The wording of conclusions
in relational reasoning
Jean-Baptiste Van der Hensta,*, Walter Schaekenb
aInstitut des Sciences Cognitive, CNRS, 67 Boulevard Pinel, Bron 69675, FrancebLaboratory of Experimental Psychology, Department of Psychology,
Tiensestraat 102, Leuven B-3000, Belgium
Received 9 February 2004; accepted 25 June 2004
Abstract
Literature on relational reasoning mainly focuses on the performance question. It is typically
argued that problem difficulty relies on the number of “mental models” compatible with the
problem. However, no study has ever investigated the wording of conclusions that participants
formulate. In the present work, we analyze the relational terms that people use in drawing
conclusions from spatial relation problems (A is to the left of B, B is to the left C, D is in front of
A, E is in front C, What is the relation between D and E?). We observed a general preference for
expressing conclusions with ‘left’ rather than conclusions with ‘right’. We also found that three
factors had an influence on the wording of the conclusions: the linguistic form of premises, the
question type and the presentation format. On the other hand, the number of models and premise
order did not affect the wording of conclusions. Our study shows that the type of conclusion
produced provides a new key to identifying the mental processes involved in spatial reasoning.
Implications for the two main approaches to reasoning processes (i.e. the analogical and the
propositional approaches) are discussed.
q 2004 Elsevier B.V. All rights reserved.
Keywords: Relational reasoning; Mental models; Spatial relations
Cognition 97 (2005) 1–22
www.elsevier.com/locate/COGNIT
0022-2860/$ - see front matter q 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cognition.2004.06.008
* Corresponding author.
E-mail addresses: [email protected] (J.-B. Van der Henst), [email protected]
(W. Schaeken).
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–222
Here is a typical problem used in tasks involving relational reasoning:
Problem I:
A is to the left of B
B is to the left of C
D is in front of A
E is in front of C
What is the relation between D and E?
How might this problem be solved? One possibility consists of building in one’s mind
an analogical representation, also called a mental model, which depicts the relations
described in the premises:
A B C
D E
From this representation one can immediately read-off the relation between D and E.
According to this approach, the information given in the premises is integrated in a single
representation format. The analogical representation is initially built on the basis of the
first premise and is incrementally updated each time a new premise is encountered.
Another possibility is to build a propositional representation for each premise (i.e. Left
(A,B); Left (B,C).). In contrast with the preceding account, each premise has its own
representation and is independently stored in memory. Once the premises are represented,
inference rules are applied to them until the required relation is derived (Hagert, 1984).
Here are examples of such rules:
Left (x, y) and Left (y, z)/Left (x, z)
Left (x, y)4Right (y, x)
Left (x, y) & Front (z, y)/Left (x, z)
In the 1960s and 1970s, these two approaches were respectively labeled the
‘analogical’ approach (DeSoto, London, & Handel, 1965; Huttenlocher, 1968) and
the ‘linguistic’ approach (Clark, 1969a,b) as they related to representational processes. In
the 1980s and 1990s, they were labeled the “mental model” (Byrne & Johnson-Laird,
1989; Johnson-Laird, 1983) and the “mental logic” approaches (Braine & O’Brien, 1998;
Hagert, 1984; Rips, 1994) and focussed more on inferential processes. According to the
mental model theory, problem difficulty is mainly related to the number of models
compatible with a given problem and according to mental logic or the propositional view,
it is mainly related to the length of the formal derivation. Numerous studies have
attempted to discriminate between these two views. To compare them, researchers have
relied on performance results (for reviews see Evans, Newstead, & Byrne, 1993, chap 6;
Johnson-Laird, 1972; Schaeken & Van der Henst, submitted; Van der Henst, 2002). These
considered the correctness of the conclusion or the response time. Factors related to
problem difficulty were also methodically investigated.
At the outbreak of the debate, both approaches led to similar predictions and were hardly
distinguishable at the empirical level (see Evans et al., 1993; Johnson-Laird & Byrne, 1991).
However, during the last decade a significant number of studies, following the work initiated
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 3
by Byrne and Johnson-Laird (1989), seemed to have definitely ruled out the propositional
approach to relational reasoning (Boudreau & Pigeau, 2001; Byrne & Johnson Laird,
1989; Carreiras & Santamaria, 1997; Roberts, 2000; Schaeken, Girotto, & Johnson-Laird,
1998; Schaeken & Johnson-Laird, 2000; Schaeken, Johnson-Laird & d’Ydewalle, 1996a,b;
Vandierendonck & de Vooght, 1997, 1998). In these studies, the authors claim that the
number of models compatible with a problem, but not the length of the formal derivation,
constitutes the relevant factor for predicting problem difficulty. Let us illustrate this point by
comparing Problem I presented above and Problem II presented below:
Problem II:
A is to the left of C
B is to the left of C
D is in front of B
E is in front of C
What is the relation between D and E?
Two different models are compatible with the set of premises given in Problem II and
both support the same conclusion that “D is to the left of E”:
A B C B A C
D E D E
The presence of two models comes from the indeterminacy of the relation between A
and B. Given that two models are harder to construct and maintain in working memory
than a single one, mental model theory predicts that subjects should err more on Problem II
than on Problem I.
Alternatively, the propositional approach is presumed to lead to the opposite prediction.
Inferring the relation between D and E in Problem I, requires the reasoner to ascertain the
relation between A and C. This relation has itself to be inferred by the application of a
transitivity rule to the first two premises: Left (A,B) & Left (B,C)/Left (A,C). On the
other hand, for Problem II, the relation between the items to which D and E are related
(i.e. B and C) does not need to be inferred since it is directly expressed in the second
premise. Hence, Problem II should require one less inferential step than Problem I and
should consequently be less difficult than Problem I. All the above-mentioned studies
confirmed mental model theory’s prediction against that of the propositional approach and
showed that Problem II generated more erroneous answers than Problem I. Such a result
has been viewed as one of the major findings supporting the mental model theory and there
is no recent empirical work from the propositional camp that advocates the propositional
view in the field of relational reasoning.
However, in a theoretical paper, Van der Henst (2002) holds that although the greater
difficulty of Problem I over Problem II nicely fits mental model theory, it could not be
considered as a decisive case against the rule approach. He argues that the opponents of the
propositional view only envisage the impact of indeterminate relations (i.e. the relation
between A and B in Problem II) from the model perspective but do not consider how it could
impair reasoning within a mental logic framework. The first two premises of Problem II
generate an indeterminacy regarding the relation between A and B so that the reasoner may
indeed construct two models. However, the opponents of the syntactic view do not envisage
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–224
that inference rules could be applied to the first premise which is actually irrelevant for
answering the question. Van der Henst (2002) argues first that reasoning on the basis of rules
should not preclude the application of rules to the first premise. Second, and more importantly,
he claims that if participants take this premise into account and reason on the basis of rules,
Problem II should result in at least as many inferential steps as Problem I. Moreover, some of
the intermediate conclusions inferred in Problem II should be harder to store since they will
have a disjunctive form while for Problem I intermediate conclusions will only be categorical
ones. For instance, the following rule could be applied to the first two premises of Problem II:
Left (X,Z) & Left (Y,Z)/Left (X,Y) OR Left (Y,X). It would thus result in a first
intermediate conclusion: “A is to the left B or B is to the left of A”. Such a conclusion would be
harder to store than the first intermediate conclusion for Problem I (i.e. “A is to the left of C”).
