Reasoning by model: The case of multiple quantification.

Abstract

A theory of deductive reasoning is presented fora major class of inferences that has not been investigated by psychologists: inferences that depend on multiply-quantified premises (e.g., of the Princeton letters is in the same place as any of the Dublin letters). It is argued that reasoneis construct mental models based on their knowledge of the meanings of quantifiers (and other terms, including relational expressions). Three experiments corroborate the model theory's prediction that inferences that require the construction of only 1 model will be easier than those that require more than 1 model. The model theory assumes that the logical properties of quantifiers emerge from their meanings and are not mentally represented in rules of inference. How such a semantic process can occur compositionally (i.e., guided by the syntactic analysis of sentences) is described. Deductive reasoning is a process of thought that yields new information from old and aims to establish valid conclusions, that is, conclusions that are necessarily true given the truth of the initial premises or observations. The study of its underlying mental mechanisms is almost as old as experimental psychology, but remains a matter of controversy. There are three main views that have been proposed in both cognitive psychology and artificial intelligence. First, the reasoning mechanism depends on formal rules of inference; second, it depends on content-specific rules of inference; and, third, it depends on semantic procedures that search for interpretations (or models) of the premises that are counterexamples to conclusions. The principal goal of this article is to establish a theory of deductive reasoning for a major class of inferences that has not been investigated before by psychologists: those that depend on multiply-quantified premises. There are theories of relational reasoning and of syllogistic reasoning (i.e., from singly quantified premises), but multiple quantification is more powerful, and its logical analysis calls for the full resources of that branch of logic known as the first-order predicate calculus. In this article we develop a theory based on the manipulation of models and report experimental evidence that confirms this theory. An example of a multiply-quantified assertion is as follows: None of the artists is than any of the beekeepers. Such assertions contain a relational expression—here, a two-place relation, taller than; its arguments are quantified by such expressions as all, some, none, and any. These quantifiers behave in ways that are similar to the quantifiers of the firstorder predicate calculus, but there are other nonstandard