In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [8] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming. We believe the results of this paper are not only relevant by themselves, but can also potentially be used for future work on the correspondence between argumentation and logic programming semantics.
In this paper, we present a discussion game for argumentation under stable semantics. Our work is inspired by Vreeswijk and Prakken, who have defined a similar game for preferred semantics. In the current paper, we restate Vreeswijk and Prakken's work using the approach of argument labellings and then show how it can be adjusted for stable semantics. The nature of the resulting argument game is somewhat unusual, since stable semantics does not satisfy the property of relevance.
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