Problem II should thus be harder to solve than Problem I. Van der Henst concludes that both
approaches could equally account for the greater difficulty of Problem II over Problem I and
questions the relevance of performance data to distinguish the two views.
If measuring the difference of performance between determinate (e.g. Problem I) and
indeterminate problems (e.g. Problem II) is not suitable for contrasting both approaches,
then looking at other types of data might turn out to be valuable. In this paper we will
focus, not on the rates of correct responses as it is usually done, but on the wording of
conclusions that people draw. In the above examples, the answers “D is to the left of E”
and “E is to the right of D” are both correct since they are logically equivalent. But which
of these two conclusions do people actually formulate? How do the processes described by
the two sorts of theories contribute to account for the wording of the conclusions? In this
article, we want to show that taking into account this sort of data can reveal several
important mechanisms that occur in reasoning from spatial relational descriptions.
Moreover, we argue that the two approaches lead to different predictions regarding the
conclusions that people should formulate.
It is noteworthy that no study has ever investigated the type of conclusions that people
express in the domain of relational reasoning. It is rather surprising that psychologists of
reasoning have ignored this question since in another field of deductive reasoning, namely
reasoning involving quantifiers like “all”, “none”, and “some”, this issue was one of the
first to be investigated under the guise of the ‘atmosphere’ effect (Begg & Denny, 1969;
Woodworth & Sells, 1935). This effect, which has since been extensively explored (see
Evans et al., 1993 for review) refers to the fact that universal premises (All A are B)
prompt universal conclusions, particular premises (Some A are B) prompt particular
conclusions, affirmative premises prompt affirmative conclusions and negative premises
prompt negative conclusions. The atmosphere effect shows that some participants are
biased by superficial linguistic cues when formulating their own conclusions and tend not
to rest on logical reasoning. Consider the following problem:
Some A are B
Some B are C
What if anything follows?
The two premises are particular and affirmative. Empirical results reveal that many
individuals draw the particular and affirmative conclusion “Some A are C”. This conclusion
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 5
is actually erroneous since a situation where “no A are C” is true, is compatible with the
premises and contradicts the conclusion “Some A are C”. The only correct response to this
problem is “nothing follows”. Wetherick and Gilhooly (1990) also suggested that with two
different quantifiers in the premises, participants tend to make a conclusion which matches
the premise containing the most conservative quantifier: they will prefer “some”, “no” and
“some.not” to “all” and “no” to “some”.
In the field of propositional reasoning, Van der Henst, Yang, and Johnson-Laird (2002)
showed that the type of strategy that people develop in solving three-premise problems has
an effect on the wording of the conclusion that reasoners produce. Consider the following
example:
There is an A or else there is a B but not both,
There is a B if and only if there is a C,
There is a C or there is a D or both,
What if anything follows?
Faced with this type of problems, some participants developed a diagrammatic strategy
that consists in drawing a diagram representing all the possibilities compatible with the
premises. However, it is not easy to succinctly summarize this set of possibilities.
Participants thus described each possibility separately as a disjunct of a complex
disjunctive conclusion. For participants adopting this strategy, conclusions from the above
example were often like the following: “there is an A and a D or there is a B and a C, or
there is a B, a C and a D”. Alternatively, other participants adopted a strategy consisting of
making a supposition and deriving the intermediate conclusions following that
supposition. Such a strategy resulted in a small rate of disjunctive conclusions and in a
high rate of conditional ones (e.g. If there is an A then there is D).
In the field of relational reasoning, our primary aim is to investigate the process that
leads one to formulate a particular conclusion rather than another. In what follows, we will
make predictions on the basis of the two theoretical views above mentioned and we will
raise six questions addressing various aspects of cognitive processing that could have an
effect on the wording of the conclusions. On the first two issues, the analogical and
propositional approaches lead to distinct predictions. On the two subsequent questions, the
two accounts lead to the same predictions. Finally, for the last two questions, we focus on
the possibility that some characteristics of the task will favor the occurrence of
propositional processing, while others will favor the occurrence of analogical processing,
so that both types of processes could be jointly envisaged. The reasoning problems that we
will refer to and that our participants received appear in Table 1.
1. Is there an effect of the linguistic form of the premises?
According to mental model theory (Johnson-Laird, 1983; Mani & Johnson Laird,
1982), there are two stages in representing the premises that correspond to two different
stages of comprehension. The first stage consists of forming a propositional representation
that is close to the surface form of the sentence. The second stage consists of using that
Table 1
The 16 problems used in the experiment (the question is either “what is the relation between D and E?” or “What
is the relation between E and D?”)
(a) One-model problems
Pb1* Pb2* Pb3* Pb4* Pb5** Pb6** Pb7** Pb8**
A left B A left B B right A B right A A left B A left B B right A B right A
B left C C right B B left C C right B B left C C right B B left C C right B
D front A D front A D front A D front A E front C E front C E front C E front C
E front C E front C E front C E front C D front A D front A D front A D front A
(b) Two-model problems (first premise always irrelevant)
Pb9* Pb10* Pb11* Pb12* Pb13** Pb14** Pb15** Pb16**
A left B A left B B right A B right A A left B A left B B right A B right A
A left C C right A A left C C right A A left C C right A A left C C right A
D front A D front A D front A D front A E front C E front C E front C E front C
E front C E front C E front C E front C D front A D front A D front A D front A
The symbols ‘*’ and ‘**’ characterise respectively ‘type-1’ and ‘type-2’ problems.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–226
representation as a basis for constructing a mental model that is analogous to the situation
described in the premises. Forming a propositional representation is thus only a
prerequisite for building the mental model. The model representation of a premise requires
more effort than the propositional one (Johnson Laird & Bethell Fox, 1978) and
corresponds to a greater level of comprehension of that premise. However, once the model
is built, the propositional representation and the linguistic details of the premises tend to be
forgotten (Mani & Johnson Laird, 1982). The formulation of the conclusion relies only on
the model, which does not keep track of the relational expression (i.e. “to the left of”, “to
the right of”) involved in the premises. Hence, the relational term of the premises should
not be used more often than its contrary in formulating the conclusion. ‘Left–left’
problems, whose first two premises contain the term ‘left’ (problems 1–5–9–13 in Table 1)
should not prompt more ‘left’ conclusions than ‘right–right’ problems whose first two
premises contain the term ‘right’ (problems 4–8–12–16 in Table 1). In short, if participants
do construct mental models of the premises, the wording of the premises should have no
effect on the wording of the conclusions.
