Reasoning 629circle. Third, in some cases, the reasoner constructs alterna-
tive models of the information in order to verify (or disprove)
the conclusion drawn (Johnson-Laird, 1999; Johnson-Laird
& Byrne, 1991). For example, suppose that the reasoner had
been given a different assertion, such as that There is not a
circlein addition to the rule If there is a circle then there is
a square. This time, in order to verify the conclusion to be
drawn from the conditional rule plus this new assertion, the
reasoner would need to flesh out the implicit model indicated
in the ellipsis of the initial model. For example, according to
a material implication interpretation of the conditional rule,
he or she would need to flesh out the implicit model as
follows:
~❍❑
~❍ ~❑where ~ refers to negation.
By using the fleshed out model above, the reasoner would
be able to conclude that there is no definite conclusion to be
drawn about the presence or absence of a square given the as-
sertionThere is not a circleand the rule If there is a circle
then there is a square. There is no definite conclusion that can
be drawn because in the absence of a circle (i.e., ~ ❍), a
square may or may not also be absent. The first two steps in
mental model theory—the construction of an initial explicit
model and the generation of a conclusion—involve primarily
comprehension processes. The third step, the search for alter-
native models or the fleshing out of the implicit model, de-
fines the process of reasoning (Evans, Newstead, et al., 1993;
Johnson-Laird & Byrne, 1991).
The theory of mental models can be further illustrated
withcategorical syllogisms,which form a standard task
used in reasoning experiments (e.g., Johnson-Laird, 1994;
Johnson-Laird & Bara, 1984; Johnson-Laird & Byrne, 1991;
Johnson-Laird, Byrne, & Schaeken, 1992). Categorical syllo-
gisms consist of two quantified premises and a quantified
conclusion. The premises reflect an implicit relation between
a subject (S) and a predicate (P) via a middle term (M),
whereas the conclusion reflects an explicit relation between
the subject (S) and predicate (P). The set of statements below
is an example of a categorical syllogism.
ALL S are M
ALL M are P
ALL S are PEach of the premises and the conclusion in a categorical
syllogism takes on a particular form or mood such as All S are
M, Some S are M, Some S are not M,orNo S are M. The va-
lidity of syllogisms can be proven using either proof-
theoretical methods or, more commonly, a model-theoretical
method. According to the model-theoretical method, a valid
syllogism is one whose premises cannot be true without its
conclusion also being true (Garnham & Oakhill, 1994).
The validity of syllogisms can also be defined using proof-the-
oretical methods that involve applying rules of inference in
much the same way as one would in formulating a math-
ematical proof (see Chapter 4 in Garnham & Oakhill, 1994, for
a detailed description of proof-theoretical methods).
Mental model theory has been used successfully to ac-
count for participants’ performance on categorical syllogisms
(Evans, Handley, Harper, & Johnson-Laird, 1999; Johnson-
Laird & Bara, 1984; Johnson-Laird & Byrne, 1991). A num-
ber of predictions derived from the theory have been tested
and observed. For instance, one prediction suggests that par-
ticipants should be more accurate in deriving conclusions
from syllogisms that require the construction of only a single
model than from syllogisms that require the construction of
multiple models for their evaluation. An example of a single-
model categorical syllogism is shown below:Syllogism: ALL S are M
ALL M are P
ALL S are P
Model:S =M=Pwhere=refers to an identity function.
In contrast, a multiple-model syllogism requires that
participants construct at least two models of the premises in
order to deduce a valid conclusion or determine that a valid
conclusion cannot be deduced. Johnson-Laird and Bara
(1984) tested the prediction that participants should be more
accurate in deriving conclusions from single-model syllo-
gisms than from multiple-model syllogisms by asking 20 un-
trained volunteers to make an inference from each of 64 pairs
of categorical premises randomly presented. The 64 pairs of
premises included single-model and multiple-model prob-
lems. An analysis of participants’ inferences revealed that
valid conclusions declined significantly as the number of
models that needed to be constructed to derive a conclusion
increased (Johnson-Laird & Bara, 1984, Table 6). Although
numerous studies have shown that performance on multiple-
model categorical syllogisms is inferior to performance on
single-model categorical syllogisms, Greene (1992) has
suggested that inferior performance on multiple-model syllo-
gisms may have little to do with constructing multiple
models. Instead, Greene has suggested that participants may
find the conclusions from valid, multiple-model categorical
syllogisms awkward to express because they have the form