This paper presents a comprehensive study of argumentation frameworks with necessities (AFNs), a bipolar extension of Dung Abstract argumentation frameworks (AFs) where the support relation captures a positive interaction between arguments having the meaning of necessity: the acceptance of an argument may require the acceptance of other argument(s). The paper discusses new main acceptability semantics for AFNs and their characterization both by a direct approach and a labelling approach. It examines the relationship between AFNs and Dung (...) AFs and shows the gain provided by the former in terms of concision. Finally, the paper shows how to represent an AFN as a normal logic program (LP) and vice versa and in both cases establishes a one-to-one correspondence between extensions under the main acceptability semantics (except for semi-stable semantics where the correspondence is not completely full) of an AFN and particular cases of 3-valued stable models of normal LPs. (shrink)

We consider the problem of learning argumentation frameworks from a given set of labelings such that every input is a σ-labeling of these argumentation frameworks. Our new algorithm takes labelings and computes attack constraints for each argument that represent the restrictions on argumentation frameworks that are consistent with the input labelings. Having constraints on the level of arguments allows for a very effective parallelization of all computations. An important element of this approach is maintaining (...) a representation of all argumentation frameworks that satisfy the input labelings instead of simply finding any suitable argumentation framework. This is especially important, for example, if we receive additional labelings at a later time and want to refine our result without having to start all over again. The developed algorithm is compared to previous works and an evaluation of its performance has been conducted. (shrink)

Dung’s (1995) argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, w.r.t. a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions about the compatibility of the setting with a logical formalism (i.e., whether it is possible (...) to instantiate it properly from a logical knowledge base), and about the significance of the various semantics in the application context. In this paper we tackle the above questions. We first propose to fill in the previous gap by extending Dung’s (1995) framework. The idea is to consider all the ingredients involved in an argumentation process. We start with the notion of an abstract monotonic logic which consists of a language (defining the formulas) and a consequence operator. We show how to build, in a systematic way, arguments from a knowledge base formalised in such a logic. We then recall some basic postulates that any instantiation should satisfy. We study how to choose an attack relation so that the instantiation satisfies the postulates. We show that symmetric attack relations are generally not suitable. However, we identify at least one ‘appropriate’ attack relation. Next, we investigate under stable, semi-stable, preferred, grounded and ideal semantics the outputs of logic-based instantiations that satisfy the postulates. For each semantics, we delimit the number of extensions an argumentation system may have, characterise the extensions in terms of subsets of the knowledge base, and finally characterise the set of conclusions that are drawn from the knowledge base. The study reveals that stable, semi-stable and preferred semantics either lead to counter-intuitive results or provide no added value w.r.t. naive semantics. Besides, naive semantics either leads to arbitrary results or generalises the coherence-based approach initially developed by Rescher and Manor (1970). Ideal and grounded semantics either coincide and generalise the free consequence relation developed by Benferhat, Dubois, and Prade (1997), or return arbitrary results. Consequently, Dung’s (1995) framework seems problematic when applied over deductive logical formalisms. (shrink)

We reported a series of experiments carried out to confront the underlying intuitions of value-based argumentation frameworks (VAFs) with the intuitions of ordinary people. Our goal was twofold. On the one hand, we intended to test VAF as a descriptive theory of human argument evaluations. On the other, we aimed to gain new insights from empirical data that could serve to improve VAF as a normative model. The experiments showed that people’s acceptance of arguments deviates from VAF’s semantics (...) and is rather correlated with the importance given to the promoted values, independently of the perceptions of argument interactions through attacks and defeats. Furthermore, arguments were often perceived as promoting more than one value with different relative strengths. Individuals’ analyses of scenarios were also affected by external factors such as biases and arguments not explicit in the framework. Finally, we confirmed that objective acceptance, that is, the acceptance of arguments under any order of the values, was not a frequent behavior. Instead, participants tended to accept only the arguments that promoted the values they subscribe. (shrink)