On the other hand, according to a strict propositional approach, the relational term of
the conclusion should be congruent with that of the premises. Indeed, the predicates used
in the inference rule will match those used in the premises. For instance, the rule ‘LEFT
(X,Y) & LEFT (Y,Z)/LEFT (X,Z)’ could be applied to the first two premises of Problem
1 (Left (A,B), Left (B,C)). The intermediate inference (Left (A,C)) and the final
conclusion (Left (D,E)) will, therefore, inherit the same relational term as those of the first
two premises. Consequently, ‘left–left’ problems should prompt more ‘left’ conclusions
than ‘right–right’ problems.
It also follows that the relational term of the conclusion will be more congruent with that
of a relevant premise than with that of an irrelevant premise. For all problems of Table 1b,
the first premise is irrelevant in answering the question about the relation between D and E.
Though an irrelevant premise is likely to be processed and to impair reasoning (Van der
Henst, 2002), it cannot lead to the inference of the conclusion mentioned in the question.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 7
The derivation of the conclusion will result from the application of an inference rule to the
relevant premise. Problems 11 and 15 (see Table 1b), which contain an irrelevant premise
with ‘right’ and a relevant premise with ‘left’, should then prompt more ‘left’ conclusions
than Problems 10 and 14 (see Table 1b), which contain an irrelevant premise with ‘left’ and a
relevant premise with ‘right’.
Let us note that the assumption we described is close to the principle of congruence
developed by Clark (1969a) in his ‘linguistic’ model. According to this principle,
retrieving an information in memory is easier when the question is congruent to that
information than when it is incongruent. For instance, in the context of the premises “A is
taller than B, B is taller than C”, the question “who is the tallest?” will be easier to answer
than the question “who is the smallest?” The reason is that the premises are represented
with the adjective “tall” and the former question requires for information containing the
same adjective, whereas the latter question requires for information that is not
immediately available in the premises’ representation.
2. Is there an asymmetry effect?
There are two possibilities to describe a relation between a pair of items. In the given
examples, one could correctly answer the questions with either “D is to the left of E” or “E
is to the right of D”. Will participants have a general preference, other things being equal,
for one relational expression over the other? What cognitive principles could be
responsible for such an asymmetry, if any? The analogical and the propositional
approaches both make different predictions about this issue.
One of the core principles of Clark’s linguistic theory (1969a) is the principle of
linguistic marking. It stipulates that some relational expressions are cognitively less
complex than their opposites. The less complex terms are said to be unmarked, like “good”,
“long” and “wide”, and the more complex ones are said to be marked, like “bad”, “short” and
“narrow”. The main difference is that, in contrast with marked terms, unmarked terms can be
used in a neutral context. For instance, when a speaker says “John is better than Pete”, she/he
does not necessarily make any presupposition about the “goodness” of John and Pete, and
such a statement would be perfectly acceptable if John and Pete were both very bad.
However, if she/he says “Pete is worse than John”, she/he presupposes that both Pete and
John are quite bad, and such a statement would be inappropriate if Pete and John were both
very good. Carrying a presupposition endows marked terms with a greater complexity than
unmarked ones and Clark (1969a) argues thus that the sense of marked terms is less
immediately accessible than those of unmarked ones. It follows that individuals would be
more likely to use unmarked terms than marked ones.
Clark (1973; see also Chase & Clark, 1971, 1972) also referred to a principle of lexical
marking for spatial terms. According to Clark, the structure of space determines to a large
extent the linguistic structure of spatial terms. Consequently, the properties of perceptual
space coincide with the properties of spatial terms. Unequivocal asymmetries occur in the
perception of space and are linked to the organization of the human body. For instance,
perceptual stimuli are easier to process when they occur in front of the body rather than
when they occur in back. Moreover, objects located above the ground level are easier to
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–228
detect than objects located below. Forwardness and upness are thus the positive, or
standard, directions in the perception of space. Interestingly, psycholinguistic studies
revealed that asymmetries in processing spatial terms do occur and parallel perceptual
asymmetries. In particular, Chase and Clark (1971, 1972) showed that the terms “above”
and “front” were easier to process than the terms “below” and “back” respectively, in the
context of sentence picture verification task.
Clark also underlined that symmetry occurs in the perception of space: “the reference
plane separating left from right is symmetrical, and therefore, there appears to be no
reason, at least perceptually, to choose either leftward or rightward as being the positive
direction” (Clark, 1973, p. 33). One can thus predict that the terms ‘left’ and ‘right’ should
have the same degree of linguistic complexity. From such a view, it follows that the
occurrence of “left” and “right” conclusions should be roughly equal in the problems we
gave our participants. However, Olson and Laxar (1973) did observe an asymmetry in
processing the terms ‘left’ and ‘right’ and found that the term ‘right’ was easier to process,
and was said to be the unmarked term, than the term “left”, which was said to be the
marked term. They linked this linguistic asymmetry to the fact that most people are right-
handed so that ‘right’ is linguistically less complex than ‘left’. Consequently, participants
should be less inclined to formulate a ‘left’ conclusion than a ‘right’ conclusion. In short,
the propositional account predicts that participants should either have no preference or
should have a preference for “right” conclusions.
However, other factors than the linguistic complexity of the relational terms are prone
to elicit a left–right asymmetry. If people construct a mental model, the prevalence of one
relational expression may reveal the “direction towards which” individuals scan the model
they constructed. If they scan their model in a ‘left-to-right’ direction, and describe the
conclusion while they do the scanning, they will be likely to make a ‘left’ conclusion since
the first element they encounter, which is likely to be the first element mentioned in the
conclusion, is on the left part of the model. Alternatively, if participants scan their model
in a ‘right-to-left’ direction, they will be likely to make a ‘right’ conclusion.
