The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.

dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

The study of extension-based semantics within the seminal abstract argumentation model of Dung has largely focused on definitional, algorithmic and complexity issues. In contrast, matters relating to comparisons of representational limits, in particular, the extent to which given collections of extensions are expressible within the formalism, have been under-developed. As such, little is known concerning conditions under which a candidate set of subsets of arguments are "realistic" in the sense that they correspond to the extensions of some argumentation framework AF for a semantics of interest. In this paper we present a formal basis for examining extension-based semantics in terms of the sets of extensions that these may express within a single AF. We provide a number of characterization theorems which guarantee the existence of AFs whose set of extensions satisfy specific conditions and derive preliminary complexity results for decision problems that require such characterizations.

We provide a logical analysis of abstract argumentation frameworks and their dynamics. Following previous work, we express attack relation and argument status by means of propositional variables and define acceptability criteria by formulas of propositional logic. We here study the dynamics of argumentation frameworks in terms of basic operations on these propositional variables, viz.

Reasoning with the maximally consistent subsets (MCS) of the premises is awell-known approach for handling contradictory information. We introduce two argumentation-based methods for doing so: a declarative approach that is related to Dung-style semantics for abstract argumentation, and a computational approach that is based on extensions of Gentzen-type proofs systems. This brings about a new perspective on reasoning with MCS which shows a strong link between the latter and argumentation systems, and which can be extended to related formalisms. A by-product of this is the introduction of a dynamic proof system for classical logic and rebuttal attacks, which is sound and complete with respect to Dung's stable semantics for the associated argumentation framework.

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.