Socially Assistive Robots (SARs) i.e., robots that assist humans through social interactions with them, have shown potential to improve the quality of life of their users. Nonetheless, the state-of-the-art SARs face challenges that prevent them from or limit them in assisting humans in the real world. Although current SARs display cues that simulate social behaviours, the interactions that they generate are often not realistic and fail to engage their users for long periods of time. Most of the challenges currently faced by SARs are a consequence of the lack of social awareness and understanding of the cognitive procedures of individual users. In human interactions, people develop cognitive models of each other to achieve social goals and to respond to the needs of their peers according to their emotional states. Therefore, the present research project proposes to develop a mathematical model of human cognition, based on Theory of Mind (ToM), and to implement it for SARs. To do so, the cognitive processes behind human behaviour in social interactions are carefully investigated and formalised, and a model of human cognition is presented. Two formulations of the model are proposed and compared. The model is implemented using Fuzzy Cognitive Map (FCM), and is then qualitatively analysed and quantitatively assessed. It is concluded that, to accurately estimate the cognitive states of humans, the model must comprise user-specific variables that describe agents throughout interactions, the linkages of the FCM must be represented as functions, and the model must be personalised to every user.