Numerous studies from different fields of cognitive science have shown that reading
and writing habits are responsible for directional scanning biases in various visuo-spatial
tasks. DeSoto et al. (1965) observed that when their participants (who were left-to-right
readers) had to represent premises like ‘A is lighter than B’, ‘B is lighter than C’ by
ordering A, B, C items along a horizontal line, they exhibited a directional preference for
proceeding from left to right rather than from right to left. Vaid, Singh, Sakhuja, and Gupta
(2002) investigated the influence of reading habits on the direction of stroke movement in
drawing figures. They observed that readers of Urdu, who read from right to left, drew the
figures in right-to-left direction, while readers of Hindi, who read from left to right, did not
show such a bias. In Nachshon, Shefler, and Samocha’s study (1977) left-to-right readers
of English recalled horizontally presented figures in a left-to-right way while right-to-left
readers of Hebrew exhibited an opposite pattern. A similar directional scanning effect was
also obtained by Padakannaya, Devi, Zaveria, Chengappa, and Vaid (2002) in naming and
recall tasks with Arabic right-to-left readers and Kannada left-to-right readers. In a line
extension task, Chokron, Bernard, and Imbert (1997) also observed that French left-to-
right readers had greater troubles in completing a half-line, in order to obtain a whole line,
when they proceed in the right-to-left direction than in the left-to-right direction.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 9
In contrast, Israeli right-to-left readers did not exhibit such a bias (see also Singh, Vaid, &
Sakhuja, 2000). Finally, in an eye movement study Abed (1991) showed that left-to-right
readers (Western subjects) had the highest number of left-to-right eye movements when
they observed visual stimuli while right-to-left readers (Middle eastern participants) had
the highest number of right-to-left movements. This set of studies suggests that reading
habits strongly influence scanning direction1. It follows that if our participants, who were
left-to-right readers construct a mental model of the premises, they are likely to inspect it
from left to right and if their conclusion reflect this preferential scanning, they should
produce more ‘left’ conclusions than ‘right’ conclusions.
3. Is there an effect of the question?
Another factor that might govern the direction of model inspection is the question. The
question given in the above examples (What is the relation between D and E?) initially
directs attention to the left side of the models since ‘D’ is mentioned first in the question
and is located on the models’ left side. Consequently, such a question is likely to induce a
‘left-to-right’ inspection and a ‘left’ conclusion. Inversely, the question “What is the
relation between E and D?” is less likely to induce a ‘left’ conclusion.
As suggested by an anonymous reviewer, this prediction is actually not specific to the
analogical approach and it can also be derived from the propositional account. One may
indeed argue that, for simplicity reasons, there is a correspondence between the syntactic order
in which the terms D–E appear in the question and the order in which they appear in the
conclusion. The question “what is the relation between D and E?” should thus induce con-
clusions with D as a subject (i.e. “D is to the left of E”) and the question “what is the relation
between E and D” should prompt conclusions with E as a subject (i.e. “E is to the right of D”).
4. Is there an effect of premise order?
The order in which the items are inserted within the model might direct model-
inspection. If the premise containing ‘D’ is provided before the premise containing ‘E’,
then ‘D’ will be inserted before ‘E’ in the model and the construction of the D–E line will
proceed from left to right (granted that D is to the left of E as in all problems of Table 1).
Payne (1993) has shown that people tend to keep track of the construction process of the
analogical representation in long-term memory. One can extend this approach and
speculate that keeping track of the construction process may induce people to scan their
model in the direction of its construction. In other words, Type-1 problems (see Table 1)
for which the premise introducing ‘D’ occurs before the premise introducing ‘E’ should
generate more ‘left’ conclusions than Type-2 problems (see Table 1) for which the last two
premises occur in a reverse order.
1 A great piece of evidence showing the influence of reading habits on scanning direction also comes from line
bisection tasks (see Fischer, 2001; Jewell & McCourt, 2000 for reviews).
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2210
Again this prediction is not specific to the analogical view and one could argue that the
syntactic order of the D–E items within the conclusion will follow the order in which the
terms are introduced by the premises. As a result, if the premises introduce D before E,
then D will be subject of the conclusion: “first in, first out”.
5. Is there an effect of indeterminacy?
We earlier mentioned that the proponents of mental model theory compared
determinate and indeterminate problems to ascertain that multiple-model problems were
harder to solve than single-model problems. However, Mani and Johnson Laird (1982);
see also Johnson-Laird, 1983) also used this comparison to show the existence of two
levels of representation: the propositional level and the analogical level (see our first
question). For an indeterminate description there is a need to construct not one but several
mental models in order to correctly represent its meaning. The attempt to construct several
models may overload working memory capacities so that no models would be constructed.
It follows that people are more prone to stay at the propositional level of representation
when dealing with indeterminate descriptions (Johnson-Laird, 1983). In line with this
proposal, Mani and Johnson Laird (1982) observed a crossover effect: On one hand,
participants recalled more linguistic details for indeterminate descriptions than for
determinate ones; on the other hand, they were better at remembering the gist of
determinate descriptions than the gist of indeterminate ones.
According to such a mix-approach, effects linked to a propositional representation
should more frequently occur with indeterminate problems than with determinate ones.
The relational term used in the conclusion could thus be more often congruent with the one
used in the premises for two-model problems than for one-model problems: ‘Left–left’
two-model problems should prompt more ‘left’ responses than ‘left–left’ one-model
problems and ‘right–right’ two model-problems should prompt more ‘right’ responses
than ‘right–right’ one-model problems. Moreover, a left-to-right scanning and ‘left’
conclusions are also less likely to occur for multiple-model problems.
However, Payne (1993) failed to replicate the crossover effect reported by Mani and
Johnson-Laird. Actually, Payne used a more accurate control of gist memory in his
experiments. It might thus be that one-model problems do not induce more analogical
processing than two-model problems. If so, the effects linked to a propositional representation
should not occur more often for indeterminate problems than for determinate ones.
6. Is there an effect of presentation format?
The presentation format might also have an effect on the type of representation
involved (Ormrod, 1979; Potts & Scholz, 1975; Roberts, 2000; Schaeken & Johnson-
Laird, 2000) and, consequently, on the type of conclusion formulated. With simultaneous
presentation, all premises are presented together with the question and remain available
during the task. Sequential presentation places more load on working memory:
the premises are presented one at a time and disappear with the arrival of a new premise
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 11
or the question. It has been argued (Ormrod, 1979) that an analogical representation is
more likely to occur with a sequential presentation. The reason is that with a propositional
representation each relation—given in the premises or inferred from them—is stored
separately whereas with a model representation, all relations are integrated within a single
representational format. Thus, when working memory load increases it becomes harder to
keep track of all the premises and inferences separately; a mental model becomes a more
efficient and concise mode of representation. Hence, according to this mix-approach,
fewer conclusions with a relational term congruent with that of the premises would be
produced for the sequential presentation than for the simultaneous one. Moreover, one
could expect a greater asymmetry effect (i.e. a higher rate of ‘left’ conclusions) with a
sequential presentation than with a simultaneous one.
Table 2 summarizes the predictions described in the forgoing issues.
6.1. Experiment
6.1.1. Participants
The participants were 174 first-year psychology students from the University of
Leuven.