Argumentation is a form of reasoning where a claim is accepted or rejected according to the analysis of the arguments for and against it; furthermore, it provides a reasoning mechanism able to handle contradictory, incomplete and uncertain information in real-world situations. We combine Bipolar Argumentation Frameworks (an extension of Dung’s work) with an Algebra of Argumentation Labels modeling two independent types of interaction between arguments, representing meta-information associated with arguments, and introducing an acceptability notion that will (...) give more information for arguments acceptability. (shrink)

Dung’s argumentation frameworks have been applied for over twenty years to the analysis of argument justification. This representation focuses on arguments and the attacks among them, abstracting away from other features like the internal structure of arguments, the nature of utterers, the specifics of the attack relation, etc. The model is highly attractive because it reduces most of the complexities involved in argumentation processes. It can be applied to different settings, like the argument evaluation of an individual (...) agent or the case of dialectic disputes between two agents (pro and con), or even in multi-agent collective argumentation. The latter case involves agents with possibly different arguments and/or opinions on how to evaluate them, leading to the possibility of considering multiple sets of arguments and attack relations. Two basic questions can be asked here, namely ‘what to aggregate’ and ‘how to aggregate’. The former concerns what kinds of entities do the agents intend to choose (arguments, attacks, assessments, etc.), while the second one focuses on which aggregation mechanisms yield rational choices (voting on arguments, merging procedures to obtain a common argumentation framework, deliberation processes, etc.). In particular, the question about the rationality of a collective argument choice relates this topic to Social Choice and Judgment Aggregation theories, while its associated strategic issues relate it to Game Theory. The research efforts on the disparate problems elicited by collective argumentation have generated a considerable corpus of literature that deserves an orderly evaluation. This survey is intended as a contribution to that end. (shrink)

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. (shrink)

We explore the computational complexity of justification, stability and relevance in incomplete argumentation frameworks (IAFs). IAFs are abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. These IAFs can be completed by deciding for each uncertain argument or attack whether it is present or absent. Such a completion is an abstract argumentation framework, for which it can be decided which arguments are acceptable under a given semantics. The justification (...) status of an argument in a completion then expresses whether the argument is accepted (in), not accepted because it is attacked by an accepted argument (out) or neither (undec). For a given IAF and certain argument, the justification status of that argument need not be the same in all completions. This is the issue of stability, where an argument is stable if its justification status is the same in all completions. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? In this paper, we define justification, stability and relevance for IAFs and provide a complexity analysis for these problems under grounded, complete, preferred and stable semantics. (shrink)

In this article we consider argumentation as an epistemic process performed by an agent to extend and revise her beliefs and gain knowledge, according to the information provided by the environment. Such a process can also generate the suspension of the claim under evaluation. How can we account for such a suspension phenomenon in argumentation process? We propose: (1) to distinguish two kinds of suspensions – critical suspension and non-critical suspension – in epistemic change processes; (2) to introduce (...) a Paraconsistent Weak Kleene logic (PWK) based belief revision theory which makes use of the notion of topic to distinguish the two kinds of suspensions previously mentioned, and (3) to develop a PWK-style argumentation framework and its expansion. By doing that, we can distinguish two kinds of suspensions in an epistemic process by virtue of the notion of topic. (shrink)

Over the last decade, several extensions of Dung’s Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as (...) necessity. Currently, to determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung’s AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung’s argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN). (shrink)

Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated (...) to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity. (shrink)

Dung’s argumentation frameworks are formalisms widely used to model interaction among arguments. Although their study has been profusely developed in the field of Artificial Intelligence, it is not common to see its treatment among those less connected to computer science within the logical-philosophical community. In this paper we propose to bring to that audience a proof-theory for argument justification based on tableaux, very similar to those the Logic students are familiar with. The tableaux enable to calculate whether an (...) argument or subset of arguments are accepted or rejected in accordance to Dung’s preferred and grounded extension-based semantics. Soundness and completeness results regarding those semantics are provided. (shrink)

