Differential equation based on cost for recursive argumentation graph (DECRAG): Continuous framework for recursive bipolar argumentation with similarity

This paper introduces an argumentation framework, differential equation based on cost for recursive argumentation graph (DECRAG), for natural language arguments. DECRAG’s argumentation graph is so flexible that attack and support relations, recursive relations, similarity relations between arguments, and default values can be represented. The base score and the necessity relation can be simulated by the framework. DECRAG maps an argumentation graph to a general system, and the solution of the system is used as the values of the nodes and edges of the graph. We illustrate interesting solutions such as multiple fixed points for the dilemma of even-length cycles and limit cycles for the paradox of odd-length cycles. DECRAG also satisfies many important properties. In this paper, focusing on the theoretical aspect of DECRAG, we show examples, properties, and evaluations of the framework.