MASQ (Multi-Agent Systems based on Quadrants) is a generic metamodel that integrates many of the concepts issued from the research in the multiagent systems field by defining four perspectives over agent-based interaction according to two axes: internal/external and individual/collective. The aim of this paper is to provide a formal description of MASQ by specifying clear relations between the basic elements of the four quadrants and by analysing the dynamics of a multi-agent system through its transitions and through the classical mind cycle. The proposed formal model has been designed as a theoretical framework and therefore the specifications of many components of a multi-agent system such as the internal architecture of minds, the casual laws of environments or the social laws in organizations and institutions are intentionally left generic to allow for many further concretizations.