Defense semantics of argumentation: encoding reasons for accepting arguments

In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with a new notion of defense equivalence of argument graphs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Then, based on defense semantics, we define two kinds of reasons for accepting arguments, i.e., direct reasons and root reasons, and a notion of root equivalence of argument graphs. Finally, we show how the notion of root equivalence can be used in argumentation summarization.Comment: 14 pages, first submitted on April 30, 2017; 16 pages, revised in terms of the comments from MIREL2017 on August 03, 201

Metalogical Contributions to the Nonmonotonic Theory of Abstract Argumentation

The study of nonmonotonic logics is one mayor field of Artificial Intelligence (AI). The reason why such kind of formalisms are so attractive to model human reasoning is that they allow to withdraw former conclusion. At the end of the 1980s the novel idea of using argumentation to model nonmonotonic reasoning emerged in AI. Nowadays argumentation theory is a vibrant research area in AI, covering aspects of knowledge representation, multi-agent systems, and also philosophical questions. Phan Minh Dung’s abstract argumentation frameworks (AFs) play a dominant role in the field of argumentation. In AFs arguments and attacks between them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. Although, Dung-style AFs are among the simplest argumentation systems one can think of, this approach is still powerful. It can be seen as a general theory capturing several nonmonotonic formalisms as well as a tool for solving well-known problems as the stable-marriage problem. This thesis is mainly concerned with the investigation of metalogical properties of Dung’s abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics

Initial Sets in Abstract Argumentation Frameworks

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

Equivalence in Logic-Based Argumentation

International audienceThis paper investigates when two abstract logic-based argumentation systems are equivalent. It defines various equivalence criteria, investigates the links between them, and identifies cases where two systems are equivalent with respect to each of the proposed criteria. In particular, it shows that under some reasonable conditions on the logic underlying an argumentation system, the latter has an equivalent finite subsystem, called core. This core constitutes a threshold under which arguments of the system have not yet attained their final status and consequently adding a new argument may result in status change. From that threshold, the statuses of all arguments become stable

On the Existence of Characterization Logics and Fundamental Properties of Argumentation Semantics

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its fundamental intrinsic properties, is indispensable and provides the basis of an informed choice. One such intrinsic property of logic-based knowledge representation languages is the context-dependency of pieces of knowledge. In classical propositional logic, for example, there is no such context-dependence: whenever two sets of formulas are equivalent in the sense of having the same models (ordinary equivalence), then they are mutually replaceable in arbitrary contexts (strong equivalence). However, a large number of commonly used formalisms are not like classical logic which leads to a series of interesting developments. It turned out that sometimes, to characterize strong equivalence in formalism L, we can use ordinary equivalence in formalism L0: for example, strong equivalence in normal logic programs under stable models can be characterized by the standard semantics of the logic of here-and-there. Such results about the existence of characterizing logics has rightly been recognized as important for the study of concrete knowledge representation formalisms and raise a fundamental question: Does every formalism have one? In this thesis, we answer this question with a qualified “yes”. More precisely, we show that the important case of considering only finite knowledge bases guarantees the existence of a canonical characterizing formalism. Furthermore, we argue that those characterizing formalisms can be seen as classical, monotonic logics which are uniquely determined (up to isomorphism) regarding their model theory. The other main part of this thesis is devoted to argumentation semantics which play the flagship role in Dung’s abstract argumentation theory. Almost all of them are motivated by an easily understandable intuition of what should be acceptable in the light of conflicts. However, although these intuitions equip us with short and comprehensible formal definitions it turned out that their intrinsic properties such as existence and uniqueness, expressibility, replaceability and verifiability are not that easily accessible. We review the mentioned properties for almost all semantics available in the literature. In doing so we include two main axes: namely first, the distinction between extension-based and labelling-based versions and secondly, the distinction of different kind of argumentation frameworks such as finite or unrestricted ones