6.1.2. Design
Participants received 16 problems: eight one-model problems (Table 1a) and eight two-
model problems (Table 1b). In half of the problems, the first two premises had the same
Table 2
Expected effects according to the theoretical perspectives
Linguistic form
of the premises
Asymmetry Question Premise order
Propositional
approach
Congruence
between the
relation used in the
premises and that
of the conclusion
If any, preference for
“right” conclusions
The first item of the
question should be
the subject of the
conclusion more
often than the
second item
The order of the
two elements in the
conclusion should
more often reflect
premise order than
the opposite order
Analogical
approach
No effect Preference for “left”
conclusions
Same prediction
as above
Same prediction
as above
Mix-approacha Congruence effect
for indeterminate
problems and
simultaneous
presentation
If any, preference for
“right” conclusions for
indeterminate pro-
blems and simul-
taneous presentation
Same prediction
as above
Same prediction
as above
No effect for
determinate pro-
blems and sequen-
tial presentation
Preference for “left”
conclusions for deter-
minate problems and
sequential presen-
tation
a A mix-approach assumes that both analogical and propositional processes contribute to the wording of
conclusions but that the prevalence of one over the other depends upon task’s features.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2212
relational term (i.e. ‘left–left’ and ‘right–right’ problems); in the remaining half, the first
two premises had different relational terms (i.e. ‘left–right’ and ‘right–left’ problems).
Moreover for half of the problems (Type-1 problems), the premise introducing the item
located on the left (i.e. ‘D’) was given before the premise introducing the item located on
the right (i.e. ‘E’; Problems 1–4 and 9–12). For the other half (Type-2 problems), this
presentation order was reversed (Problems 5–8 and 13–16).
There were two between-participant manipulations. One concerned the presentation:
participants received the problems either in a simultaneous presentation format or in a
sequential one. The other concerned the first item mentioned in the question, which was
either the item mentioned in the third premise (i.e. “what is the relation between D and E?”
for Type-1 problems and “what is the relation between E and D?” for Type-2 problems) or
the item mentioned in the fourth premise (i.e. “what is the relation between E and D?” for
Type-1 problems or “what is the relation between D and E?” for Type-2 problems).
6.1.3. Procedure and materials
Participants were tested in groups of 12–20 individuals. The instructions and the
problems were displayed on a screen via a data projector. Participants received 2 training
problems and 16 randomly ordered test problems with contents relating to vegetables. In
the simultaneous conditions, each problem was displayed for 50 s. In the sequential
conditions, each premise and the question appeared for 10 s. Participants wrote their
responses on an answer sheet.
6.1.4. Results
Performance was in line with the relational reasoning literature: One-model problems
were easier to solve than two-model problems (83 vs. 73%, Wilcoxon’s TZ1787, nZ131,
P!0.00001). Moreover, as one could have expected, performance was higher for the
simultaneous condition (81% of correct answers) than for the sequential condition (75% of
correct answers Mann–Whitney UZ3139,5, n1Z92, n2Z82, P!0.05). Overall, there
were 58% of ‘left’ conclusions, 29% of ‘right’ conclusions and 13% of indefinite answers
(“nothing follows”, “I don’t know”, “D and E are next to each other”.). The preference
for ‘left’ conclusions suggests that mental models are constructed and are scanned in a
‘left-to-right’ direction. The rates of ‘left’ conclusions were roughly equal in both the
simultaneous and sequential conditions (59 vs. 58%). We examined the influence of the
above-listed factors on the conclusions’ wording by means of a MANOVA 2 (presentation
format)!2 (type of question)!2 (determinacy of problems)!2 (premise order)!4
(wording of the premises) design. The percentages of ‘left’ responses are displayed in
Table 3. The analysis we performed took into account both correct and incorrect answers
but we also made a non-parametric statistical analysis in which we discarded the wrong
answers (see Van der Henst and Schaeken, 2002) and the results remained in line with the
present findings.
First, there was a significant main effect of the wording of the premises (F (3, 510)Z6.771, P!0.0001), which boils down to more ‘left’ responses (64%) when the two first
premises contained ‘left’ (‘left–left’ problems) than when the two first premises contained
‘right’ (‘right–right’ problems, 52%). Moreover, there was a significant interaction
between the wording of the premises and presentation format (F (3, 510)Z4.198,
Table 3
Percentage of ‘left’ answers for the 16 problems
(a) One-model problems
Presentation Question Pb1*
A left B
B left C
D front A
E front C
Pb2*
A left B
C right B
D front A
E front C
Pb3*
B right A
B left C
D front A
E front C
Pb4*
B right A
C right B
D front A
E front C
Pb5**
A left B
B left C
E front C
D front A
Pb6**
A left B
C right B
E front C
D front A
Pb7**
B right A
B left C
E front C
D front A
Pb8**
B right A
C right B
E front C
D front A
Simultaneous D–E? for type–1
E–D? for type–2
77.5 80 72.5 72.5 72.5 57.5 55 47.5
Simultaneous E–D? for type–1
D–E? for type–2
55.8 67.3 40.4 48.1 82.7 73.1 69.2 44.2
Sequential D–E? for type–1
E–D? for type–2
77.8 88.9 69.4 72.2 61.1 44.4 50 50
Sequential E–D? for type–1
D–E? for type–2
43.5 39.1 32.6 45.7 65.2 78.3 71.7 60.9
(b) Two-model problems (first premise always irrelevant)
Presentation Question Pb9*
A left B
A left C
D front A
E front C
Pb10*
A left B
C right A
D front A
E front C
Pb11*
B right A
A left C
D front A
E front C
Pb12*
B right A
C right A
D front A
E front C
Pb13**
A left B
A left C
E front C
D front A
Pb14**
A left B
C right A
E front C
D front A
Pb15**
B right A
A left C
E front C
D front A
Pb16**
B right A
C right A
E front C
D front A
Simultaneous D–E? for type–1
E–D? for type–2
70 50 77.5 55 60 40 45 35
Simultaneous E–D? for type–1
D–E? for type–2
55.8 50 53.8 50 73.1 46.2 67.3 42.3
Sequential D–E? for type–1
E–D? for type–2
77.8 61.1 83.3 66.7 58.3 58.3 55.6 50
Sequential E–D? for type–1
D–E? for type–2
28.6 41.3 34.8 47.8 69.6 63 58.7 67.4
The symbols ‘*’ and ‘**’ characterize, respectively, ‘type-1’ and ‘type-2’ problems.
J.-B.
Va
nd
erH
enst,
W.
Sch
aeken
/C
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nitio
n9
7(2
00
5)
1–
22
13
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2214
P!0.01). In the simultaneous condition, ‘left–left’ problems elicited more ‘left’
conclusions than ‘right–right’ problems (68 vs. 48%, F (1, 170)Z26.196, P!0.0001),
but in contrast, in the sequential condition there was no influence of the premises’ wording
since the rate of ‘left’ conclusions was essentially the same in both types of problems
(60% for ‘left–left’ problems vs. 58% for ‘right–right’ problems).
