From non-monotonic syntax-based entailment to preference-based argumentation

A key ingredient of computational argumentation in AI is the generation of arguments in favor of or against claims under scrutiny. In this paper we look at the complexity of argument construction and reasoning in the prominent structured formalism of assumption-based argumentation (ABA). We point out that reasoning in ABA by means of constructing an abstract argumentation framework (AF) gives rise to two main sources of complexity: (i) constructing the AF and (ii) reasoning within the constructed graph. Since both steps are intractable in general, it is no surprise that the best performing state-of-the-art ABA reasoners skip the instantiation procedure entirely and perform tasks directly on the input knowledge base. Driven by this observation, we identify and study atomic and symmetric ABA, two ABA fragments that preserve the expressive power of general ABA, and that can be utilized to have milder complexity in the first or second step. We show that using atomic ABA allows for an instantiation procedure for general ABA leading to polynomially-bounded AFs and that symmetric ABA can be used to create AFs that have mild complexity to reason on. By an experimental evaluation, we show that using the former approach with modern AF solvers can be competitive with state-of-the-art ABA solvers, improving on previous AF instantiation approaches that are hindered by intractable argument construction.

In this paper, we extend the abstract argumentation framework proposed by [1] in order to take into account two kinds of interaction between arguments: a positive interaction (an argument can help, support another argument) and a negative interaction (an argument can attack another argument). In this new abstract argumentation framework, called a bipolar argumentation framework, we propose a gradual interaction-based valuation process. With this process, the value of each argument A only depends on the value of the arguments which are directly interacting with A in the argumentation system.

Based on Dung’s argumentation framework, using Dung’s extended argumentation semantics, importing reasoning argument and fact argument, design and implementing Jess-based argumentative E-commerce system, the system has important significance and high reference value for studying E-commerce argumentative negotiation systems.

This paper addresses the issue of the dynamic enforcement of a constraint in an argumentation system. The system consists in (1) an argumentation framework, made up, notably, of a set of arguments and of an attack relation, (2) an evaluation semantics, and (3) the evaluation result, computed from (1) and (2). An agent may want another agent to consider a new attack, or to have a given argument accepted, or even to relax the definition of the semantics. A constraint on any of the three components is thus defined, and it has to be enforced in the system. The enforcement may result in changes on components of the system. The paper surveys existing approaches for the dynamic enforcement of a constraint and its consequences, and reveals challenging enforcement cases that remain to be investigated.

In this paper we further progress the analysis of the recently introduced multi-valued argumentation frameworks (MVAFs). MVAFs are an extension of Dung's abstract argumentation, where arguments have a degree of truth associated with them. Here we describe a list of properties of MVAFs considering the major multi-valued logics such as those proposed by Gödel, Zadeh and Łukasiewicz. We then propose a computational framework that joins multi-valued and probabilistic argumentation frameworks to handle situations where arguments affected by vagueness and/or probabilities coexist. The findings are a contribution to the field of non-monotonic approximate reasoning and they also represent a well-grounded proposal towards the introduction of gradualism in argumentation systems.

We present a novel automated approach for the computation and verification of preferences in an abstract argumentation system. Various argumentation semantics have been developed for identifying acceptable sets of arguments, however, there is a lack of explanatory justification for their acceptability based on preferences. We present an algorithm which takes an abstract argumentation framework and a single extension (conflict-free set of arguments) as input, and outputs preference relations that explain why a set of arguments are acceptable as opposed to their attackers. We also present an algorithm to verify that the output preferences when used with the given argumentation framework induce the input extension.

The changing of arguments and their attack relation is an intrinsic property of a variety of argumentation systems. So, it is very important to efficiently figure out how the status of arguments in a system evolves when the system is updated. However, unlike other areas of argumentation that have been deeply explored, such as argumentation semantics, proof theories, and algorithms, etc., dynamics of argumentation systems has been comparatively neglected. In this paper, we introduce a general theory (called a division-based method) to cope with this problem based on a new concept: the division of an argumentation framework. When an argumentation framework is updated, it is divided into three parts: an unaffected, an affected, and a conditioning part. The status of arguments in the unaffected sub-framework remains unchanged, while the status of the affected arguments is computed in a special argumentation framework (called a conditioned argumentation framework, or briefly CAF) that is composed of an affected part and a conditioning part. We have proved that under a certain semantics that satisfies the directionality criterion (complete, preferred, ideal, or grounded semantics), the extensions of the updated framework are equal to the result of a combination of the extensions of an unaffected sub-framework and sets of the extensions of a set of assigned CAFs. The theory shows that the complexity of computing the dynamics of argumentation will decrease to a lesser or greater extent, depending on the types of argumentation semantics, the topologies of argumentation frameworks, and the number of affected arguments with respect to an addition or a deletion. As a result, this theory is expected to be very useful in various kinds of argumentation systems where arguments and attacks are dynamics, due to the changing of underlying knowledge and information.