A PWK-style Argumentation Framework and Expansion

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

On the input/output behavior of argumentation frameworks

This paper tackles the fundamental questions arising when looking at argumentation frameworks as interacting components, characterized by an Input/Output behavior, rather than as isolated monolithical entities. This modeling stance arises naturally in some application contexts, like multi-agent systems, but, more importantly, has a crucial impact on several general application-independent issues, like argumentation dynamics, argument summarization and explanation, incremental computation, and inter-formalism translation. Pursuing this research direction, the paper introduces a general modeling approach and provides a comprehensive set of theoretical results putting the intuitive notion of Input/Output behavior of argumentation frameworks on a solid formal ground. This is achieved by combining three main ingredients. First, several novel notions are introduced at the representation level, notably those of argumentation framework with input, of argumentation multipole, and of replacement of multipoles within a traditional argumentation framework. Second, several relevant features of argumentation semantics are identified and formally characterized. In particular, the canonical local function provides an input-aware semantics characterization and a suite of decomposability properties are introduced, concerning the correspondences between semantics outcomes at global and local level. The third ingredient glues the former ones, as it consists of the investigation of some semantics-dependent properties of the newly introduced entities, namely S-equivalence of multipoles, S-legitimacy and S-safeness of replacements, and transparency of a semantics with respect to replacements. Altogether they provide the basis and draw the limits of sound interchangeability of multipoles within traditional frameworks. The paper develops an extensive analysis of all the concepts listed above, covering seven well-known literature semantics and taking into account various, more or less constrained, ways of partitioning an argumentation framework. Diverse examples, taken from the literature, are used to illustrate the application of the results obtained and, finally, an extensive discussion of the related literature is provided

Analysis of some features of Indian English: a study in linguistic method

The role which the English` Language has played in India, and the impact it had on Indian languages has been the theme of many monographs and Theses. There is another aspect"of this contact of the Lanruages and Cultures; that is the influence of Indian languages and contexts on the English language in India. This aspect is interesting both as a linguistic study and as a cultural study. This is, perhaps, the first investigation in this direction, which attempts to study the English language in a language-contact situation in India taking into consideration Indian contexts too. In the hands of Indians, the English language has acquired certain characteristics at all formal levels which make it distinct .f.r om other varieties of English, whether spoken and written as primary languages or secondary languages. In this study descriptive linguistic methods have been used in order to find the Indianness of Indian English as opposed to the Englishness of English. The term "Indian English" has been used as a cover-term for the texts under discussion which are chosen from the upper point on the Cline of bi-lingualism (cf. 1.5.3. ), and could perhaps be called, alternatively, "Standard Indian English" or "Educated Indian English" for the purpose of description. By Indian English I. " do not, however, imply an ontological status equal to those varieties of English which are spoken and written as primary languages. The body of Indian English writings covered in this study is widely read by Indians as well as non-Indians, and most of the writers included here (e. g. K, A. Abbas, M. R. Anand, B. Bhattacharya, K. Narkandaya, R. K. Narayan, Raja Rao, B. Rajan, etc. ) are considered representative English writers of India. I- have extended the scope by including some "restricted languages" from Indian English newspapers and-Parliamentary Debates. This is not, however, a definitive analysis of Indian English, nor does it claim to be a complete survey of all the aspects of Indian English. I have only attempted to raise certain theorteical and procedural problems for which I have drawn illustrative material from Indian English sources. I am conscious of the limitations of this work. The difficulties involved in it have been the greater because I am a non-native speaker of En. Mlish. In this type of work a non-native speaker of English has both disadvantages and, advantages. His disadvantages are that he himself uses Indian English and 'sifting' Indian English from British English 'in,,, the source material was a major problem. All the Indian English formations were put to a test of "acceptance" or "rejection" by native speakers of English. (It was not easy because, as, we know, two native speakers do not always agree! ) He has advantages in the sense that he, as a non-native speaker, can depend on his knowledge of native contexts and, posdiblyt in a formal and contextual analysis, he is better equipped to relate formal items to the "contextual sectors"