To resolve conflicts among norms, various nonmonotonic formalisms can be used to perform prioritized normative reasoning. Meanwhile, formal argumentation provides a way to represent nonmonotonic logics. In this paper, we propose a representation of prioritized normative reasoning by argumentation. Using hierarchical abstract normative systems, we define three kinds of prioritized normative reasoning approaches, called Greedy, Reduction, and Optimization. Then, after formulating an argumentation theory for a hierarchical abstract normative system, we show that for a totally ordered hierarchical abstract normative system, Greedy and Reduction can be represented in argumentation by applying the weakest link and the last link principles respectively, and Optimization can be represented by introducing additional defeats capturing the idea that for each argument that contains a norm not belonging to the maximal obeyable set then this argument should be rejected.
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using interactive and automated reasoning tools. This enables the formal analysis and verification of meta-theoretical properties as well as the flexible generation of extensions and labellings with respect to well-known argumentation semantics.
Edinburgh Law School, University of Edinburgh（爱丁堡大学法学院）
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal ontologies, the current paper presents a structured argumentation framework particularly for reasoning in legal contexts on the basis of ASPIC+, and translates the legal ontology into formulas and rules of an argumentation theory. With a particular focus on the design of autonomous vehicles from the perspective of legal AI, we show that using this combined th…
Labelling-based formal argumentation relies on labelling functions that typically assign one of 3 labels to indicate either acceptance, rejection, or else undecided-to-be-either, to each argument. While a classical labelling-based approach applies globally uniform conditions as to how an argument is to be labelled, they can be determined more locally per argument. Abstract dialectical frameworks (ADF) is a well-known argumentation formalism that belongs to this category, offering a greater labelling flexibility. As the size of an argumentation increases in the numbers of arguments and argument…
University of Brescia（布雷西亚大学）；University of Liverpool（利物浦大学）
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack b…
Facets in Argumentation: A Formal Approach to Argument Significance
Department of Computer and Information Science, Linköping University, Sweden（林雪平大学计算机与信息科学系）；Leibniz Universität Hannover, Germany（汉诺威莱布尼茨大学）；Univ. Artois, CNRS, France（阿诺伊大学）；CSAIL, Massachusetts Institute of Technology, USA（麻省理工学院计算机科学与人工智能实验室）；DICE group, Paderborn University, Germany（波德生大学DICE小组）
Abstract Persuasion Argumentation (APA) is a dynamic argumentation formalism that extends Dung argumentation with persuasion relations. In this work, we show through two-counter Minsky machine encoding that APA dynamics is Turing-complete.
Imperial College London（伦敦帝国理工学院）；National Institute of Informatics（国立信息学研究所）
Automatically reasoning with conflicting generic clinical guidelines is a burning issue in patient-centric medical reasoning where patient-specific conditions and goals need to be taken into account. It is even more challenging in the presence of preferences such as patient's wishes and clinician's priorities over goals. We advance a structured argumentation formalism for reasoning with conflicting clinical guidelines, patient-specific information and preferences. Our formalism integrates assumption-based reasoning and goal-driven selection among reasoning outcomes. Specifically, we assume app…
Imperial College London（帝国理工学院）；Université d’Evry（埃夫里大学）
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of actions towards resolving it. In this paper, we develop a methodology to verify debates formalised as abstract argumentation frameworks. We first present a translation from debates to transition systems. Such transition systems can model debates and represent their evolution over time using a finite set of states. We then formalise relevant debate properties usi…
University of Brescia（布雷西亚大学）；Cardiff University（卡迪夫大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；Amazon（亚马逊）
The sixth assessment of the international panel on climate change (IPCC) states that "cumulative net CO2 emissions over the last decade (2010-2019) are about the same size as the 11 remaining carbon budget likely to limit warming to 1.5C (medium confidence)." Such reports directly feed the public discourse, but nuances such as the degree of belief and of confidence are often lost. In this paper, we propose a formal account for allowing such degrees of belief and the associated confidence to be used to label arguments in abstract argumentation settings. Differently from other proposals in proba…
In this paper, we discuss necessary and sufficient explanations for formal argumentation - the question whether and why a certain argument can be accepted (or not) under various extension-based semantics. Given a framework with which explanations for argumentation-based conclusions can be derived, we study necessity and sufficiency: what (sets of) arguments are necessary or sufficient for the (non-)acceptance of an argument?
