Characteristic Operator

The characteristic operator ΓD\Gamma_D of an ADF DD maps a three-valued interpretation vv to ΓD(v)\Gamma_D(v) with ΓD(v)(a)=⊓{w(Ca)∣w∈[v]2}\Gamma_D(v)(a) = \sqcap \{ w(C_a) \mid w \in [v]_2 \} for all a∈Aa \in A, where [v]2[v]_2 are the completions of vv and ⊓\sqcap is the consensus.

Reference

Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J.P. & Woltran, S. (2013). Abstract Dialectical Frameworks Revisited. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI 2013), pp. 803–809. AAAI Press.

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