A computational account of children’s analogical reasoning:
balancing inhibitory control in working memory and relational
Robert G. Morrison,
Leonidas A.A. Doumas
and Lindsey E. Richland
1. Department of Psychology, Loyola University Chicago, USA
2. Department of Psychology, University of Hawaii at Manoa, USA
3. Department of Education, University of California, Irvine, USA
Theories accounting for the development of analogical reasoning tend to emphasize either the centrality of relational knowledge
accretion or changes in information processing capability. Simulations in LISA (Hummel & Holyoak, 1997, 2003), a neurally
inspired computer model of analogical reasoning, allow us to explore how these factors may collaboratively contribute to the
development of analogy in young children. Simulations explain systematic variations in United States and Hong Kong children’s
performance on analogies between familiar scenes (Richland, Morrison & Holyoak, 2006; Richland, Chang, Morrison & Au,
2010). Specifically, changes in inhibition levels in the model’s working-memory system explain the developmental progression in
US children’s ability to handle increases in relational complexity and distraction from object similarity during analogical
reasoning. In contrast, changes in how relations are represented in the model best capture cross-cultural differences in
performance between children of the same ages (3–4 years) in the United States and Hong Kong. We use these results and
simulations to argue that the development of analogical reasoning in children may best be conceptualized as an equilibrium
between knowledge accretion and the maturation of information processing capability.
Analogy provides a framework for comparing the
structure of elements within a domain with the structure
of elements of other elements in the same or another
domain (Gentner, 1983; Gick & Holyoak, 1980). In other
words, the elements of a source may be compared and
subsequently mapped to a target. An important conse-
quence of this comparison process is the ability to make
inferences about the elements of the target domain. Thus
analogy is an important way that people can learn about
new things based on prior knowledge (Holyoak & Tha-
gard, 1995; Hofstadter, 2001). Children’s development of
analogical reasoning allows them to notice correspon-
dences and make inferences about relationally similar
phenomena across contexts. This skill greatly enhances
their capacity for transfer of learning and schema
abstraction, two essential aspects of children’s learning
and cognitive development (Chen, Sanchez & Campbell,
1997; Gentner, 1977; Goswami, 2001; Halford, 1993;
Holyoak, Junn & Billman, 1984). While many have
argued that analogy is important for children’s cognitive
development, there is considerable disagreement on the
mechanisms underlying children’s development of
mature, adult-like analogical reasoning.
Computational models of analogy have contributed
immensely to understanding the constraints shaping
analogical reasoning in adults (e.g. Falkenhainer, Forbus
& Gentner, 1989; Holyoak & Thagard, 1989a, 1989b;
Hummel & Holyoak, 1997, 2003; Keane & Brayshaw,
1988; Keane, Ledgeway & Duff, 1994; Morrison, Kra-
wczyk, Holyoak, Hummel, Chow, Miller & Knowlton,
2004; Viskontas, Morrison, Holyoak, Hummel &
Knowlton, 2004); however, they have played a relatively
minor role in helping to elucidate the factors important
for the development of analogical reasoning in children
(see Doumas, Hummel & Sandhofer, 2008; Halford,
Wilson, Guo, Gayler, Wiles & Stewart, 1994; Gentner,
Rattermann, Markman & Kotovsky, 1995; and Leech,
Mareschal & Cooper, 2008, for notable exceptions). Our
intent in this paper is to demonstrate the efficacy of using
a neurally inspired symbolic-connectionist computa-
tional model of analogy (i.e. LISA; Hummel & Holyoak,
1997, 2003) to examine how various factors important
for analogical processing relatively impact the develop-
ment of analogical reasoning in children.
