This gives an overview of the recent research on the representation of Abstract Dialectical Frameworks (ADFs) with Binary Decision Diagrams (BDDs). It summarises the results of the already published LPNMR (International Conference on Logic Programming and Non-monotonic Reasoning) paper and COMMA (International Conference on Computational Models of Argument) paper. In addition current research, which has not been published so far is discussed.
Abstract dialectical frameworks (ADFs) are a well-studied generalisation of the prominent argumentation frameworks due to Phan Minh Dung. In this paper we propose to use reduced ordered binary decision diagrams (roBDDs) as a suitable representation of the acceptance conditions of arguments within ADFs. We first show that computational complexity of reasoning on ADFs represented by roBDDs is milder than in the general case, with a drop of one level in the polynomial hierarchy. Furthermore, we present a framework to systematically define heuristics for search space exploitation, based on easily retrievable properties of roBDDs and the recently proposed approach of weighted faceted navigation for answer set programming. We present preliminary experiments of an implementation of our approach showing promise both when compared to state-of-the-art solvers and when developing heuristics for reasoning. Finally the new web-application adf-bdd.dev is shown.
Slides can be downloaded here.