@electronic{DBLP:journals/corr/abs-1807-06685,
  abstract = { This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works, and introduce the notion of a modular acceptability semantics. A semantics is modular if it cleanly separates aggregation of attacking and supporting arguments (for a given argument a) from the computation of their influence on a's initial weight.
We show that the various semantics for bipolar argumentation graphs from the literature may be analysed as a composition of an aggregation function with an influence function. Based on this modular framework, we prove general convergence and divergence theorems. We demonstrate that all well-behaved modular acceptability semantics converge for all acyclic graphs and that no sum-based semantics can converge for all graphs. In particular, we show divergence of Euler-based semantics (Amgoud et al.) for certain cyclic graphs. Further, we provide the first semantics for bipolar weighted graphs that converges for all graphs.},
  added-at = {2018-11-08T14:42:42.000+0100},
  archiveprefix = {arXiv},
  author = {Mossakowski, Till and Neuhaus, Fabian},
  bdsk-url-1 = {http://arxiv.org/abs/1807.06685},
  bibsource = {dblp computer science bibliography, https://dblp.org},
  biburl = {https://www.bibsonomy.org/bibtex/221d0a4ade4840188710bdb7361143fff/tillmo},
  date-added = {2018-08-27 17:33:14 +0200},
  date-modified = {2018-08-28 10:50:11 +0200},
  eprint = {1807.06685},
  interhash = {4c06c694a9ece0c31a8c107bef234b06},
  intrahash = {21d0a4ade4840188710bdb7361143fff},
  keywords = {argumentation myown},
  primaryclass = {cs.AI},
  timestamp = {2018-11-08T14:42:42.000+0100},
  title = {Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs},
  url = {http://arxiv.org/abs/1807.06685},
  year = 2018
}