Address for correspondence: Robert G. Morrison, Loyola University Chicago, Department of Psychology, 1032 W Sheridan Road, Chicago, IL 60660,
USA; e-mail: firstname.lastname@example.org
!2010 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
Developmental Science 14:3 (2011), pp 516–529 DOI: 10.1111/j.1467-7687.2010.00999.x
Developmental change in analogy
Hypotheses for explaining age-related behavioral differ-
ences have typically focused on the importance of rela-
tional knowledge acquisition or on the maturation of
executive resources including working memory and ⁄or
Goswami (1992, 2001; Goswami & Brown, 1989) has
argued that children are attuned to and able to
map relations in a rudimentary manner from early
infancy, but their later analogical reasoning skills
build on prerequisite content knowledge. Citing Piaget’s
tasks using fairly sophisticated relations such as ‘steering
mechanism’, as an example, Goswami argues that chil-
dren must have the necessary relational knowledge in
order to reason analogically; however, given that
knowledge they should be successful in reasoning ana-
logically. Knowledge is thus viewed somewhat quantita-
tively, such that with greater knowledge acquisition one
accrues increasing numbers of prerequisites to reason
analogically across more and varied contexts.
In an alternative theoretical framework, Gentner and
Rattermann (1991; Gentner, 1988; Rattermann & Gent-
ner, 1998) have posited a causal role for knowledge
acquisition in shifting children’s reasoning from focusing
on object properties to focusing on relations. They
hypothesized a domain-specific ‘relational shift’during
cognitive development such that as children build
knowledge in a domain, they move from attending to
similarity based on object features (i.e. perceptual prop-
erties of the entities being compared) to relational simi-
larity (i.e. correspondences between the relations in each
entity being compared). This hypothesis is supported by
patterns identified in children’s processing of metaphors
(Billow, 1975; Gentner, 1988) and causal analogies
(Rattermann & Gentner, 1998), as well as children’s ease
of making analogies in very familiar domains (e.g. the
human body; Inagaki & Hatano, 1987).
Proponents of the relational shift hypothesis postulate
that change in a child’s analogical reasoning is not age-
related per se, but rather is directly tied to knowledge
acquisition. The relational shift is domain specific, based
upon knowledge acquisition, and can be observed in
adults when learning new content as well as children
(Gentner & Ratterman, 1991). This argument aligns with
classic findings demonstrating that adult experts in a
domain tend to attend to relations, while novices attend
to object features (Chi, Feltovich & Glaser, 1981).
Gentner et al. (1995) used the structure mapping engine
(SME) to model the results of Gentner and Ratterman
(1991), and modeled the relational shift by using more
‘object-centered’representations, containing only lower-
level relational representations, to model younger chil-
dren, and using more ‘relation-centered’representations,
using a higher-order relation to link two lower-level
relations, to model older children and adults. Because of
the systematicity constraint, SME showed a mapping
advantage for the representation containing the higher-
order relation. It is interesting to note, however, that while
this solution does result in improved performance in
SME, it also results in an increase in processing demands
for the system. This is not a problem for SME because the
model is not subject to processing constraints, but may
suggest that the solution is not plausible for humans with
limited working-memory capacity. It is also important to
note that technically both representations are relation
centered (not object centered) in that they both make
explicit use of relations. While this rerepresentation of
knowledge can account for the change in reasoning noted
by Gentner and Ratterman in SME, it does not explain
why children sometimes do not reason relationally in spite
of being fully aware of the relations in use (Goswami,
1991) and demonstrating knowledge of higher-order
relations (Richland et al., 2006).
More recent work suggests that the relational shift may
have more to do with pragmatics rather than just a shift.
Specifically, reasoners may develop skills to determine
whether object or relational similarity provides the
information necessary to solve a particular problem
(Bulloch & Opfer, 2009). In a task with 3-, 4-, 5-year-olds
and adults, older children and adults were more sensitive
to the predictive accuracy of each type of similarity. On
problems where relational similarity was predictive, these
participants made more relational judgments over time,
while on problems in which object similarity was more
predictive, participants made increasing object similarity
In an alternative to Gentner et al.’s (1995) approach,
Leech et al. (2008) have proposed a theory of relational
priming as a mechanism for the development of chil-
dren’s ability to make analogies. Citing the lack of an
explicit theory of how structured representations are
learned, this approach posits that analogy does not use
explicit representations of relations. Instead, relations are
state transformations, and analogy is simply priming of
one state given another as a cue. The challenge with this
model of knowledge acquisition is to explain the diffi-
culty of documenting implicit relational priming in
adults (Spellman, Holyoak & Morrison, 2001), and
children’s and adults’ability to reason about relations in
explicit, flexible ways that are unsupported by implicit
representations (e.g. Brown & Kane, 1988; Kotovsky &
Gentner, 1996; Namy & Gentner, 2002; Smith, 1984;
Holyoak & Thagard, 1995). In addition, Doumas et al.
