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In this paper, we propose a new method for computing general allocatorsdirectly from completeness conditions. A general allocator is an abstraction ofall complete labelings for an argumentation framework. Any complete labeling isobtained from a general allocator by assigning logical constants to variables.We proved the existence of the general allocators in our previous work.However, the construction requires us to enumerate all complete labelings forthe framework, which makes the computation prohibitively slow. The methodproposed in this paper enables us to compute general allocators withoutenumerating complete labelings. It also provides the solutions of localallocation that yield semantics for subsets of the framework. We demonstratetwo applications of general allocators, stability, and a new concept forframeworks, termed arity. Moreover, the method, including local allocation, isapplicable to broad extensions of frameworks, such as argumentation frameworkswith set-attacks, bipolar argumentation frameworks, and abstract dialecticalframeworks.

Compiling Arguments in an Argumentation Framework into Three-valued Logical Expressions