Previous logic-based handling of arguments has mainly focused on explanation or justification in presence of inconsistency. As a consequence, only one type of argument has been considered, namely the explanatory type; several argumentation frameworks have been proposed for generating and evaluating explanatory arguments. However, recent investigations of argument-based negotiation have emphasized other types of arguments, such as threats, rewards, tips, and warnings. In parallel, cognitive psychologists recently started studying the characteristics of these different types of arguments, and the conditions under which they have their desired effect. Bringing together these two lines of research, we present in this article some logical definitions as well as some criteria for evaluating each type of argument. Empirical findings from cognitive psychology validate these formal results.