(2008) have recently proposed a theory and implemented
a computational model (DORA) of how explicit
structured representations can be learned from unstruc-
tured examples, thereby eliminating one of the major
Development of analogical reasoning 517
!2010 Blackwell Publishing Ltd.
criticisms of using structured representations to simulate
An information processing view provides a third per-
spective on the role of knowledge acquisition in chil-
dren’s development of analogical reasoning. Based on
this perspective, we posit that while a prerequisite
knowledge base is essential, qualitative changes in rela-
tional knowledge representations can reduce processing
demands. Doing so would thereby free resources to
enable more sophisticated analogical reasoning within
the constraints of limited working-memory capacity at
any given point during maturation. This is of particular
importance for young children, since resources known to
be required for analogical reasoning such as working-
memory capacity and inhibitory control (Baddeley,
Emslie, Kolodny & Duncan, 1998; Krawczyk, Morrison,
Viskontas, Holyoak, Chow, Mendez, Miller & Knowl-
ton, 2008; Kubose, Holyoak & Hummel, 2002; Morri-
son, Holyoak & Truong, 2001; Morrison et al., 2004;
Morrison, 2005; Viskontas et al., 2004; Waltz, Knowlton,
Holyoak, Boone, Mishkin, de Menezes Santos, Thomas
& Miller, 1999; Waltz, Lau, Grewal & Holyoak, 2000)
gradually increase during childhood (e.g. Bjorklund &
Harnishfeger, 1990; Diamond, 2002; Diamond, Kirkham
& Amso, 2002).
Knowledge acquisition alone does not appear to explain
all identified patterns of analogical reasoning (Goswami,
1991). Even when knowledge is held fairly constant
across conditions, children exhibit differential success on
analogical reasoning problems depending on the execu-
tive resources demanded of the problems themselves
(Richland et al., 2006).
Halford (1993) has argued for a primary role of matu-
ration of children’s working-memory capacity in devel-
opment of children’s analogical reasoning. In particular,
he has argued that working-memory capacity is crucial to
the ability to process complex relations, an important
characteristic of mature, adult analogical reasoning.
Halford and colleagues (Andrews & Halford, 2002;
Halford, Andrews, Dalton, Boag & Zielinski, 2002) have
demonstrated that young children have difficulty in
complex relational tasks in which they must process
multiple relations simultaneously. Specifically, they pro-
posed a theory of relational complexity to categorize
relations by the number of sources of variation that are
related and must be processed in parallel. For example,
the simplest level of relational complexity, a binary
relation, is defined as a relationship between two argu-
ments, both of which are sources of variation. Thus ‘boy
chases girl’specifies a single relation (chase) between two
arguments (boy and girl). A reasoner would have to hold
both arguments and the relevant relation in mind to
reason on the basis of this relationship. The next level of
relational complexity, a ternary relation, includes three
arguments as sources of variation. Integrating two bin-
ary relations with three arguments such as ‘Mom chases
a boy who chases a girl’is also considered a ternary
relation. Halford (1993) suggested that on average, chil-
dren’s working-memory capacity is such that after age 2,
children can process binary relations (a relationship
between two objects), and after age 5 they could process
ternary relations. Thus, children of age 2 could perform
very simple analogy problems, but not problems that
require integrating multiple relations.
