In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [15] with the aim of characterising the nature of argument based reasoning. In doing so, we consider two possible interpretations of the consequence relation, and describe which axioms are met by aspic^+ under each of these interpretations. We then consider the links between these axioms and the rationality postulates. Our results indicate that argument based reasoning as characterised by aspic^+ is—according to the axioms of [15]—non-cumulative and non-monotonic, and therefore weaker than the weakest non-monotonic reasoning systems considered in [15]. This weakness underpins aspic^+ ’s success in modelling other reasoning systems. We conclude by considering the relationship between aspic^+ and other weak logical systems.
We consider two teams of agents engaging in a debate to persuade an audience of the acceptability of a central argument. This is modelled by a bipartite abstract argumentation framework with a distinguished topic argument, where each argument is asserted by a distinct agent. One partition defends the topic argument and the other partition attacks the topic argument. The dynamics are based on flag coordination games: in each round, each agent decides whether to assert its argument based on local knowledge. The audience can see the induced sub-framework of all asserted arguments in a given round, and thus the audience can determine whether the topic argument is acceptable, and therefore which team is winning. We derive an analytical expression for the probability of either team winning given the initially asserted arguments, where in each round, each agent probabilistically decides whether to assert or withdraw its argument given the number of attackers.
We provide an overview on the argumentation libraries of the Tweety library collection to artificial intelligence and knowledge representation. These libraries comprise of implementations to abstract argumentation frameworks, as well as the most popular approaches to structured argumentation, and various further aspects. We briefly sketch the functionalities of these libraries and give some pointers to how they can be used.
The structure-preference (SP) order is a way of defining argument preference relations in structured argumentation theory that takes into account how arguments are constructed. The SP order was first introduced in the context of endowing Brewka’s prioritised default logic (PDL) with sound and complete argumentation semantics. In this paper, we further articulate the underlying intuitions of the SP order in terms of how an agent should construct arguments. We also compare the SP order to other argument preference relations and illustrate the different results one would obtain. Finally, we prove that the SP order allows for the original version of PDL to satisfy Brewka’s and Eiter’s postulates.
Multiple extensions of Dung’s argumentation frameworks (AFs) have been proposed in order to model features of argumentation that cannot be directly modeled in AFs. One technique that has already previously proven useful to study and combine such extensions is the meta-argumentation methodology involving the notion of a flattening. In order to faithfully model the interaction between explanation argumentation in scientific debates, Šešelja and Straßer have introduced Explanatory Argumentation Frameworks (EAFs). In this paper, we first prove that the flattening technique works as expected for recursive (higher-order) attacks. Then we apply this technique in order to combine EAFs with multiple other extensions that have been proposed to AFs, namely with recursive attacks, joint attacks and a support relation between arguments. This gives rise to Extended Explanatory Argumentation Frameworks (EEAFs). We illustrate the applicability of EEAFs by using them to model a piece of argumentation from a research-level philosophy book.
In this paper we introduce hypersequent-based frameworks for the modeling of defeasible reasoning by means of logic-based argumentation. These frameworks are an extension of sequent-based argumentation frameworks, in which arguments are represented not only by sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the weaknesses of logical argumentation reported in the literature and to prove several desirable properties, stated in terms of rationality postulates. For this, we take the relevance logic RM as the deductive base of our formalism. This logic is regarded as "by far the best understood of the Anderson-Belnap style systems" (Dunn and Restall, Handbook of Philosophical Logic, vol. 6). It has a clear semantics in terms of Sugihara matrices, as well as sound and complete Hilbert- and Gentzen-type proof systems. The latter are defined by hypersequents and admit cut elimination. We show that hypersequent-based argumentation yields a robust defeasible variant of RM with many desirable properties (e.g., rationality postulates and crash-resistance).
Combining computational models of argumentation with probability theory has recently gained increasing attention, in particular with respect to abstract argumentation frameworks. Approaches following this idea can be categorised into the constellations and the epistemic approach. While the former considers probability functions on the subgraphs of abstract argumentation frameworks, the latter uses probability theory to represent degrees of belief in arguments, given a fixed framework. In this paper, we investigate the case where probability functions are given on the extensions of abstract argumentation frameworks. This generalises classical semantics in a straightforward fashion and we show that our approach also complies with many postulates for epistemic probabilistic argumentation.
We propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate explanations and natural deduction style arguments. We discuss an instantiation of ASPIC-END that models argumentation about explanations of semantic paradoxes (e.g. the Liar paradox), and we show that ASPIC-END satisfies rationality postulates akin to those satisfied by ASPIC+.
In this paper we propose a novel algorithm for the computation of the semantics of argumentation frameworks. The algorithm can generate all complete extensions and thus can be used in problems involving the grounded, complete, preferred and stable semantics. The algorithm takes advantage of the constraints imposed on legal labelling functions to prune the search space of possible solutions.
