Modelling defeasible and prioritized support in bipolar argumentation

Cayrol and Lagasquie-Schiex introduce bipolar argumentation frameworks by introducing a second relation on the arguments for representing the support among them. The main drawback of their approach is that they cannot encode defeasible support, for instance they cannot model an attack towards a support relation. In this paper, we introduce a way to model defeasible support in bipolar argumentation frameworks. We use the methodology of meta-argumentation in which Dung??s theory is used to reason about itself. Dung??s well-known admissibility semantics can be used on this meta-argumentation framework to compute the acceptable arguments, and all properties of Dung??s classical theory are preserved. Moreover, we show how different contexts can lead to the alternative strengthening of the support relation over the attack relation, and converse. Finally, we present two applications of our methodology for modeling support, the case of arguments provided with an internal structure and the case of abstract dialectical frameworks.     

Reasoning about preferences in argumentation frameworks

The abstract nature of Dung's seminal theory of argumentation accounts for its widespread application as a general framework for various species of non-monotonic reasoning, and, more generally, reasoning in the presence of conflict. A Dung argumentation framework is instantiated by arguments and a binary conflict based attack relation, defined by some underlying logical theory. The justified arguments under different extensional semantics are then evaluated, and the claims of these arguments define the inferences of the underlying theory. To determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments. However, preference information is often itself defeasible, conflicting and so subject to argumentation. Hence, in this paper we extend Dung's theory to accommodate arguments that claim preferences between other arguments, thus incorporating meta-level argumentation based reasoning about preferences in the object level. We then define and study application of the full range of Dung's extensional semantics to the extended framework, and study special classes of the extended framework. The extended theory preserves the abstract nature of Dung's approach, thus aiming at a general framework for non-monotonic formalisms that accommodate defeasible reasoning about as well as with preference information. We illustrate by formalising argument based logic programming with defeasible priorities in the extended theory.     

Weighted argument systems: Basic definitions, algorithms, and complexity results

We introduce and investigate a natural extension of Dung's well-known model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsistency we are prepared to tolerate: given an inconsistency budget β, we would be prepared to disregard attacks up to a total weight of β. The key advantage of this approach is that it permits a much finer grained level of analysis of argument systems than unweighted systems, and gives useful solutions when conventional (unweighted) argument systems have none. We begin by reviewing Dung's abstract argument systems, and motivating weights on attacks (as opposed to the alternative possibility, which is to attach weights to arguments). We then present the framework of weighted argument systems. We investigate solutions for weighted argument systems and the complexity of computing such solutions, focussing in particular on weighted variations of grounded extensions. Finally, we relate our work to the most relevant examples of argumentation frameworks that incorporate strengths.     

Instantiating abstract argumentation with classical logic arguments: Postulates and properties

In this paper we investigate the use of classical logic as a basis for instantiating abstract argumentation frameworks. In the first part, we propose desirable properties of attack relations in the form of postulates and classify several well-known attack relations from the literature with regards to the satisfaction of these postulates. Furthermore, we provide additional postulates that help us prove characterisation results for these attack relations. In the second part of the paper, we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic. We then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics.     

Characterizing strong equivalence for argumentation frameworks

Since argumentation is an inherently dynamic process, it is of great importance to understand the effect of incorporating new information into given argumentation frameworks. In this work, we address this issue by analyzing equivalence between argumentation frameworks under the assumption that the frameworks in question are incomplete, i.e. further information might be added later to both frameworks simultaneously. In other words, instead of the standard notion of equivalence (which holds between two frameworks, if they possess the same extensions), we require here that frameworks F and G are also equivalent when conjoined with any further framework H. Due to the nonmonotonicity of argumentation semantics, this concept is different to (but obviously implies) the standard notion of equivalence. We thus call our new notion strong equivalence and study how strong equivalence can be decided with respect to the most important semantics for abstract argumentation frameworks. We also consider variants of strong equivalence in which we define equivalence with respect to the sets of arguments credulously (or skeptically) accepted, and restrict strong equivalence to augmentations H where no new arguments are raised.     

Abstract argumentation

In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the admissibility semantics for all these formalisms has a natural argumentation-theoretic interpretation and proof procedure, which seem to correspond well with informal argumentation.In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its non-provability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of non-provability claims.     

