A formalism is presented for the social identity approach—a family of successful social-psychological theories explaining inter- and intra-group dynamics. The proposition of this paper is that a formalism may contribute to the further sophistication of social simulation modelling by distilling the logical essence of the social identity approach and presenting it in a form that can readily be implemented in software. Moreover, several key explanations the social identity approach offers simply follow. The paper sets up the formalism and uses it to explain the emergence and stability of group identity and the phenomenon of group polarisation. Hypothetical examples of both are presented to illustrate how the formalism would apply to empirical cases.