Two-Valued Completions

The two-valued completions of a three-valued interpretation vv of an ADF are [v]2={w∣v≤iw and w−1(u)=∅}[v]_2 = \{ w \mid v \leq_i w \text{ and } w^{-1}(\mathsf{u}) = \emptyset \}, where ≤i\leq_i is the information ordering.

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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