ABSTRACTThis paper studies abduction in abstract argumentation frameworks. Given an argument, an agent verifies whether the argument is justified or not in its argumentation framework. If the argument is not justified in the argumentation framework, the agent seeks conditions to explain the justification state by hypothesising arguments in the universal argumentation framework. We formulate such abductive reasoning in argumentation semantics and provide its computation in logic programming. We also apply abduction to enforcement and simple (...) dialogue games in argumentation frameworks. (shrink)

In many domains of public discourse such as arguments about public policy, there is an abundance of knowledge to store, query, and reason with. To use this knowledge, we must address two key general problems: first, the problem of the knowledge acquisition bottleneck between forms in which the knowledge is usually expressed, e.g., natural language, and forms which can be automatically processed; second, reasoning with the uncertainties and inconsistencies of the knowledge. Given such complexities, it is labour and knowledge intensive (...) to conduct policy consultations, where participants contribute statements to the policy discourse. Yet, from such a consultation, we want to derive policy positions, where each position is a set of consistent statements, but where positions may be mutually inconsistent. To address these problems and support policy-making consultations, we consider recent automated techniques in natural language processing, instantiating arguments, and reasoning with the arguments in argumentation frameworks. We discuss application and “bridge” issues between these techniques, outlining a pipeline of technologies whereby: expressions in a controlled natural language are parsed and translated into a logic (a literals and rules knowledge base), from which we generate instantiated arguments and their relationships using a logic-based formalism (an argument knowledge base), which is then input to an implemented argumentation framework that calculates extensions of arguments (an argument extensions knowledge base), and finally, we extract consistent sets of expressions (policy positions). The paper reports progress towards reasoning with web-based, distributed, collaborative, incomplete, and inconsistent knowledge bases expressed in natural language. (shrink)

Dung’s abstract argumentation provides us with a general framework to deal with argumentation, non-monotonic reasoning and logic programming. For the extension-based semantics, one of the basic principles is I-maximality which is in particular related with the notion of skeptical justification. Another one is directionality which can be employed for the study of dynamics of argumentation. In this paper, we introduce two new extension-based semantics into Dung’s abstract argumentation, called grounded-like semantics and initial semantics which satisfy the (...) I-maximality and directionality principles. The initial semantics has many good properties and can be expected to play a central role in studying other extension-based semantics, such as admissible, complete and preferred semantics. (shrink)

Discussion among individuals about a given issue often induces polarization and bipolarization effects, i.e. individuals radicalize their initial opinion towards either the same or opposite directions. Experimental psychologists have put forward Persuasive Arguments Theory as a clue for explaining polarization. PAT claims that adding novel and persuasive arguments pro or contra the debated issue is the major cause for polarization. Recent developments in abstract argumentation provide the tools for capturing these intuitions on a formal basis. Here Bipolar Argumentation (...) Frameworks are employed as a tool for encoding the information of agents in a debate relative to a given issue a. A probabilistic extension of BAF allows to encode the likelihood of the opinions pro or contra a before and after information exchange. It is shown, by a straightforward example, how these measures provide the basis to capture the intuitions of PAT. (shrink)

Tailoring assistive systems for guiding and monitoring an individual in daily living activities is a complex task. This paper presents ALI, an assistive system combining a formal possibilistic argumentation system and an informal model of human activity: the Cultural-Historic Activity Theory, facilitating the delivery of tailored advices to a human actor. We follow an activity-centric approach, taking into consideration the human’s motives, goals and prioritized actions. ALI tracks a person in order to I) determine what activities were performed over (...) a period of time (activity recognition tracking), and II) send personalized notifications suggesting the most suitable activities to perform (decision-making monitoring). The ALI system was evaluated in a formative pilot study related to promote social activities and physical exercise. (shrink)

