On Controversiality of Arguments and Stratified Labelings

We investigate the space of ordinal semantics, where the status of an argument is interpreted by a natural number. In doing so we do not only consider the usual acceptability-based approach for generalizing classical semantics to multivalued semantics, i. e., positioning “undecided” arguments to be in between “in” and “out” arguments, but also a controversiality-based approach where we interpret the value “undecided” as being the most controversial status of an argument. We introduce stratified labelings as a novel semantical approach that follows the idea of a controversiality-based order of truth-values. We investigate general properties for ordinal semantics and of our approach of stratified labelings in particular.