The wording of conclusions in relational reasoning

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).

http://www.elsevier.com/locate/COGNIT

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


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


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.


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.


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


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.


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).


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


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.


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

og

nitio

n9

7(2

00

5)

1–

22

13


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.


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


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.


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


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:


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,


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.


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.

References

Abed, F. (1991). Cultural influences on visual scanning patterns. Journal of Cross Cultural Psychology, 22, 525–

534.

Begg, I., & Denny, J. P. (1969). Empirical reconciliation of atmosphere and conversion interpretations of

syllogistic reasoning errors. Journal of Experimental Psychology, 81, 351–354.

Boudreau, G., & Pigeau, R. (2001). The mental representation and processes of spatial deductive reasoning with

diagrams and sentences. International Journal of Psychology, 36, 42–52.

Braine, M. D. S., & O’Brien, D. P. (Eds.). (1998). Mental logic. Mahwah, NJ: Lawrence Erlbaum.

Byrne, R. M., & Johnson Laird, P. N. (1989). Spatial reasoning. Journal of Memory and Language, 28, 564–575.

Carreiras, M., & Santamaria, C. (1997). Reasoning about relations: Spatial and nonspatial problems. Thinking and

Reasoning, 3(3), 191–208.

Chase, W. G., & Clark, H. H. (1971). Semantics in the perception of verticality. British Journal of Psychology,

62, 311–326.

Chase, W. G., & Clark, H. H. (1972). Mental operations in the comparison of sentences and pictures. In: L. Gregg

(Ed.), Cognition in learning and memory. New York: Wiley.

Chokron, S., Bernard, J. M., & Imbert, M. (1997). Length representation in normal and neglect subjects with

opposite reading habits studied through a line extension task. Cortex, 33, 47–64.

Clark, H. H. (1969a). Linguistic processes in deductive reasoning. Psychological Review, 76, 387–404.

Clark, H. H. (1969b). Influence of language on solving three term series problems. Journal of Experimental

Psychology, 82, 205–215.

Clark, H. H. (1973). Space, time, semantics, and the child. In: T. E. Moore (Ed.), Cognitive development and the

acquisition of language. Oxford, England: Academic Press.

DeSoto, C. B., London, M., & Handel, S. (1965). Social reasoning and spatial paralogic. Journal of Personality

and Social Psychology, 2, 293–307.

Evans, J. S. B. T., Newstead, S. E., & Byrne, R. M. J. (1993). Human reasoning: The psychology of deduction.

Hillsdale, NJ, England: Lawrence Erlbaum.

Fischer, M. H. (2001). Cognition in the bisection task. Trends in Cognitive Sciences, 5, 460–462.

Hagert, G. (1984). Modeling mental models: Experiments in cognitive modeling spatial reasoning. In: T. O’Shea

(Ed.), Advances in artificial intelligence. Amsterdam: North-Holland.

Huttenlocher, J. (1968). Constructing spatial images: a strategy in reasoning. Psychological Review, 75, 550–560.

Jewell, G., & McCourt, M. E. (2000). Pseudoneglect: A review and meta-analysis of performance factors in line

bisection tasks. Neuropsychologia, 38, 93–110.

Johnson-Laird, P. N. (1972). The three term series problems. Cognition, 1, 58–82.

Johnson-Laird, P. N. (1983). Mental models. Cambridge, MA: Cambridge University Press.

Johnson Laird, P. N., & Bethell Fox, C. E. (1978). Memory for questions and amount of processing. Memory and

Cognition, 6, 496–501.

Johnson-Laird, P. N., & Byrne, R. J. M. (1991). Deduction. Hove, UK: Lawrence Erlbaum.

Johnson-Laird, P. N., Savary, F., & Bucciarelli, M. (2000). Strategies and tactics in reasoning. In: W. S.

Schaeken, G. de Vooght, A. Vandierendonck, & G. d’Ydewalle (Eds.), Deductive reasoning and strategies.

Mahwah, NJ: Erlbaum.

Mani, K., & Johnson Laird, P. N. (1982). The mental representation of spatial descriptions. Memory and

Cognition, 10, 181–187.

Nachshon, I., Shefler, G. E., & Samocha, D. (1977). Directional scanning as a function of stimulus characteristics,

reading habits, and directional set. Journal of Cross Cultural Psychology, 8, 83–99.