In many domains of public discourse such as arguments about public policy, there is an abundance of knowledge to store, query, and reason with. To use this knowledge, we must address two key general problems: first, the problem of the knowledge acquisition bottleneck between forms in which the knowledge is usually expressed, e.g., natural language, and forms which can be automatically processed; second, reasoning with the uncertainties and inconsistencies of the knowledge. Given such complexities, it is labour and knowledge intensive (...) to conduct policy consultations, where participants contribute statements to the policy discourse. Yet, from such a consultation, we want to derive policy positions, where each position is a set of consistent statements, but where positions may be mutually inconsistent. To address these problems and support policy-making consultations, we consider recent automated techniques in natural language processing, instantiating arguments, and reasoning with the arguments in argumentation frameworks. We discuss application and “bridge” issues between these techniques, outlining a pipeline of technologies whereby: expressions in a controlled natural language are parsed and translated into a logic (a literals and rules knowledge base), from which we generate instantiated arguments and their relationships using a logic-based formalism (an argument knowledge base), which is then input to an implemented argumentation framework that calculates extensions of arguments (an argument extensions knowledge base), and finally, we extract consistent sets of expressions (policy positions). The paper reports progress towards reasoning with web-based, distributed, collaborative, incomplete, and inconsistent knowledge bases expressed in natural language. (shrink)

Tailoring assistive systems for guiding and monitoring an individual in daily living activities is a complex task. This paper presents ALI, an assistive system combining a formal possibilistic argumentation system and an informal model of human activity: the Cultural-Historic Activity Theory, facilitating the delivery of tailored advices to a human actor. We follow an activity-centric approach, taking into consideration the human’s motives, goals and prioritized actions. ALI tracks a person in order to I) determine what activities were performed over (...) a period of time (activity recognition tracking), and II) send personalized notifications suggesting the most suitable activities to perform (decision-making monitoring). The ALI system was evaluated in a formative pilot study related to promote social activities and physical exercise. (shrink)

Argumentation Frameworks provide a fruitful basis for exploring issues of defeasible reasoning. Their power largely derives from the abstract nature of the arguments within the framework, where arguments are atomic nodes in an undifferentiated relation of attack. This abstraction conceals different senses of argument, namely a single-step reason to a claim, a series of reasoning steps to a single claim, and reasoning steps for and against a claim. Concrete instantiations encounter difficulties and complexities as a result of conflating (...) these senses. To distinguish them, we provide an approach to instantiating AFs in which the nodes are restricted to literals and rules, encoding the underlying theory directly. Arguments in these senses emerge from this framework as distinctive structures of nodes and paths. As a consequence of the approach, we reduce the effort of computing argumentation extensions, which is in contrast to other approaches. Our framework retains the theoretical and computational bene.. (shrink)

This research explores the relationship between the bounded in-degree and out-degree of an argumentation framework and the computational complexity of the problems of Credulous Acceptance ( CredA ) and Skeptical Acceptance ( SkepA ) under preferred extensions. Researchers have studied the complexity of these problems when the in-degree [Formula: see text] and out-degree [Formula: see text] of the arguments are restricted to [Formula: see text]. Despite this restriction, the computational complexities of CredA and SkepA persist. Based on these results, (...) we presents new results that provide deeper insights into the impact of additional constraints on the argumentation framework. Specifically, we show that when “[Formula: see text]” or “[Formula: see text]” is restricted to [Formula: see text], both problems CredA and SkepA can be solved in polynomial time. Subsequently, we impose additional constraints on the argumentation framework by analyzing the quantities “[Formula: see text],” “[Formula: see text],” and “[Formula: see text].” For an argumentation framework [Formula: see text] and all arguments “[Formula: see text]” of [Formula: see text], the parameter “[Formula: see text]” indicates the maximum number of attackers that any argument “[Formula: see text]” can have among all those that are not attacked by “[Formula: see text]” [Formula: see text], “[Formula: see text]” indicates the maximum number of arguments that any argument “[Formula: see text]” attacks among all those that do not attack “[Formula: see text]”, and “[Formula: see text]” denotes the maximum number of arguments that any argument “[Formula: see text]” attacks among those that attack “[Formula: see text]”. Surprisingly, even when all these quantities are restricted to [Formula: see text], the computational complexity of CredA persists. Furthermore, we explore the influence of symmetric attacks by fixing “[Formula: see text]” to zero, while setting “[Formula: see text]” and “[Formula: see text]” to [Formula: see text]. Remarkably, the complexity of CredA persists under this restriction as well. (shrink)

