Abstract Argumentation via Monadic Second Order Logic
Proceedings of SUM 2012, Sixth International Conference on Scalable Uncertainty Management, Marburg, Germany, September 17-19, 2012. Lecture Notes in Computer Science, vol. 7520, pp. 85-98, Springer 2012.
We propose the formalism of Monadic Second Order Logic (MSO) as a unifying framework for representing and reasoning with various semantics of abstract argumentation. We express a wide range of semantics within the proposed framework, including the standard semantics due to Dung, semi-stable, stage, cf2, and resolution-based semantics. We provide building blocks which make it easy and straight-forward to express further semantics and reasoning tasks. Our results show that MSO can serve as a lingua franca for abstract argumentation that directly yields to complexity results. In particular, we obtain that for argumentation frameworks with certain structural properties the main computational problems with respect to MSO-expressible semantics can all be solved in linear time. Furthermore, we provide a novel characterization of resolution-based grounded semantics.