University of Groningen（格罗宁根大学）；King's College London（伦敦国王学院）
The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they…
我们扩展了结构化论证的$ASPIC^+$框架，以便允许应用的情况下，推理方案的可废止的参数。给定一个带有结论“$A$ or $B$”的论证，一个基于$A$带有结论$C$的论证，以及一个基于$B$带有结论$C$的论证，我们允许构造一个带有结论$C$的论证。我们展示了我们的框架如何导致不同的结果比其他方法在非单调逻辑处理析取信息，如析取默认理论或方法的基础上的OR规则（允许导出一个可废止的规则“如果（$A$或$B$），然后$C$”，给出两个可废止的规则“如果$A$，然后$C$”和“如果$B$，然后$C$”）。我们提出了新的问题，推理的微妙之处defeably与析取信息，并表明其形式化是更复杂的比一个人会假设。
Universität Leipzig（莱比锡大学）；TU Dresden（德累斯顿工业大学）；TU Wien（维也纳工业大学）
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labelled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this pa…
Abstract argumentation has emerged as a method for non-monotonic reasoning that has gained popularity in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined over the years are typically evaluated from a formal logics perspective; an analysis that is based on models of economically rational decision-making does not exist. In this paper, we work towards addressing this issue by analyzing abstract argumentation from the perspective of the rational man paradigm in microeconomic theory. To assess under which conditi…
Recently, abstract argumentation-based models of case-based reasoning ($AA{\text -}CBR$ in short) have been proposed, originally inspired by the legal domain, but also applicable as classifiers in different scenarios, including image classification, sentiment analysis of text, and in predicting the passage of bills in the UK Parliament. However, the formal properties of $AA{\text -}CBR$ as a reasoning system remain largely unexplored. In this paper, we focus on analysing the non-monotonicity properties of a regular version of $AA{\text -}CBR$ (that we call $AA{\text -}CBR_{\succeq}$). Specific…
A negotiation process by 2 agents e1 and e2 can be interleaved by another negotiation process between, say, e1 and e3. The interleaving may alter the resource allocation assumed at the inception of the first negotiation process. Existing proposals for argumentation-based negotiations have focused primarily on two-agent bilateral negotiations, but scarcely on the concurrency of multi-agent negotiations. To fill the gap, we present a novel argumentation theory, basing its development on abstract persuasion argumentation (which is an abstract argumentation formalism with a dynamic relation). Inco…
On the Complexity of the Grounded Semantics for Infinite Argumentation Frameworks
Department of Mathematics University of Wisconsin-Madison（威斯康星大学麦迪逊分校数学系）；Dipartimento di Ricerca e Innovazione Umanistica University of Bari, Italy（巴里大学人文研究与创新系）
Logic Programming and Argumentation Group, TU Dresden, Germany（图灵编程与论证组，德累斯顿理工大学，德国）；Knowledge-Based Systems Group, TU Dresden, Germany（知识系统组，德累斯顿理工大学，德国）；DIMES - University of Calabria, Italy（迪梅斯-卡拉布里亚大学，意大利）
Enhancing Conflict Resolution in Language Models via Abstract Argumentation
School of Philosophy, Zhejiang University（浙江大学哲学系）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；The State Key Lab of Brain-Machine Intelligence（脑机智能国家重点实验室）
Recently, abstract argumentation-based models of case-based reasoning ($AA{\text -} CBR$ in short) have been proposed, originally inspired by the legal domain, but also applicable as classifiers in different scenarios. However, the formal properties of $AA{\text -} CBR$ as a reasoning system remain largely unexplored. In this paper, we focus on analysing the non-monotonicity properties of a regular version of $AA{\text -} CBR$ (that we call $AA{\text -} CBR_{\succeq}$). Specifically, we prove that $AA{\text -} CBR_{\succeq}$ is not cautiously monotonic, a property frequently considered desirab…
University of Nebraska Omaha（内布拉斯加大学奥马哈分校）；IRIT（图卢兹计算机科学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and u…
University of Helsinki（赫尔辛基大学）；Graz University of Technology（格拉茨工业大学）
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential r…
An \textit{abstract argumentation framework} ({\sc af} for short) is a directed graph $(A,R)$ where $A$ is a set of \textit{abstract arguments} and $R\subseteq A \times A$ is the \textit{attack} relation. Let $H=(A,R)$ be an {\sc af}, $S \subseteq A$ be a set of arguments and $S^+ = \{y \mid \exists x\in S \text{ with }(x,y)\in R\}$. Then, $S$ is a \textit{stable extension} in $H$ if and only if $S^+ = A\setminus S$. In this paper, we present a thorough, formal validation of a known backtracking algorithm for listing all stable extensions in a given {\sc af}.
