We provide new insights into the area of combining abstract argumentation frameworks with probabilistic reasoning. In particular, we consider the scenario when assessments on the probabilities of a subset of the arguments is given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalize this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistent-tolerant reasoning.

argumentation frameworks (AFs) are one of the central formalisms in AI; equipped with a wide range of semantics, they have proven useful in several application domains. We contribute to the systematic analysis of semantics for AFs by connecting two recent lines of research -- the work on input/output frameworks and the study of the expressiveness of semantics. We do so by considering the following question: given a function describing an input/output behaviour by mapping extensions (resp.

Formalizing dynamics of argumentation has received increasing attention over the last years. While AGM-like representation results for revision of argumentation frameworks (AFs) are now available, similar results for the problem of merging are still missing. In this paper, we close this gap and adapt model-based propositional belief merging to define extension-based merging operators for AFs. We state an axiomatic and a constructive characterization of merging operators through a family of rationality postulates and a representation theorem. Then we exhibit merging operators which satisfy the postulates. In contrast to the case of revision, we observe that obtaining a single framework as result of merging turns out to be a more subtle issue. Finally, we establish links between our new results and previous approaches to merging of AFs, which mainly relied on axioms from Social Choice Theory, but lacked AGM-like representation theorems.

A central question in knowledge representation is the following: given some knowledge representation formalism, is it possible, and if so how, to simplify parts of a knowledge base without affecting its meaning, even in the light of additional information? The term strong equivalence was coined in the literature, i.e. strongly equivalent knowledge bases can be locally replaced by each other in a bigger theory without changing the semantics of the latter. In contrast to classical (monotone) logics where standard and strong equivalence coincide, it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature.

Autonomous agents operating in a dynamic environment must be able to reason and make decisions about actions in pursuit of their goals. In addition, in a normative environment an agent's actions are not only directed by the agent's goals, but also by the norms imposed on the agent. Practical reasoning is reasoning about what to do in a given situation, particularly in the presence of conflicts between the agent's practical attitude such as goals, plans and norms. In this thesis we aim: (i) to introduce a model for normative practical reasoning that allows the agents to plan for multiple and potentially conflicting goals and norms at the same time (ii) to implement the model both formally and computationally, (iii) to identify the best plan for the agent to execute by means of argumentation framework and grounded semantics, (iv) to justify the best plan via argumentation-based persuasion dialogue for grounded semantics.

argumentation frameworks (AFs) are one of the central formalisms in AI; equipped with a wide range of semantics, they have proven useful in several application domains. In the thesis we want to complete and extend the recent study on expressiveness of argumentation semantics and use these and other theoretical results for implementations of reasoning tasks in AFs. Moreover, we plan to utilize results on realizability in dynamic scenarios of abstract argumentation, such as revision of argumentation frameworks. Hereby, the knowledge of which extensions can occur together is of central interest when trying to achieve a certain outcome. In other words, the ultimate goal of the thesis is to gain theoretical insights on argumentation semantics in order to employ them in practically efficient reasoning systems for both the evaluation and evolution of AFs.

argumentation frameworks (AFs) provide the basis for various reasoning problems in the area of Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straight-forward reduction-based approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexity-sensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semi-stable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SAT-based instantiation of our novel approach outperforms existing systems.

dialectical frameworks (ADFs) are a powerful generalization of Dung's abstract argumentation frameworks. ADFs allow to model argumentation scenarios such that ADF semantics then provide interpretations of the scenarios. Among the considerable number of ADF semantics, the naive-based ones are built upon the fundamental concept of conflict-freeness. Intuitively, a three-valued interpretation of an ADF's statements is conflict-free iff all true statements can possibly be accepted, and all false statements cannot possibly be accepted. In this paper, we perform an exhaustive analysis of the computational complexity of naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.

Argumentation is an inherently dynamic process. Consequently, recent years have witnessed tremendous research efforts towards an understanding of how the seminal AGM theory of belief change can be applied to argumentation, in particular for Dung's abstract argumentation frameworks (AFs). However, none of the attempts has yet succeeded in handling the natural situation where the revision of an AF is guaranteed to be representable by an AF as well. In this work, we present a generic solution to this problem which applies to many prominent I-maximal argumentation semantics. In order to prove a full representation theorem, we make use of recent advances in both areas of argumentation and belief change. In particular, we utilize the concepts of realizability in argumentation and the notion of compliance as used in Horn revision.

We study the problem of aggregation of Dung's abstract argumentation frameworks. Some operators for this aggregation have been proposed, as well as some rationality properties for this process. In this work we study the existing operators and new ones that we propose in light of the proposed properties, highlighting the fact that existing operators do not satisfy a lot of these properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem also too demanding.