Argumentation is an important research area in the field of AI. There is a substantial amount of work on different aspects of Dung’s abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are: i) extending the framework to account for recursive attacks and supports, and ii) considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on High-Order Argumentation Frameworks with Necessities (HOAFNs) which allow for (...) attack and support relations (interpreted as necessity) not only between arguments but also targeting attacks and supports at any level. We propose an approach for the incremental evaluation of the credulous acceptance problem in HOAFNs, by “incrementally” computing an extension (a set of accepted arguments, attacks and supports), if it exists, containing a given goal element in an updated HOAFN. In particular, we are interested in monitoring the credulous acceptance of a given argument, attack or support (goal) in an evolving HOAFN. Thus, our approach assumes to have a HOAFN Δ, a goal \rho occurring in Δ, an extension E for Δ containing \rho, and an update u establishing some changes in the original HOAFN, and uses the extension for first checking whether the update is relevant; for relevant updates, an extension of the updated HOAFN containing the goal is computed by translating the problem to the AF domain and leveraging on AF solvers. We provide formal results for our incremental approach and empirically show that it outperforms the evaluation from scratch of the credulous acceptance problem for an updated HOAFN. (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots$$ affirms the falsity of $$\ldots$$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the (...) sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

We describe a tool that allows the merging of extensions of argumentation frameworks, following the approach defined by 33–42). The tool is implemented in Java, and is highly modular thanks to Object Oriented Programming principles. We describe a short experimental study that assesses the scalability of the approach, as well as the impact on runtime of using an integrity constraint.

We consider scenarios where a group of agents wish to simplify a given abstract argumentation framework—specifying a set of arguments and the attacks between them—by eliminating cycles in the attack-relation on the basis of their preferences over arguments. They do so by first aggregating their individual preferences into a collective preference order and then removing any attacks involved in a cycle that go against that order. Our analysis integrates insights from formal argumentation and social choice theory. We obtain (...) sweeping impossibility results for essentially all standard methods of preference aggregation, showing that no Condorcet method and no positional scoring rule can uphold the fundamental principle expressing that views held by every single member of the group must be respected. But we also find that so-called representative-agent rules do offer this guarantee. (shrink)

Group polarization occurs when an initial attitude or belief of individuals becomes more radical after group discussion. Polarization often leads subgroups towards opposite directions. Since the 1960s this effect has been observed and repeatedly confirmed in lab experiments by social psychologists. Persuasive Arguments Theory emerged as the most convincing explanation for this phenomenon. This paper is a first attempt to frame the PAT explanation more formally by means of Bipolar Argumentation Frameworks. In particular, I show that polarization may (...) emerge in a BAF by simple and rational belief updates by participants. (shrink)

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. (shrink)

1. Argumentation, by considering arguments and their interactions, is a way of reasoning that has proven successful in many contexts, for instance, in multi-agent applications (Carrera & Iglesias,...

solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have...

In this paper, we propose a framework for fostering argumentative skills in a systematic way in Philosophy and Ethics classes. We start with a review of curricula and teaching materials from the German-speaking world to show that there is an urgent need for standards for the teaching and learning of argumentation. Against this backdrop, we present a framework for such standards that is intended to tackle these difficulties. The spiral-curricular model of argumentative competences we sketch helps teachers introduce the (...) relevant concepts and skills to students early on in their school career. The focus is on secondary schools, but the proposal can also be of use for learning and teaching in universities, especially in introductory classes. (shrink)