Two-Valued Interpretation

A three-valued interpretation vv of an ADF is two-valued iff v(a)∈{t,f}v(a) \in \{\mathsf{t}, \mathsf{f}\} for all a∈Aa \in A.

Properties

Among all three-valued interpretations, the two-valued ones are the maximal elements with respect to the information ordering ≤i\leq_i; those that extend a three-valued interpretation vv are its completions [v]2[v]_2 (Brewka et al., 2013).

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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