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4. 5. R. Baumann, G. Brewka, and R. Wong legally IN iff x is labeled IN and ∀b : (b, a) ∈ R, b is labeled OUT, legally OUT iff x is labeled OUT and ∃b : (b, a) ∈ R and b is labeled IN, illegally IN iff it is not legally IN, illegally OUT iff it is not legally OUT, super-illegally IN iff it is illegally IN and ∃b : (b, a) ∈ R and b is legally IN or UNDEC. The algorithm for computing all preferred labellings (Algorithm 1) starts by assigning to all arguments the label IN (labelling LIN ), and initializing an empty set in which candidate labellings are to be stored.
Among the 100 AFs, we observed an average improvement by 50-51% and by 54% for preferred and stable semantics respectively. The data contained some inconclusive examples which had “marred” the results to some extent. 2. No instance, neither for preferred semantics nor for stable, was found in which the execution with splitting lasted longer than the one without. This shows that the additional overhead introduced by splitting is negligible. 3. The optimized type of splitting did better than the non-optimized type in cases when the AF without splitting had a relatively long runtime.
Intell. 77(2), 321–358 (1995) 4. : Splitting a logic program. In: ICLP, pp. 23–37 (1994) 5. : Proof theories and algorithms for abstract argumentation frameworks. R. ) Argumentation in Artificial Intelligence, pp. 105–132. Springer, Heidelberg (2009) 6. : An abstract framework for argumentation with structured arguments. Argument and Computation 1, 93–124 (2010) 7. : Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972) 8. : Splitting a default theory. In: Proc. AAAI 1996, pp.