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

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

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

Belief Revision in Structured Probabilistic Argumentation

In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data with varying degrees of uncertainty attached. Likewise, an important aspect of the effort associated with maintaining knowledge bases is deciding what information is no longer useful; pieces of information (such as intelligence reports) may be outdated, may come from sources that have recently been discovered to be of low quality, or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing the basic issues of handling contradictory and uncertain data. Then, to address the last issue, we focus on the study of non-prioritized belief revision operations over probabilistic PreDeLP programs. We propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how such operations should behave, and study a class of operators along with theoretical relationships with the proposed postulates, including a representation theorem stating the equivalence between this class and the class of operators characterized by the postulates

CF2-extensions as answer-set models

Extension-based argumentation semantics have shown to be a suitable approach for performing practical reasoning. Since extension-based argumentation semantics were formalized in terms of relationships between atomic arguments, it has been shown that extension-based argumentation semantics based on admissible sets such as stable semantics can be characterized in terms of answer sets. In this paper, we present an approach for characterizing SCC-recursive semantics in terms of answer set models. In particular, we will show a characterization of CF2 in terms of answer set models. This result suggests that not only extension-based argumentation semantics based on admissible sets can be characterized in terms of answer sets; but also extension-based argumentation semantics based on Strongly Connected Components can be characterized in terms of answer sets.Peer ReviewedPreprin

Abduction and Dialogical Proof in Argumentation and Logic Programming

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e., finding hypothe- ses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.Comment: Appears in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014