Phil Johnson-Laird and I have a new paper the describes a theory and computational model of how people reason about properties. The theory holds that people construct small-scale mental simulations of entities linked to their properties, and that the more mental simulations they build, the harder a problem will be. A computer model, mReasoner, simulates human reasoning across 200+ separate inferences. The theory is now out in Psychological Review, and its abstract is here:
We present a theory of how people reason about properties. Such inferences have been studied since Aristotle’s invention of Western logic. But, no previous psychological theory gives an adequate account of them, and most theories do not go beyond syllogistic inferences, such as: All the bankers are architects; Some of the chefs are bankers; What follows? The present theory postulates that such assertions establish relations between properties, which mental models represent in corresponding relations between sets of entities. The theory combines the construction of models with innovative heuristics that scan them to draw conclusions. It explains the processes that can generate a conclusion from premises, decide if a given conclusion is necessary or possible, assess its probability, and evaluate the consistency of a set of assertions. A computer program implementing the theory embodies an intuitive system 1 and a deliberative system 2, and it copes with quantifiers such as more than half the architects. It fit data from over 200 different sorts of inference, including those about the properties of individuals, the properties of a set of individuals, and the properties of several such sets in syllogisms. Another innovation is that the program accounts for differences in reasoning from one individual to another, and from one group of individuals to another: Some tend to reason intuitively but some go beyond intuitions to search for alternative models. The theory extends to inferences about disjunctions of properties, about relations rather than properties, and about the properties of properties.
You can read the full paper here.