Olson, G. M., & Laxar, K. (1973). Asymmetries in processing the terms ‘right’ and ‘left’. Journal of Experimental


Ormrod, J. E. (1979). Cognitive processes in the solution of three-term series problems. American Journal of


Padakannaya, P., Devi, M. L., Zaveria, B., Chengappa, S. K., & Vaid, J. (2002). Directional scanning effect and

strength of reading habit in picture naming and recall. Brain and Cognition, 48, 484–490.

Payne, S. J. (1993). Memory for mental models of spatial descriptions: An episodic-construction-trace

hypothesis. Memory and Cognition, 21, 591–603.

Potts, G. R., & Scholz, K. W. (1975). The internal representation of a three-term series problem. Journal of

Verbal Learning and Verbal Behavior, 14, 439–452.

Rips, L. J. (1994). The psychology of proof. Deductive reasoning in human thinking. Cambridge, Massachusetts:

MIT Press, Bradford.

Roberts, M. J. (1993). Human reasoning: deduction rules or mental models, or both. The Quarterly Journal of

Experimental Psychology, 46A, 569–589.

Roberts, M. J. (2000). Strategies in relational reasoning. Thinking and Reasoning, 6, 1–26.

Schaeken, W., Girotto, V., & Johnson-Laird, P. N. (1998a). The effect of irrelevant premise on temporal and

spatial reasoning. Kognitionswissenchaft, 7, 27–32.

Schaeken, W., Girotto, V., & Johnson-Laird, P. N. (1998b). The effect of irrelevant premise on temporal and

spatial reasoning. Kognitionswissenchaft, 7, 27–32.

Schaeken, W., & Johnson-Laird, P. N. (2000). Strategies in temporal reasoning. Thinking and Reasoning, 6, 193–219.

Schaeken, W., Johnson Laird, P. N., & d’Ydewalle, G. (1996a). Tense, aspect, and temporal reasoning. Thinking

and Reasoning, 2, 309–327.

Schaeken, W., Johnson Laird, P. N., & d’Ydewalle, G. (1996b). Mental models and temporal reasoning.

Cognition, 60, 205–234.

Schaeken, W., & Van der Henst, J. B. (submitted). Isomeric mental models.

Shaver, P., Pierson, L., & Lang, S. (1974). Converging evidence for the functional significance of imagery in

problem solving. Cognition, 3, 359–375.

Singh, M., Vaid, J., & Sakhuja, T. (2000). Reading/writing vs handedness influences on line length estimation.

Brain and Cognition, 43, 398–402.

Sternberg, R. J. (1980). Representation and process in linear syllogistic reasoning. Journal of Experimental

Psychology: General, 109, 119–159.

Vaid, J., Singh, M., Sakhuja, T., & Gupta, G. C. (2002). Stroke direction asymmetry in figure drawing: Influence

of handedness and reading/writing habits. Brain and Cognition, 48, 597–602.

Van der Henst, J. B. (2002). Mental model theory versus the inference rule approach in relational reasoning.

Thinking and Reasoning, 8, 193–203.

Van der Henst, J.B. & Schaeken (2002). Deriving a conclusion from relational premises. In D. Gray and C.D.

Schunn (Eds.) Proceedings of the 24th annual meeting of the Cognitive Science Society. Lawrence Erlbaum

Associates, P. 908–912.

Van der Henst, J. B., Yang, Y., & Johnson Laird, P. N. (2002). Strategies in sentential reasoning. Cognitive

Science, 26, 425–468.

Vandierendonck, A. (1998). Mental models and working memory in temporal and spatial reasoning. In: V. de

Keyser, & G. d’Ydewalle (Eds.), Time and the dynamic control of behavior. Kirkland, WA: Hogrefe & Huber.

Vandierendonck, A., & de Vooght, G. (1997). Working memory constraints on linear reasoning with spatial and

temporal contents. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 50A,

803–820.

Wetherick, N. E., & Gilhooly, K. J. (1990). Syllogistic reasoning: Effects of premise order. In: K. Gilhooly, M.

Keane, R. Logie, & G. Erdos (Eds.), Lines of thinking: Reflections on the psychology of thinking.

Woodworth, R. S., & Sells, S. B. (1935). An atmosphere effect in formal syllogistic reasoning. Journal of

Experimental Psychology, 18, 451–460.

Documents

The wording of conclusions in relational reasoning