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We propose a theory of immediate inferences from assertions containing a single quantifier, such as: All
of the artists are bakers; therefore, some of the bakers are artists. The theory is based on mental models and
is implemented in a computer program, mReasoner. It predicts three main levels of increasing difficulty:
(a) immediate inferences in which the premise and conclusion have identical meanings; (b) those in
which the initial mental model of the premise yields the correct conclusion; and (c) those in which
only an alternative to the initial model establishes the correct conclusion. These levels of difficulty
were corroborated for inferences to necessary conclusions (in a reanalysis of data from Newstead, S.
E., and Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square
of opposition. Journal of Verbal Learning and Verbal Behavior, 22, 535–546), for inferences to modal
conclusions, such as, it is possible that all of the bakers are artists (Experiment 1), for inferences with
unorthodox quantifiers, such as, most of the artists (Experiment 2), and for inferences about the consistency
of pairs of quantified assertions (Experiment 3). The theory also includes three parameters in a
stochastic system that predicted quantitative differences in accuracy within the three main sorts of