The model theory is an alternative to the view that deduction depends on formal rules of inference akin to those of a logical calculus. The distinction between the two sorts of theories parallels the one in logic between proof-theoretic methods based on formal rules and model-theoretic methods based, say, on truth tables. It is also an alternative to the view that deduction depends on Bayesian probability calculations. Which psychological theory provides a better account of naive human reasoning is controversial.
Introductory references for formal rule theories
Rips, L.J. (1994). The Psychology of Proof. Cambridge, Mass., MIT Press.
Braine, M. D. S. & O’ Brien, D. P. (Editors). (1998). Mental Logic. Mahwah, NJ: Lawrence Erlbaum Associates:
Introductory references for domain-specific inference rule theories
Cheng, P.W. & Holyoak, K.J. (1985). Pragmatic Reasoning Schemas. Psychology. 17, 391-416.
Cosmides, L, Tooby, J., Fiddick, L. & Bryant, G. (2005). Detecting cheaters. Trends in Cognitive Sciences, 9, 505–506.
Introductory references for probabilistic theories
Evans, J.St.B.T. & Over, D. (2004). If. Oxford: Oxford University Press.
Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.
Some references for specific criticisms of the model theory of deduction
Bonatti, L. (1994). Propositional reasoning by model? Psychological Review, 101, 725-733.
Evans, J. St. B. T.; Over, D. E.; Handley, S. J. (2005). Suppositions, extensionality, and conditionals: A critique of the mental model theory of Johnson-Laird and Byrne (2002). Psychological Review, Vol 112, 4, 1040-1052
Greene, S.B. (1992). Multiple explanations for multiply quantified sentences: are multiple models necessary? Psychological Review, 99, 184-187.
O’Brien, D.P., Braine, M.D.S., & Yang, Y. (1994). Propositional reasoning by mental models? Simple to refute in principle and in practice. Psychological Review, 101, 711-724.
A collection of criticisms is contained in the Behavioral and Brain Sciences open peer commentaries (pp. 334-380) following:
Johnson-Laird, P.N. & Byrne, R.M.J. (1993). Precis of Deduction. Behavioral and Brain Sciences, 16, 323-334.