Argument and Computation 3 (2-3):143 - 202 (2012)

Jonathan Woods
Jadavpur University
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
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DOI 10.1080/19462166.2012.704397
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References found in this work BETA

On the Evaluation of Argumentation Formalisms.Martin Caminada & Leila Amgoud - 2007 - Artificial Intelligence 171 (5-6):286-310.
Reasoning About Preferences in Argumentation Frameworks.Sanjay Modgil - 2009 - Artificial Intelligence 173 (9-10):901-934.

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Citations of this work BETA

Theory of Disjunctive Attacks, Part I.D. Gabbay & M. Gabbay - 2016 - Logic Journal of the IGPL 24 (2):186-218.
Modal and Temporal Argumentation Networks.H. Barringer, D. M. Gabbay & J. Woods - 2012 - Argument and Computation 3 (2-3):203 - 227.
The Attack as Strong Negation, Part I.D. Gabbay & M. Gabbay - 2015 - Logic Journal of the IGPL 23 (6):881-941.

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