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By gaining insight into the structure and behaviours of objects drawn at random from a general class, it is often possible to develop algorithms and techniques which ameliorate the computational difficulty of decision questions arising in the general case. In this paper we present a number of approaches for the random generation of value-based argumentation frameworks (VAFs) built on n arguments and using k values. Via an empirical study we consider the behaviour of the associated random VAFs with respect to the issue of how many arguments within them have the property of being “objectively accepted”. Our studies indicate that the property of having no objectively accepted argument exhibits a so-called “phasetransition effect”, similar in nature to those observed in many other well-established AI studies.
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