Similarly, for indeterminate problems, which all rely on an irrelevant premise, the
findings indicated that in the simultaneous condition participants were prone to
formulating conclusions congruent with the relevant premise: there were 61% of ‘left’
conclusions when only the relevant premise contained the term ‘left’ while there were 45%
of ‘left’ conclusions when only the relevant premise contained the term ‘right’ (F (1,
170)Z8.437, P!0.005). However, given sequential presentation, participants were not
really inclined to formulate a conclusion congruent with the relevant premise (58% of
“left” answers for “left-relevant” problems vs. 56% for “right-relevant” problems). This
set of results indicates that when the premises were not available, participants were not
inclined to use the relational term of the premises more than its contrary.
The question did influence the wording of the premises. This is revealed by the
significant interaction between the question and problem type (F (1, 170)Z64.239,
P!0.0001), meaning that with ‘left-to-right’ questions (D–E?) there were more ‘left’
conclusions (68%) than with ‘right-to-left’ questions (E–D?; 49%). Interestingly, the
extent to which the question influenced the incidence of ‘left’ conclusions depended on
presentation format as indicated by a three-way interaction (question!problem type!presentation format, F (1, 170)Z5.083, P!0.05). Given the ‘left-to-right’ question (that a
part of participants received for Type-1 problems and the other for Type-2 problems),
simultaneous presentation gave rise to 65% of ‘left’ conclusions while sequential
presentation led to 71% of ‘left’ conclusions. For the ‘right-to-left’ question (that a part of
participants received for Type-1 problems and the other for Type-2 problems),
simultaneous presentation gave rise to 52% of ‘left’ conclusions and sequential
presentation resulted in 46% of ‘left’ conclusions. The bias induced by the question is
thus enhanced by a sequential presentation.
One might have expected that when the premises provide the left-side item before the right-
side item (i.e. when D is given before E as for Type-1 problems), more ‘left’ conclusions
would occur than in the reverse presentation order (i.e. when E is given before D as for Type-2
problems). This was not the case since there was no main effect of premise order: There were
59% of ‘left’ conclusions for Type-1 problems and 58% for Type-2 problems.
There was a significant interaction between the wording of the premises and premise
order (F(3, 510)Z4.03, P!0.01): While there were significantly more ‘left’ responses to
‘left–left’ Type-2 problems (68%) than to ‘right–right’ Type-2 problems (49%) this
difference, although in the same direction, was not significant for Type-1 problems (61 vs.
57%). There were no differences on the ‘left–right’ and ‘right–left’ problems.
There was a main effect of the number of models (i.e. the indeterminacy): more ‘left’
responses were observed with one-model problems than with two-model problems (61 vs.
56%; F (1, 170)Z10.610, P!0.005). However, as we indicated at the beginning of this
section, the number of models significantly influences performance: two-model problems
are harder and are consequently more likely to elicit indefinite responses (e.g. “nothing
follows”, “I don’t know”, “D and E are next to each other”.) than one-model problems.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 15
In fact, the greater rate of ‘left’ responses for two-model problems than for one-model
problems does not result from a greater tendency to follow a left-to-right scanning for one-
model problems but can rather be explained by the higher rate of indefinite answers
for two-model problems than for one-model problems (16,6 vs. 9.6%) F(2, 172Z49,77,
P!0.0005). If we discard those answers, the proportions of ‘left’ answers for one-model
and two-model problems are actually similar (66.9 and 67%).
Moreover, although there was a significant interaction between the number of models
and the wording of the premises (F (3, 510)Z4.949, P!0.005), the number of models did
not affect the congruence between the wording of the premises and that of the conclusion as
it could have been hypothesized: there was no significant difference between ‘left–left’ one-
model problems and ‘left–left’ two-model problems regarding the rate of ‘left’ answers (68
vs. 62%) nor was the difference between ‘right–right’ one-model problems and ‘right–right’
two-model problems (55 vs. 51%). The difference between ‘right–left’ one-model problems
and two-model problems was not significant either (57 vs. 60% of ‘left’ conclusions).
Hence, the interaction is caused by the difference between ‘left–right’ one-model and ‘left–
right’ two-model problems (66 vs. 51%; F (1, 170)Z26.013, P!0.0001). This difference
can be explained by the presence of a ‘right’ relevant premise for ‘left–right’ two-model
problems. Hence, in contrast with what could have been expected on the basis of Mani and
Johnson-Laird’ study (1982), the number of models did not seem to affect the type of the
processing involved. We will come back to this point in the general discussion.
Finally, one effect remains to be explained: the number of models significantly
interacted with presentation format (F (1, 170)Z4.729, P!0.05). There were more ‘left’
responses to one-model problems than to multiple-model problems in the simultaneous
condition (63 vs. 54%), but not in the sequential condition (59 vs. 58%).
In order to give a more complete account of the data, we decided to look for individual
differences. As it appears in the description of the predictions (see also Table 2), the
different factors susceptible of influencing the wording of the conclusions are not
independent: They often point to the same answer: a ‘left’ response to a ‘left–left’ one-
model problem is expected on the basis of a congruence effect, on the basis of a preference
for ‘left’, on the basis of a D–E question and on the basis of a Type-1 premise order. For
other problems, these factors predict another answer or do not result in precise predictions.
Consequently, it is impossible to distinguish participants who are completely in line with
the propositional approach from those who are in line with the analogical one across the
sixteen problems. However, for six out of the 16 presented problems, the two approaches
make opposite predictions, so that we can actually categorize participants on the basis of
these six problems, and see the proportions of participants who exhibit a pattern of answers
in line with the propositional approach and those who exhibit a pattern of answers in line
with the analogical approach. Indeed, for Problems 4, 8, 10, 12, 14 and 16 (see Table 1),
participants who adopt a propositional strategy should express ‘right’ conclusions (due to
the congruence effect) whereas those who adopt an analogical strategy should express
‘left’ conclusions (due to a ‘left-to-right’ scanning effect). Participants who formulated
a ‘right’ conclusion for at least four of these problems were categorized as
“propositionalists” and those who formulated a ‘left’ conclusion for at least four of
these problems were categorized as “analogists”. In the simultaneous condition, 27% were
propositionalists, 38% were analogists and 35% could not be classified in either one of
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2216
these two categories. In the sequential condition 6% were propositionalists, 55% were
analogists and 39% and could not be classified in either one of these categories. The
proportions of participants in each category of answers differed across the two conditions.
In particular, there were significantly more propositionalists in the simultaneous condition
than in the sequential one (c2(1)Z13.5, P!0.05) and there were significantly less
analogists in the simultaneous condition than in the sequential one (c2(1)Z4.95,
P!0.05).2 This allowed us to see if performance differed according to the strategy
participants adopted. In the simultaneous condition, the propositionalists produced 86% of
correct answers to the 16 problems and the analogists produced 88% of correct answers,
which is not different from each other. In the sequential cond‘ition however,
propositionalists produced more correct answers than analogists (88 vs. 83%; Mann–
Whitney UZ62,5, n1Z45, n2Z5, P!0.05). However, given the very low number of
propositionalists in this condition, this significant difference is hard to interpret.
