logical standard of proof is not sufficient to determine the relevant form of valid legal proof. There are at least three standards of legal proof – proof without reasonable doubt, proof by clear and convincing evidence, and proof by preponderance of the evidence. Each of them differs significantly from the formal-logical standard. The conclusion of this research is this: it cannot be said that general logic does not work at all in the field of law. However, in order to reason and argue like a successful jurist, one must to grasp and use, without any exceptions, the special legal logic that belongs to the domain of contemporary informal logic.

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.

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.

One of the epistemological results emerging from the present study is that the different forms of correlational inference, known in the Islamic jurisprudence as qiyās, represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical argumentation studied in contemporary philosophy of science.

argumentation frameworks (AFs) are a well-known formalism for modelling and deciding many argumentation problems. Computational issues and evaluation algorithms have been deeply investigated for static AFs, whose structure does not change over the time. However, AFs are often dynamic as a consequence of the fact that argumentation is inherently dynamic. In this paper, we tackle the problem of incrementally computing extensions for dynamic AFs: given an initial extension and an update (or a set of updates), we devise a technique for computing an extension of the updated AF under four well-known semantics (i.e., complete, preferred, stable, and grounded). The idea is to identify a reduced (updated) AF sufficient to compute an extension of the whole AF and use state-of-the-art algorithms to recompute an extension of the reduced AF only. The experiments reveal that, for all semantics considered and using different solvers, the incremental technique is on average two orders of magnitude faster than computing the semantics from scratch.

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.

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.

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.

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.

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.

Several techniques for improving web search have been developed over the last years. Most existing approaches are still limited, mainly due to the absence of qualitative criteria for ranking results and insensitivity to user preferences for guiding the search. At the same time, defeasible argumentation evolved as a successful approach in AI to model commonsense qualitative reasoning with applications in many areas, such as agent theory, knowledge engineering and legal reasoning. This paper presents ARGUENET, a recommender system that classifies search results according to preference criteria declaratively specified by the user. The proposed approach integrates a traditional web search engine with a defeasible argumentation framework.

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.