Computational complexity of flat and generic Assumption-Based Argumentation, with and without probabilities

Reasoning with probabilistic information has recently attracted considerable attention in argumentation, and formalisms of Probabilistic Abstract Argumentation (PAA), Bipolar (PBA) Structured (PSA) have been proposed. These foundational advances complemented investigations on the complexity some approaches to PAA PBA, but not PSA. We study an existing form PSA, namely Assumption-Based (PABA), a powerful, implemented formalism which subsumes several forms other Specifically, we establish membership (general upper bounds) completeness (instantiated lower reasoning PABA for class FP#P (of functions #P-oracle counting solutions NP problem) respect newly introduced verification, credulous sceptical acceptance function problems under ABA semantics. As by-product necessary results, provide comprehensive picture landscape (for both flat generic, possibly non-flat ABA) classical decision existence, those