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

Present and Future of Formal Argumentation

This report documents the program and the outcomes of Dagstuhl Perspectives Workshop 15362 “Present and Future of Formal Argumentation”. The goal of this Dagstuhl Perspectives Workshop was to gather the world leading experts in formal argumentation in order to develop a SWOT (Strength, Weaknesses, Opportunities, Threats) analysis of the current state of the research in this field and to draw accordingly some strategic lines to ensure its successful development in the future. A critical survey of the field has been carried out through individual presentations and collective discussions. Moreover, working group activity lead to identify several open problems in argumentation

Set- and Graph-theoretic Investigations in Abstract Argumentation

Abstract argumentation roots to similar parts in philosophy, linguistics and artificial intelligence. The core (syntactic) notions of argument and attack are commonly visualized via digraphs, as nodes and directed edges, respectively. Semantic evaluation functions then provide a meaning of acceptance (i.e. acceptable sets of arguments also called extensions) for any such abstract argumentation structure. In this thesis, for the very first time, we tackle the questions of acceptance and conflict from a graph- and set-theoretic point of view. We elaborate on the interspace between syntactic conflict/independence (defined by attack structure) and their semantic counterparts (defined by joint acceptance of arguments). Graph theory regards the filters and techniques we use to, respectively, categorize and describe abstract argumentation structures. Set theory regards the issues we have to deal with particularly for non-finite argument sets. For argumentation in the arbitrarily infinite case this thesis can and should be seen as reference work. For the matter of conflicts in abstract argumentation we further provide a solid base and formal framework for future research. All in all, this is a mathematicians view on abstract argumentation, deepening the field of conception and widening the angle of applicability

On the responsibility for undecisiveness in preferred and stable labellings in abstract argumentation

Different semantics of abstract Argumentation Frameworks (AFs) provide different levels of decisiveness for reasoning about the acceptability of conflicting arguments. The stable semantics is useful for applications requiring a high level of decisiveness, as it assigns to each argument the label “accepted” or the label “rejected”. Unfortunately, stable labellings are not guaranteed to exist, thus raising the question as to which parts of AFs are responsible for the non-existence. In this paper, we address this question by investigating a more general question concerning preferred labellings (which may be less decisive than stable labellings but are always guaranteed to exist), namely why a given preferred labelling may not be stable and thus undecided on some arguments. In particular, (1) we give various characterisations of parts of an AF, based on the given preferred labelling, and (2) we show that these parts are indeed responsible for the undecisiveness if the preferred labelling is not stable. We then use these characterisations to explain the non-existence of stable labellings. We present two types of characterisations, based on labellings that are more (or equally) committed than the given preferred labelling on the one hand, and based on the structure of the given AF on the other, and compare the respective AF parts deemed responsible. To prove that our characterisations indeed yield responsible parts, we use a notion of enforcement of labels through structural revision, by means of which the preferred labelling of the given AF can be turned into a stable labelling of the structurally revised AF. Rather than prescribing how this structural revision is carried out, we focus on the enforcement of labels and leave the engineering of the revision open to fulfil differing requirements of applications and information available to users

Algorithms for argument systems

Argument systems are computational models that enable an artificial intelligent agent to reason via argumentation. Basically, the computations in argument systems can be viewed as search problems. In general, for a wide range of such problems existing algorithms lack five important features. Firstly, there is no comprehensive study that shows which algorithm among existing others is the most efficient in solving a particular problem. Secondly, there is no work that establishes the use of cost-effective heuristics leading to more efficient algorithms. Thirdly, mechanisms for pruning the search space are understudied, and hence, further pruning techniques might be neglected. Fourthly, diverse decision problems, for extended models of argument systems, are left without dedicated algorithms fine-tuned to the specific requirements of the respective extended model. Fifthly, some existing algorithms are presented in a high level that leaves some aspects of the computations unspecified, and therefore, implementations are rendered open to different interpretations. The work presented in this thesis tries to address all these concerns. Concisely, the presented work is centered around a widely studied view of what computationally defines an argument system. According to this view, an argument system is a pair: a set of abstract arguments and a binary relation that captures the conflicting arguments. Then, to resolve an instance of argument systems the acceptable arguments must be decided according to a set of criteria that collectively define the argumentation semantics. For different motivations there are various argumentation semantics. Equally, several proposals in the literature present extended models that stretch the basic two components of an argument system usually by incorporating more elements and/or broadening the nature of the existing components. This work designs algorithms that solve decision problems in the basic form of argument systems as well as in some other extended models. Likewise, new algorithms are developed that deal with different argumentation semantics. We evaluate our algorithms against existing algorithms experimentally where sufficient indications highlight that the new algorithms are superior with respect to their running time

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