Temporal, numerical and meta-level dynamics in argumentation networks

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1 = in, 0 = out and 1 2 = undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator-prey ecological networks, flow networks, logical modal networks and more. This newpoint of viewallows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster-Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values. We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005.