We suggest semirings as a mean to parametrically represent “weighted” Argumentation frameworks (AF): different kinds of preference levels related to arguments, e.g. a score representing a “fuzziness”, a “cost” or a probability level of each argument, can be represented by choosing different semirings. The novel idea is to provide a common computational and quantitative framework where attacks (and/or supports) have an associated weight and, consequently, also the computation of the classical Dung's semantics has an associated weight representing how much inconsistency we tolerate in the solution. The proposed semiring-based AF is then casted into a Soft Constraint Satisfaction Problem. Adding suitable sets of constraints permits to characterize the solution of the soft CSP as the desired Dung semantics. This allows for the application of the several solution techniques developed for Soft CSPs to AFs.
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