Finally, we inspected the data obtained across the 16 presented problems and looked for
participants who exhibited a pattern of answers that follow almost perfectly the predictions
of the different factors we pointed out. The most consistent pattern is that of a preference for
‘left’ responses. There are 14 participants (out of 174) who formulated a ‘left’ answer at
least 15/16 times and 5 who formulated a ‘right’ answer at least 15/16 times. Interestingly,
11 of the 14 ‘left’ responders were in the sequential condition. There are definitely less
consistent responses in terms of the other factors. Five participants (out of 174) answered at
least 15/16 times according to what one can expect on the basis of the question effect (that
is, the first item of the question is the subject of the conclusion). Only 1/174 people
answered at least 15/16 times according to what one can expect on the basis of a premise
order effect (that is, the order of the two elements in the conclusion reflects premise order).
We also inspected portions of the 16 problems and looked for consistent patterns. In
particular, we inspected heterogeneous problems (i.e. problems whose first two premises
have different relational terms: ‘left–right’ and ‘right–left’ problems) separately. There are
only 5/174 participants who answered at least 7/8 problems with ‘right’, whereas there are
36/174 participants who answered at least 7/8 times with ‘left’ (19 in the sequential
condition and 17 in the simultaneous condition). We inspected homogeneous problems
(i.e. ‘left–left’ and ‘right–right’ problems) and we observed that 32/174 participants
produced ‘left’ answers to the premises at least 7/8 times, whereas only 5/174 participants
produced ‘right’answers at least 7/8 times.
7. General discussion
Our study is the first to analyze the wording of the conclusions people draw in spatial
reasoning. It brings a new set of data in a field where performance is the main variable
2 If we adopt a more stringent criterion (five instead of four ‘right’ conclusions for the propositionalist category
and five instead of four ‘left’ conclusions for the analogist category), 15% of the participants in the simultaneous
condition and 1% in the sequential condition could be categorized as propositionalists (c2(1)Z10.78, P!0.001).
Moreover, 25% of the participants could be categorized as analogists in the simultaneous condition and 22% in
the sequential condition.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 17
investigated. While analyzing answers’ correctness and response time for determinate and
indeterminate problems might be of limited scope for contrasting the analogical and
propositional approaches (Van der Henst, 2002), the present study illustrates that much
can be learned from a qualitative analysis of the answers’ formulation. We have shown
that the wording of conclusions exposes several psychological mechanisms and we now
discuss them by coming back to the six questions we raised in the introduction.
First, we asked if the linguistic form of the premises could influence the wording of the
conclusions. The propositional account predicts that there should have a congruence effect
between the relational expression used in the conclusion and that used in the premises
while the analogical approach predicts that there should have no effect. The data exhibit an
interesting picture. On one hand, the congruence was definitely present: more ‘left’
conclusions were obtained with ‘left–left’ problems than with ‘right–right’ problems in the
simultaneous condition. Furthermore, when focusing on problems containing an
irrelevant premise, the data indicated that the conclusion was congruent with that of the
relevant premise but not with that of the irrelevant one: ‘left’ relevant problems (the
relevant premise with ‘left’ and the irrelevant premise with ‘right’) generated more ‘left’
conclusions than ‘right’ relevant problems (the relevant premise with ‘right’ and the
irrelevant one with ‘left’). This shows that the congruence effect does not result from a
superficial linguistic processing leading to more ‘left’ conclusions when ‘left’ premises,
whatever their relevance, have been encountered; participants did identify the relevant
premise and based their conclusions on this premise. This congruence effect supports the
propositional account and challenges the analogical one.
However, the congruence effect was not observed when participants received the
problems in the sequential condition: there was not significantly more ‘left’ conclusions with
‘left–left’ problems (and ‘left’ relevant problems) than with ‘right–right’ problems (and
‘right’ relevant problems). The absence of a congruence effect with a sequential presentation
corroborates this time the analogical account and challenges the propositional one.
These two opposite patterns of answers first show that presentation format has an
impact on the wording of conclusions and second that both analogical and propositional
processes determine the way people express their conclusions. Consequently, a simple
theoretical model cannot account for the diversity of these data. A mix-approach that
integrates both types of processes is necessary (see below).
The second question concerned the presence of an asymmetry effect. The propositional
approach assumes that some relational terms can be linguistically more complex than their
opposites. One can either hold that ‘right’ is less complex than ‘left’ (given that ‘rightness’
is the positive direction for right-handed people) or that ‘left’ and ‘right’ are equally
complex (given the symmetry of the reference plane separating left from right). It follows
that there should either be no asymmetry or a tendency to formulate ‘right’ conclusions.
On the other hand, if people build an analogical representation, directional scanning biases
can affect the wording of the conclusion. Many studies ascertained that scanning direction
matches reading habits. Given that our participants were ‘left-to-right’ readers, one may
expect that they will scan their mental model in the left-to-right direction and will tend to
formulate ‘left’ conclusions.
The data were in line with the last account since we observed more ‘left’ conclusions
than ‘right’ conclusions. Interestingly, while the simultaneous presentation tended to elicit
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2218
more propositional processing than the sequential one (see the first question), we,
however, observed a clear preference for ‘left’ conclusions with the simultaneous
presentation. This seems to indicate that analogical processes occur not only in the
sequential condition but also in the simultaneous one. However, the asymmetry effect does
not necessarily contradict the thesis that ‘right’ is less ‘complex’ than ‘left’ or that they are
both equally complex but it contradicts the view that the linguistic complexity of those
terms has an impact on the wording of conclusions.
The third issue addressed the influence of the question. Whatever the theoretical
approach adopted, when the question is “what is the relation between D and E?”, the
conclusion is more likely to have D as a subject and ‘left’ as a relational term than when the
question is “what is the relation between E and D?”. This is exactly what we observed: there
were more ‘left’ conclusions for “D–E?” than for “E–D?” Moreover, the effect of the
question was stronger in the sequential condition than in the simultaneous condition. The
question had thus a stronger influence in a condition where analogical processing is favored.
The fourth question concerned the presence of a premise order effect. We did not
observe such an effect. There were not more conclusions with D as a subject (i.e. ‘left’
conclusions) when the premises introduced D before E than when they introduced E before
D. This does not however mean that premise order could not have any effect at all. Given
that the question has a strong influence, we might have observed a premise order effect
with less compelling questions. Instead of the questions we asked, which introduce an
order between D and E, one possibility would be to ask questions like “what is the relation
between the last two items introduced?” In such a situation, the question cannot affect the
wording of the conclusion and one might observe a premise order effect.