We investigate the relationship between the structural properties of argumentation frameworks and their argument-based characteristics, examining the characteristics of structures of Dung-style frameworks and two generalisations: extended argumentation frameworks and collective-attack frameworks. Our results show that the structural properties of frameworks have an impact on the size of extensions produced, on the proportion of subsets of arguments that determine some topic argument to be acceptable, and on the likelihood that the addition of some new argument will affect the acceptability of an existing argument, all characteristics that are known to affect the performance of argumentation-based technologies. We demonstrate the applicability of our results with two case studies.
The heureka solver is a general-purpose solver for various problems in abstract argumentation frameworks pertaining to complete, grounded, preferred and stable semantics. It is based on a backtracking approach and makes use of various heuristics to optimize the search.
This paper seeks to better understand the links between human reasoning and preferred extensions as found within formal argumentation, especially in the context of uncertainty. The degree of believability of a conclusion may be associated with the number of preferred extensions in which the conclusion is credulously accepted. We are interested in whether people agree with this evaluation. A set of experiments with human participants is presented to investigate the validity of such an association. Our results show that people tend to agree with the outcome of a version of Thimm's probabilistic semantics in purely qualitative domains as well as in domains in which conclusions express event likelihood. Furthermore, we are able to characterise this behaviour: the heuristics employed by people in understanding preferred extensions are similar to those employed in understanding probabilities.
Argumentation theory provides foundations for distributed non-monotonic reasoning in the form of inter-agent dialogues. However current dialogue models do not accommodate reasoning about possibly conflicting preferences used in arbitrating amongst attacking arguments. We provide a framework for persuasion dialogues that accommodates such reasoning. Agents exchange locutions that implicitly define an ASPIC(+) theory consisting of rules and premises. The theory's defined arguments instantiate an extended argumentation framework (EAF) that accommodates arguments claiming preferences over other arguments, so that evaluation of the EAF's justified arguments determines the outcome of the dialogue. We also evaluate the outcome of a dialogue based on the dialectical status of moves in the dialogue, propose restrictions on dialogue moves and conjecture correspondences between the two outcome definitions.
In human interactions, trust is regularly updated during a discussion. For example, if someone is caught lying, any further utterances they make will be discounted, until trust is regained. This paper seeks to model such behaviour by introducing a dialogue game which operates over several iterations, with trust updates occurring at the end of each iteration. In turn, trust changes are computed based on intuitive properties, captured through three rules. By representing agent knowledge within a preference-based argumentation framework, we demonstrate how trust can change over the course of a dialogue.
This paper provides a general overview of EqArgSolver, a solver for enumeration and decision problems in argumentation theory. The solver is implemented from the ground up as a self-contained application in C++ without the use of any other external solver (e.g., SAT, ASP, CSP) or libraries.
In the context of bipolar argumentation (argumentation with two kinds of interaction, attacks and supports), we present an axiomatic approach for taking into account a special interpretation of the support relation, the necessary support. We propose constraints that should be imposed to a bipolar argumentation system using this interpretation. Some of these constraints concern the new attack relations, others concern acceptability. We extend basic Dung’s framework in different ways in order to propose frameworks suitable for encoding these constraints. By the way, we propose a formal study of properties of necessary support.
This paper deals with an approach to opponent-modelling in argumentation-based persuasion dialogues. It assumes that dialogue participants (agents) have models of their opponents’ knowledge, which can be augmented based on previous dialogues. Specifically, previous dialogues indicate relationships of support, which refer both to arguments as abstract entities and to their logical constituents. The augmentation of an opponent model relies on these relationships. An argument external to an opponent model can augment that model with its logical constituents, if that argument shares support relationships with other arguments that can be constructed from that model. The likelihood that the constituents of supporting arguments will in fact be known to an opponent, varies according to support types. We therefore provide corresponding quantifications for each support type.
We study a number of properties concerning the behaviour of semantics for Dung style abstract argumentation when the argumentation framework changes. The properties are concerned with how the evaluation of an argumentation framework changes if an attack between two arguments is added or removed. The results provide insight into the behaviour of these semantics in a dynamic context.
Matrices and the operation of dual interchange are introduced into the study of Dung’s argumentation frameworks. It is showed that every argumentation framework can be represented by a matrix, and the basic extensions (such as admissible, stable, complete) can be determined by sub-blocks of its matrix. In particular, an efficient approach for determining the basic extensions has been developed using two types of standard matrix. Furthermore, we develop the topic of matrix reduction along two different lines. The first one enables to reduce the matrix into a less order matrix playing the same role for the determination of extensions. The second one enables to decompose an extension into several extensions of different sub-argumentation frameworks. It makes us not only solve the problem of determining grounded and preferred extensions, but also obtain results about dynamics of argumentation frameworks.
