Submitted: August 2020
Abstract
In classical abstract argumentation, semantics specify sets of arguments which form valid extensions of a given attack graph. In the more recently emerged subfield of probabilistic abstract argumentation, a clear consensus about equivalent notions is yet to be found. This thesis proposes a framework featuring probability distributions as a generalization of extensions, and functions enforcing certain formal constraints on such distributions as probabilistic counterpart to classical semantics. The formal constraints ensure the tasks of finding distributions satisfying probabilistic semantics fall within the existential theory of the reals. This allows them to be tackled by SMT solvers, as demonstrated by a proof-of-concept implementation of the framework based on the efficient Z3 solver. Additionally, a family of probabilistic semantics inspired by Bayesian networks in noisy-or form is developed and compared to existing probabilistic semantics.