Computing Arguments and Attacks in Assumption-Based Argumentation

Most computational frameworks for argumentation are based on abstract argumentation, which determines an argument's acceptability on the basis of its ability to counterattack all arguments attacking it. However, this view of argumentation doesn't address how to find arguments, identify attacks, and exploit premises. Assumption-based argumentation addresses these three issues. It's a refinement of abstract argumentation but remains general purpose, nonetheless. Rather than considering arguments to be a primitive concept, assumption-based argumentation defines them as backward deductions (using sets of rules in an underlying logic) supported by sets of assumptions. This approach reduces the notion of an attack against an argument to that of deduction of a contrary of an assumption.     

Dynamics of argumentation systems: A division-based method

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 formulate 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. Due to the efficiency of the division-based method, it is expected to be very useful in various kinds of argumentation systems where arguments and attacks are dynamics.     

Algorithms and complexity results for persuasive argumentation

The study of arguments as abstract entities and their interaction as introduced by Dung (1995) [1] has become one of the most active research branches within Artificial Intelligence and Reasoning. A main issue for abstract argumentation systems is the selection of acceptable sets of arguments. Value-based argumentation, as introduced by Bench-Capon (2003) [8], extends Dung?s framework. It takes into account the relative strength of arguments with respect to some ranking representing an audience: an argument is subjectively accepted if it is accepted with respect to some audience, it is objectively accepted if it is accepted with respect to all audiences.Deciding whether an argument is subjectively or objectively accepted, respectively, are computationally intractable problems. In fact, the problems remain intractable under structural restrictions that render the main computational problems for non-value-based argumentation systems tractable. In this paper we identify nontrivial classes of value-based argumentation systems for which the acceptance problems are polynomial-time tractable. The classes are defined by means of structural restrictions in terms of the underlying graphical structure of the value-based system. Furthermore we show that the acceptance problems are intractable for two classes of value-based systems that where conjectured to be tractable by Dunne (2007) [12].     

Minimal hypotheses: extension-based semantics to argumentation

The emptiness problem of the preferred semantics and the non-existence problem of the stable semantics are well recognized for argumentation frameworks. In this paper, we introduce two strong semantics, named s-preferred semantics and s-stable semantics, to guarantee the non-emptiness of the preferred extensions and the existence of the stable extensions respectively. Our semantics are defined by two concepts of extensions of argumentation frameworks, namely s-preferred extension and s-stable extension. Each is constructed in a similar way to the original semantics. The novelty of our semantics is that an extension of an argumentation framework is considered as a pair of sets of arguments, in which the second element of an extension is viewed as a kind of hypotheses that should be minimized. The s-preferred semantics not only solves the emptiness problem of the preferred semantics, but also coincides with the preferred semantics when nonempty preferred extensions exist. Meanwhile, the s-stable semantics ensures the existence of extensions, and coincides with the stable semantics when the stable extensions exist as well. The relations among various semantics for argumentation frameworks are discussed.     

Encoding deductive argumentation in quantified Boolean formulae

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉 where Φ is minimal subset of the knowledge-base such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation. Classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue. To better explore this issue, we use quantified Boolean formulae to characterise an approach to argumentation based on classical logic.     

A new approach for preference-based argumentation frameworks

Dung’s argumentation framework consists of a set of arguments and an attack relation among them. Arguments are evaluated and acceptable sets of them, called extensions, are computed using a given semantics. Each extension represents a coherent position. In the literature, several proposals have extended this framework in order to take into account the strength of arguments. The basic idea is to ignore an attack if the attacked argument is stronger than (or preferred to) its attacker. Semantics are then applied using only the remaining attacks. In this paper, we show that those proposals behave correctly when the attack relation is symmetric. However, when it is asymmetric, conflicting extensions may be computed leading to unintended conclusions. We propose an approach that guarantees conflict-free extensions. This approach presents two novelties: the first one is that it takes into account preferences at the semantics level rather than the attack level. The idea is to extend existing semantics with preferences. In case preferences are not available or do not conflict with the attacks, the extensions of the new semantics coincide with those of the basic ones. The second novelty of our approach is that a semantics is defined as a dominance relation on the powerset of the set of arguments. The extensions (under a semantics) are the maximal elements of the dominance relation. Such an approach makes it possible not only to compute the extensions of a framework but also to compare its non-extensions. We start by proposing three dominance relations that generalize respectively stable, preferred and grounded semantics with preferences. Then, we focus on stable semantics and provide full characterizations of its dominance relations and those of its generalized versions. Complexity results are provided. Finally, we show that an instance of the proposed framework retrieves the preferred sub-theories which were proposed in the context of handling inconsistency in weighted knowledge bases.     

