Algorithmic Aspects of Abstract Argumentation Frameworks

is, the validity of their conclusions can be disputed by other arguments.
The various Artificial Intelligence approaches to model this kind of
non-monotonic reasoning in the presence of conflicting and incomplete information
can be instantiated in the so called abstract argumentation frameworks.

This talk focuses on using graph-theoretic and algorithmic tools for the study of combinatorial structure of argumentation frameworks with the aim to improve understanding of the way in which
problems are solved and investigate aspects that would be of practical use in real life applications.

I introduced a new type of argument acceptability, which can be used when the classical approaches fail. I proved that the corresponding decision problem is complete for the class of problems decidable by co-NP computations given access to an NP-complete oracle, but I identified interesting polynomial time restrictions of it.
Since argumentation frameworks model social interactions, I introduced a discipline policy for their
construction without changing a specific outcome.
Finally, I started a polyhedral approach for describing classical extensions, which can pave the way of using linear programming techniques for selecting solutions in the case of multiple status semantics.

The results obtained show that a study of practical problems raised by argumentation frameworks using advanced graph theoretic and algorithmic tools is important and necessary. In a near future, we expect to improve some of the proposed techniques. We believe that
after working on abstract argumentation framework issues we are now prepared not only to continue to extend and apply the results obtained but also to start working on structured argumentation framework related issues.