Abstract Dung’s abstract argumentation framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Several research studies have been conducted to expand AF to encompass various aspects, such as the representation of (unquantified) uncertainty, that give rise to the so-called incomplete AF (iAF), where some of the arguments and attacks may be uncertain. In this paper, we introduce three new reasoning problems named totality, determinism and functionality, and investigate their computational complexity for both AF and iAF under several semantics. Intuitively, an argument is said to be deterministic if all extensions assign the same status (either accepted, rejected or undefined) to it, whereas it is said to be total if for all extensions it is either accepted or rejected. When both totality and determinism hold for a given argument, we say that it is functional. We also investigate the complexity of credulous and skeptical acceptance in iAF under semi-stable semantics—a problem left open in the literature. We then show that any iAF can be rewritten into an equivalent one where either only (unattacked) arguments or only attacks are uncertain.
Alfano et al. (Wed,) studied this question.
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