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 ½=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 new point of view allows 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. (shrink)

The abstract argumentation frameworks model is currently the most used tool for characterizing the justification of defeasible arguments in Artificial Intelligence. Justifications are determined on a given attack relation among arguments and are formalized as extension semantics. In this work we argue that, contrariwise to the assumptions in that model, either some argumentation frameworks are meaningless under certain concrete definitions of the attack relation, or some of the most used extension semantics in the literature, based on the defense notion of (...) admissibility, are not suitable in particular for the justification of arguments for decision making. (shrink)