  We present an extension-based approach for computing and verifying
preferences in an abstract argumentation system. Although numerous
argumentation semantics have been developed previously for identifying
acceptable sets of arguments from an argumentation framework, there is a lack
of justification behind their acceptability based on implicit argument
preferences. Preference-based argumentation frameworks allow one to determine
what arguments are justified given a set of preferences. Our research considers
the inverse of the standard reasoning problem, i.e., given an abstract
argumentation framework and a set of justified arguments, we compute what the
possible preferences over arguments are. Furthermore, there is a need to verify
(i.e., assess) that the computed preferences would lead to the acceptable sets
of arguments. This paper presents a novel approach and algorithm for
exhaustively computing and enumerating all possible sets of preferences
(restricted to three identified cases) for a conflict-free set of arguments in
an abstract argumentation framework. We prove the soundness, completeness and
termination of the algorithm. The research establishes that preferences are
determined using an extension-based approach after the evaluation phase
(acceptability of arguments) rather than stated beforehand. In this work, we
focus our research study on grounded, preferred and stable semantics. We show
that the complexity of computing sets of preferences is exponential in the
number of arguments, and thus, describe an approximate approach and algorithm
to compute the preferences. Furthermore, we present novel algorithms for
verifying (i.e., assessing) the computed preferences. We provide details of the
implementation of the algorithms (source code has been made available), various
experiments performed to evaluate the algorithms and the analysis of the
results.
