I have a new chapter out that reviews how people use mental models to reason. You can read the chapter here, and the first couple paragraphs are available here:
The theory of mental models has a long history going back to the logic diagrams of C.S. Peirce in the nineteenth century. But it was the psychologist and physiologist Kenneth Craik who first introduced mental models into psychology. Individuals build a model of the world in their minds, so that they can simulate future events and thereby make prescient decisions (Craik, 1943). But reasoning, he thought, depends on verbal rules. He died tragically young, and had no chance to test these ideas. The current “model” theory began with the hypothesis that reasoning too depends on simulations using mental models (Johnson-Laird, 1980).
Reasoning is a systematic process that starts with semantic information in a set of premises, and transfers it to a conclusion. Semantic information increases with the number of possibilities that an assertion eliminates, and so it is inversely related to an assertion’s probability (Johnson-Laird, 1983, Ch. 2; Adams, 1998). And semantic information yields a taxonomy of reasoning. Deductions do not increase semantic information even if they concern probabilities, but inductions do increase it. Simple inductions, such as generalizations, rule out more possibilities than the premises do. Abductions, which are a special case of induction, introduce concepts that are not in the premises in order to create explanations (see Koslowski, this volume). The present chapter illustrates how the model theory elucidates these three major sorts of reasoning: deduction, abduction, and induction