Reconstructing Popov v. Hayashi in a framework for argumentation with structured arguments and Dungean semantics

In this article the argumentation structure of the court??s decision in the Popov v. Hayashi case is formalised in Prakken??s (Argument Comput 1:93?C124; 2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premise, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to three corresponding kinds of defeat, after which Dung??s (Artif Intell 77:321?C357; 1995) abstract acceptability semantics can be used to evaluate the arguments. In the present paper the abstract framework is instantiated with strict inference rules corresponding to first-order logic and with defeasible inference rules for defeasible modus ponens and various argument schemes. The main techniques used in the formal reconstruction of the case are rule-exception structures and arguments about rule validity. Arguments about socio-legal values and the use of precedent cases are reduced to arguments about rule validity. The tree structure of arguments, with explicit subargument relations between arguments, is used to capture the dependency relations between the elements of the court??s decision.     

Dialectic proof procedures for assumption-based, admissible argumentation

We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system.The proof procedures find a set of assumptions, to defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter-attack all attacks.The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.     

A labelling framework for probabilistic argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.     

Argument-based agreements in agent societies

In this paper, we present an abstract argumentation framework for the support of agreement processes in agent societies. It takes into account arguments, attacks among them, and the social context of the agents that put forward arguments. Then, we define the semantics of the framework, providing a mechanism to evaluate arguments in view of other arguments posed in the argumentation process. We also provide a translation of the framework into a neural network that computes the set of acceptable arguments and can be tuned to give more or less importance to argument attacks. Finally, the framework is illustrated with an example in a real domain of a water-rights transfer market.     

一种新的辩论推理模式及其应用

文中定义了一个新的辩论推理模式,建立了一个形式化的知识表示框架,并把它应用于研究扩展逻辑程序类的说明语义,结果表明,新语义克服了择优语义的不足。作者还根据上述研究结果实现了逻辑程序设计风格下的知识框架。     

On the merging of Dung's argumentation systems

In this paper, the problem of deriving sensible information from a collection of argumentation systems coming from different agents is addressed. The underlying argumentation theory is Dung's one: each argumentation system gives both a set of arguments and the way they interact (i.e., attack or non-attack) according to the corresponding agent. The inadequacy of the simple, yet appealing, method which consists in voting on the agents' selected extensions calls for a new approach. To this purpose, a general framework for merging argumentation systems from Dung's theory of argumentation is presented. The objective is achieved through a three-step process: first, each argumentation system is expanded into a partial system over the set of all arguments considered by the group of agents (reflecting that some agents may easily ignore arguments pointed out by other agents, as well as how such arguments interact with her own ones); then, merging is used on the expanded systems as a way to solve the possible conflicts between them, and a set of argumentation systems which are as close as possible to the whole profile is generated; finally, voting is used on the selected extensions of the resulting systems so as to characterize the acceptable arguments at the group level.     

Coalitions of arguments: A tool for handling bipolar argumentation frameworks

Bipolar argumentation frameworks enable to represent two kinds of interaction between arguments: support and conflict. In this paper, we turn a bipolar argumentation framework into a meta‐argumentation framework where conflicts occur between sets of arguments, characterized as coalitions of supporting arguments. So, Dung's well‐known semantics can be used on this meta‐argumentation framework to select the acceptable arguments. © 2009 Wiley Periodicals, Inc.     

Abstract argumentation systems

In this paper, we develop a theory of abstract argumentation systems. An abstract argumentation system is a collection of “defeasible proofs”, called arguments, that is partially ordered by a relation expressing the difference in conclusive force. The prefix “abstract” indicates that the theory is concerned neither with a specification of the underlying language, nor with the development of a subtheory that explains the partial order. An unstructured language, without logical connectives such as negation, makes arguments not (pairwise) inconsistent, but (groupwise) incompatible. Incompatibility and difference in conclusive force cause defeat among arguments. The aim of the theory is to find out which arguments eventually emerge undefeated. These arguments are considered to be in force. Several results are established. The main result is that arguments that are in force are precisely those that are in the limit of a so-called complete argumentation sequence.