Cognitive models are a representation of an agent control mechanism resembling the cognitive architecture of a mind. It can be understood as a control system (e.g. a flow graph how to react) that takes sensory inputs and produces motor outputs (Piaget, 1985).
More advanced models include adaptive memory (Anderson, 1983).
Famous models include SOaR: State Operator and Result (Laird, Newell, & Rosenbloom, 1987); BDI: Belief, Desire, and Intention (Bratman, Israel, & Pollack, 1988); PECS: Physics, Emotions, Cognitive, Social (Urban & Schmidt, 2001); ACT-R: Adaptive Control of Thought – Rational (Anderson, Matessa, & Lebiere, 1997); CLARION: Connectionist Learning with Adapative Rule Induction On-line (Sun, 2006); and Agent Zero (Epstein, 2014).
The communality of all these is summed up in this slide from the University of Michigan:
Anderson, J. R. (1983). A spreading activation theory of memory. Journal of Verbal Learning and Verbal Behavior, 22(3), 261–295.
Anderson, J. R., Matessa, M., & Lebiere, C. (1997). ACT-R: A theory of higher level cognition and its relation to visual attention. Human-Computer Interaction, 12(4), 439–462.
Bratman, M. E., Israel, D. J., & Pollack, M. E. (1988). Plans and resource‐bounded practical reasoning. Computational Intelligence, 4(3), 349–355.
Epstein, J. M. (2014). Agent_Zero: Toward neurocognitive foundations for generative social science. Princeton University Press.
Laird, J. E., Newell, A., & Rosenbloom, P. S. (1987). Soar: An architecture for general intelligence. Artificial Intelligence, 33(1), 1–64.
Piaget, J. (1985). The equilibration of cognitive structures: The central problem of intellectual development. University of Chicago Press.
Sun, R. (2006). The CLARION cognitive architecture: Extending cognitive modeling to social simulation. In Cognition and multi-agent interaction: From cognitive modeling to social simulation (pp. 79–99). Cambridge University Press.
Urban, C., & Schmidt, B. (2001). PECS–agent-based modelling of human behaviour. In Emotional and Intelligent–The Tangled Knot of Social Cognition. Presented at the AAAI Fall Symposium Series, North Falmouth, MA.