The learning sciences of today recognize the tri-dimensional nature of learning as involving cognitive, social and emotional phenomena. However, many computer-supported argumentation systems still fail in addressing the socio-emotional aspects of group reasoning, perhaps due to a lack of an integrated theoretical vision of how these three dimensions interrelate to each other. This paper presents a multi-dimensional and multi-level model of the role of emotions in argumentation, inspired from a multidisciplinary literature review and extensive previous empirical work on an international corpus of face-to-face student debates. At the crossroads of argumentation studies and research on collaborative learning, employing a linguistic perspective, we specify the social and cognitive functions of emotions in argumentation. The cognitive function of emotions refers to the cognitive and discursive process of schematization (Grize, 1996, 1997). The social function of emotions refers to recognition-oriented behaviors that correspond to engagement into specific types of group talk (e. g. Mercer in "Learning and Instruction" 6(4), 359-377, 1996). An in depth presentation of two case studies then enables us to refine the relation between social and cognitive functions of emotions. A first case gives arguments for associating low-intensity emotional framing, on the cognitive side, with cumulative talk, on the social side. A second case shows a correlation between high-intensity emotional framing, and disputational talk. We then propose a hypothetical generalization from these two cases, adding an element to the initial model. In conclusion, we discuss how better understanding the relations between cognition and social and emotional phenomena can inform pedagogical design for CSCL.