Reasoning about quantities

Here are some examples of “quantified” expressions:

• All of the musicians are students
• Some of the climbers are novices
• More than six of the musicians are drummers

How do people understand such statements? The theory of mental models proposes that people reason based on the construction of small-scale models of real or imagined situations. In reasoning about quantifiers such as those above,, the theory embodies the following principles:

1. Reasoners interpret quantifier assertions as “blueprints” for building models. The human parsing system uses the syntax of a sentence and the meanings of its words to compose a representation of the meaning of the assertion. These blueprint representations are used to build models.
2. Mental models are iconic: the structure of a model corresponds to the structure of what it represents. Iconicity allows inferences not directly asserted in the premises to emerge from a model.
3. Each model represents what is common to a distinct set of possibilities. A conclusion that holds in all the models of the premises follows of necessity, a conclusion that holds in at least some of these models is possible, and a conclusion that holds in none of them is inconsistent with the premises.
4. Two systems for reasoning exist: an intuitive and a deliberative system. The intuitive system constructs a single mental model at a time, whereas the deliberative system can search for alternative models.

A computational model implementing the model theory matches human data on how people reason about quantifiers: it explains syllogistic reasoning, immediate inferences, and set membership inferences.

Collaborators

Bruno Bara, Monica Bucciarelli, Ruth Byrne, Geoff Goodwin, Phil Johnson-Laird, Sangeet Khemlani, Philipp Koralus, Max Lotstein, Jane Oakhill, Marco Ragni, Mark Steedman

Representative papers

• Bara, B., Bucciarelli, M., & Johnson-Laird, P.N. (1995). The development of syllogistic reasoning. American Journal of Psychology, 108, 157–193.
• Johnson-Laird, P.N., & Steedman, M.J. (1978). The psychology of syllogisms. Cognitive Psychology, 10, 64–99.
• Johnson-Laird, P.N. (2006). How we reason. Oxford: Oxford University Press.
• Khemlani, S., & Johnson-Laird, P.N. (2012). Theories of the syllogism: A meta-analysis. Psychological Bulletin, 138, 427-457.
• Khemlani, S., & Johnson-Laird, P.N. (2021). Reasoning about properties: A computational theory. Manuscript in press at Psychological Review.
• Khemlani, S., Lotstein, M., Trafton, J.G., & Johnson-Laird, P. N. (2015b). Immediate inferences from quantified assertions. Quarterly Journal of Experimental Psychology, 68, 2073–2096.
• Ragni, M., Khemlani, S., & Johnson-Laird, P. N. (2014). The evaluation of the consistency of quantified assertions. Memory & Cognition, 42, 53-66.