Dynamics of argumentation systems: A division-based method

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.

It is often necessary and reasonable to justify preferences before reasoning from them. Moreover, justifying a preference ordering is reduced to justifying the criterion that produces the ordering. This paper builds on the well-known ASPIC+ formalism to develop a model that integrates justifying qualitative preferences with reasoning from the justified preferences. We first introduce a notion of preference criterion in order to model the way in which preferences are justified by an argumentation framework. We also adapt the notion of argumentation theory to build a sequence of argumentation frameworks, in which an argumentation framework justifies preferences that are to underlie the next framework. That is, in our formalism, preferences become not only an input of an argumentation framework, but also an output of it. This kind of input-output process can be applied in the further steps of argumentation. We also explore some interesting properties of our formalism.

Abstract argumentation systems are formalisms for defeasible reasoning where some components remain unspecified, the structure of arguments being the main abstraction. In the dialectical process carried out to identify accepted arguments in the system some controversial situations may appear. These relate to the reintroduction of arguments into the process which cause the onset of circularity. This must be avoided in order to prevent an infinite analysis. Some systems apply the sole restriction of not allowing the introduction of previously considered arguments in an argumentation line. However, repeating an argument is not the only possible cause for the risk mentioned. A more specific restriction needs to be applied considering the existence of subarguments. In this work, we introduce an extended argumentation framework where two kinds of defeat relation are present, and a definition for progressive defeat path.KeywordsAbstract ArgumentationArgumentation FrameworkAbstract FrameworkPreference CriterionDefeasible ReasoningThese 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.

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.

Argumentation systems can be employed for detecting spatiotemporal patterns. While the idea of argumentation consists in defending specific positions, complex patterns are influenced by several factors that can be regarded as arguments against or in favor of the realisation of those patterns. The idea is to determine consistent positions of arguments which speak for specific patterns. This becomes possible by means of algorithms which have been defined for argumentation systems. The introduced method of conceptual argumentation is new in comparison to classical, i.e. value-based, argumentation systems. It has the advantage to be more flexible by enabling the definition of conceptual arguments influencing relevant patterns. There are two main results: first, conceptual argumentation frameworks do scale significantly better; secondly, investigating our approach by examining soccer games, we show that specific patterns, such as passes, can be detected with different retrieval performances depending on the chosen spatial granularity level.KeywordsDescription LogicSemantic DescriptionArgumentation FrameworkDynamic SceneDefault TheoryThese 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.

We propose a partial information state-based framework for collaborative dialogue and argument between agents. We employ a three-valued based nonmonotonic logic, NML3, for representing and reasoning about Partial Information States (PIS). NML3 formalizes some aspects of revisable reasoning and it is sound and complete. Within the framework of NML3, we present a formalization of some basic dialogue moves and the rules of protocols of some types of dialogue. The rules of a protocol are nonmonotonic in the sense that the set of propositions to which an agent is committed and the validity of moves vary from one move to another. The use of PIS allows an agent to expand consistently its viewpoint with some of the propositions to which another agent, involved in a dialogue, is overtly committed. A proof method for the logic NML3 has been successfully implemented as an automatic theorem prover. We show, via some examples, that the tableau method employed to implement the theorem prover allows an agent, absolute access to every stage of a proof process. This access is useful for constructive argumentation and for finding cooperative and/or informative answers.

Los sistemas argumentativos formalizan razonamiento de sentido común mediante la construcción, comparación y evaluación de argumentos a favor o en contra de ciertas afirmaciones. En tales sistemas existen dos nociones centrales: derrota y defensa. En el presente trabajo caracterizan ambas nociones y se discuten algunos desafíos para las caracterizaciones propuestas. Además, se realizan algunos comentarios al respecto.