The fifth issue concerned the presence of an indeterminacy effect. We tested the
prediction that determinate problems should favor more the construction of mental models
than indeterminate ones. The reason is that in order to represent indeterminate problems
several mental models have to be constructed. However, the construction of several
models is more complicated than the construction of a single model (as for determinate
problems) so that reasoners may stay at a propositional level of processing when dealing
with indeterminate problems. We did not observe effects corroborating this view. First,
there was not a greater influence of the linguistic form of the premises with indeterminate
problems than with determinate ones. Second, there was not a higher asymmetry for ‘left’
with determinate problems than with indeterminate ones. This suggests that analogical
processing is likely to occur even with indeterminate problems. This is in line with Payne’s
study (1993) in which the remembering of linguistic details was not higher for determinate
problems than for indeterminate ones. Hence, it might be argued that the processing of
one-model problems is not radically different than that of two-model problems. Schaeken
and Van der Henst (submitted) have recently developed this idea and have argued that, for
reasons of economy, most participants do not aim at constructing two mental models when
dealing with two-model problems. They claimed that rather than constructing two fully
explicit models, people construct a single model which integrates the indeterminacy (see
also Johnson-Laird, 1983, p. 164 and 409). They called such a model an isomeric mental
model. Based on a protocol analysis they observed that most of the models drawn were
isomeric like the following:
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 19
If people avoid the construction of two models when they encountered an
indeterminacy, then indeterminate problems are not radically different from determinate
ones and the same type of processes may apply to these two kinds of problems.
Interestingly, most of performance results available in the literature on relational
reasoning show that the difference between both types of problems is actually not very
high (see Schaeken & Van der Henst, submitted).
The sixth question we raised concerned the influence of presentation format. It was
predicted that analogical processes were more likely to occur when the premises appear
sequentially and that propositional processes were more likely to occur with a
simultaneous presentation. In line with this prediction, we observed a congruence effect
in the simultaneous presentation and not in the sequential one. This corroborates the idea
that constructing a mental model is helpful in representing the problem when the premises
are available for a short period of time. Indeed, representing the premises propositionally
require to store more information in memory than representing them analogically since a
propositional representation keeps track of the linguistic details of the premises like the
relational term (‘left’ or ‘right’). Hence, when memory constraints are high, as for the
sequential presentation, analogical presentation is favored. However, analogical
processing occurred even in the simultaneous presentation as indicated by a higher rate
of ‘left’ conclusions than ‘right’ conclusions in this condition. The individual differences
data indicate yet that there were many more participants who adopted an analogical
strategy in the sequential condition than in the simultaneous one. This again confirms that
reasoning on the basis of models is more appropriate in the sequential condition.
A comprehensive theoretical account of the results we obtained has to take into account
both types of processes. Mixed models have previously been adopted by several
researchers like Johnson-Laird (1983), Mani & Johnson-Laird, (1982), Shaver, Pierson, &
Lang, (1974), Sternberg, (1980). According to Sternberg and Johnson-Laird, the premises
are first decoded into a linguistic format and are subsequently represented by a spatial
mental model. However, this view concerns only the representational phase but not the
inferential one. Accordingly, it seems then that the inferential phase, during which the
reasoner produces a conclusion, relies only on the inspection of the mental model.
However, the data we obtained indicate that the formulation of a conclusion is influenced
by both analogical and linguistic factors in the simultaneous presentation, and support the
idea that both factors influence not only the representational phase but also the inferential
one. This result may be seen as problematic to approaches that assume that inferences rely
only on propositional processes or only on mental models. It seems rather that some form
of reasoning is more appropriate for some tasks and less appropriate for others, leaving
room for another form of reasoning for these latter tasks. For instance, propositional
processes are involved for answering problems in which the premises and the question are
simultaneously presented but turn out to be absent in cases of sequential presentation,
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–2220
where only model based processes arise. Indeed, keeping in mind each premise and each
intermediate conclusion in a separate propositional format is likely to be too heavy for
working memory whereas constructing a mental model integrates given and inferable
information in a single package and is therefore much more parsimonious and suitable to
the features of the task. According to this view, the mixture of propositional and analogical
processes is viewed in relation to the task’s properties and not as a sequence of ordered
steps as it is for representational processes (where propositional processes are involved in
a preliminary level of representation and analogical processes are involved in a more
elaborate level). Data on individual differences suggest too that the type of inferential
processes we described are not universal and may lead us to question the nature of these
processes. Roberts (1993) distinguishes two types of reasoning processes: fundamental
reasoning mechanisms and reasoning strategies. A “fundamental reasoning mechanism
refers to a mechanism that is used for all deductive reasoning. Whenever any such
inference is to take place, this mechanism and hence the processes that it supports will be
called into play” (Roberts, 1993, p. 570). A fundamental reasoning mechanism relies on
fundamental processes which are typically mental models or deduction rules but not both.
In contrast, a “reasoning strategy refers to a set of processes that have been shown to be
used for solving certain types of deductive tasks, but for which there is not sufficient
evidence to assert that these processes themselves constitute all or part of the fundamental
reasoning mechanism” (Roberts, 1993, p. 576). Are the mechanisms we have described
fundamental reasoning processes or are they reasoning strategies? On the one hand, these
processes (i.e. analogical and propositional processes) are often claimed to be fundamental
and thus universal. On the other hand, the universality of these processes is called into
question since both seemed to occur in our experiment. One way to deal with this dilemma
is to assume that analogical and propositional processes are the most fundamental
reasoning processes on the basis of which individuals reason, but to assume that they are
also strategic in the sense that their triggering relies on the task’s features or on individual
specific competencies. In other words, mental models and rules are deep reasoning
processes, but are not universal (let us, however, note that in the present experiment
analogical processes were more prominent than propositional ones). Alternatively, it
might be the case that the reasoning task we used did not allow us to observe fundamental
mechanisms and that both types of reasoning strategies we observed rely on some deeper
and unique fundamental reasoning mechanism. In the field of sentential reasoning,
Johnson-Laird and his colleagues advocate such a view (Johnson-Laird, Savary, &
Bucciarelli, 2000; Van der Henst et al., 2002). They described a variety of reasoning
strategies (different problems elicited different strategies and different individuals used
different strategies) but accounted for them on the basis of the same fundamental reasoning
mechanism (i.e. that of mental models manipulation). In the experiment described here,
one could describe the congruence effect observed in the simultaneous condition (a
condition where constraints on working memory are moderate and allow richer
representation) by speculating that individuals reason on the basis of rich mental models
incorporating propositional tags that bias the wording of conclusions. Regardless of
the difficulty in refuting such a proposal (see Roberts, 1993; p. 584), one would of course
need to consider the psychological plausibility of such models and see if they can be
sufficiently distinguished from propositional processes.
J.-B. Van der Henst, W. Schaeken / Cognition 97 (2005) 1–22 21
Acknowledgements
We thank Lewis Bott, Wim De Neys, Kristien Dieussaert, Ira Noveck, Jeremy Pacht,
Nausicaa Pouscoulous, Maxwell Roberts, Walter Schroyens, Niki Verschueren and two
anonymous reviewers for their helpful comments on this study.
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