This talk considers the decomposition of a Dung's argumentation framework into an arbitrary set of interacting components characterized by an Input/Output behavior. First, a suite of decomposability properties will be introduced, concerning the correspondence between semantics outcomes at global and local level. The satisfaction of these properties, considering more or less constrained ways of partitioning an argumentation framework, will be discussed for admissible, complete, stable, grounded, preferred, ideal and semi-stable semantics. Second, the talk will introduce the notion of argumentation multipole, inspired from the field of digital logic, as a general way to represent a modular component. On the basis of the semantics-specific input/output behavior of argumentation multipoles, different legitimacy properties of a replacement between multipoles can be introduced. Correspondingly, a semantics can be considered transparent if a legitimate replacement does not affect the evaluation of the arguments not involved by the replacement. The transparency properties of the above mentioned semantics will be outlined. Finally, the input/output characterization of argumentation semantics suggests a correspondence with abstract dialectical frameworks, a recent generalization of Dung's argumentation frameworks. Some interesting directions for further research will be presented in this respect.

• Thematic program: Structural aspects of problem solving (2013)

This talk aims to provide a general overview of the computational aspects of elections. Its main focus will be on the complexity of problems that model various ways of tampering with the outcome of an election, such as manipulation, control, and bribery. Each of these actions are very different in nature: while manipulation concerns the insincere behavior on the part of one or several voters, in control settings the election's chair seeks to change the outcome of an election by making structural changes in the election such as adding/deleting/partitioning either candidates or voters, and finally, bribery is given if an external agent attempts to change one or several voters' votes. These manipulative actions will be examined in the context of several voting systems, with one example being fallback voting, proposed by Brams and Sanver (2006), which - being computationally resistant to 20 of the 22 common types of control - is the system currently known to display the broadest resistance to control among all natural voting systems with an easy winner determination procedure.

• Thematic program: Structural aspects of problem solving (2013)