Zelazo, Frye and colleagues (1998; Zelazo, M!ller, Frye
& Marcovitch, 2003) have identified similar age-related
progressions using an alternative formulation of rela-
tional complexity that focuses more directly on the
importance of inhibition in executive control. Accord-
ing to their Cognitive Complexity and Control (CCC)
theory, the number of conflicting hierarchical rules that
must be maintained in order to accomplish a task
defines complexity. For example, in the Dimensional
Change Card Sort task, children were given one set of
sorting rules (color or shape) and then asked to sort by
a new rule. Children ages 3–4 were successful on each
sorting task when performing them separately, but
failed when required to integrate these two to determine
which rule to use. They explain this failure as a
maturational limitation in reflective consciousness and
While the relational complexity theory has been pro-
posed in opposition to knowledge acquisition theories of
analogical reasoning development, other findings suggest
that executive resources and at least the relational shift
may be closely related. Markman and Gentner (1993)
developed an analogy mapping task for use with adults,
which allowed participants to reason based on either
relational or object similarity. Using this task, Waltz
et al. (2000) found that increases in working-memory
load shifted adult participants from using relational
similarity to using object similarity to complete the task.
It is not clear, however, how working-memory load af-
fects this balance. One possible explanation is that
working-memory load utilizes the inhibitory resources in
working memory necessary to suppress responses based
on the salient features of objects during relational pro-
cessing and object matching, an argument previously
made by Morrison and colleagues (2004) to help explain
analogical reasoning performance in frontal patients (see
also Krawczyk et al., 2008) and older adults (Viskontas
et al., 2004).
Likewise, Richland et al. (2006) proposed that inhibi-
tory control might help to explain the relationship
518 Robert G. Morrison et al.
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between maturation and the impact of object similarity
in young children. While inhibitory control has been a
major topic in models of cognitive development (e.g.
Bjorklund & Harnishfeger, 1990; Diamond, 2002), it has
not previously been applied to understanding the devel-
opment of analogy. However, the hypothesis that inhib-
itory control is important for the development of analogy
is consistent with results from other cognitive tasks (e.g.
Diamond et al., 2002; Lorsbach & Reimer, 1997; Zelazo
et al., 2003). In one example, Diamond et al. (2002)
manipulated the day-night task, a Stroop-type task in
which children are instructed to say ‘day’when shown a
picture of a moon and ‘night’when shown a picture of a
sun. Inhibitory control is tested because presumably
children’s semantic category of ‘day’becomes activated
when they are shown a scene depicting a sun, but they are
instructed instead to generate a word with the opposing
semantic meaning, ‘night’. Children under the age of 4"
consistently failed on the task. When Diamond and
colleagues reduced the inhibitory requirements of the
task by asking participants to say ‘dog’and ‘pig’instead
of ‘day’and ‘night’, young children performed much
better, suggesting that limits in their inhibitory control
explained low success rates in the day-night version of
Changes in inhibitory control have already been useful
in explaining analogy performance in several other
groups associated with compromised executive functions.
For example, Morrison et al. (2004) found that patients
with damage to the prefrontal cortex showed a preference
for using featural over relational similarity in an analogy
mapping task, much like college students under dual-task
conditions (Waltz et al., 2000). In a follow-up study,
they systematically manipulated the need for suppression
in a verbal analogy task and found this was the best
predictor of the change in performance in analogy
problems of low relational complexity. Similar results
with frontal patients were also found in a forced-choice
visual analogy task which required patients to choose
between a relational match and either a semantic, per-
ceptual, or unrelated distractor, with patients frequently
choosing semantic distractors over relational matches
(Krawczyk et al., 2008). Likewise, Viskontas and col-
leagues (2004) showed that changes in inhibitory control
in working memory could account for older adults’
deficiencies in processing visual analogies that required
relational integration and inhibition. We believe similar
changes may also help to explain changes in featural and
relational responding as documented by Rattermann and
Gentner (1998; Gentner & Rattermann, 1991).
In our present effort we focus on understanding how
changes in inhibitory control in working memory may be
able to explain changes in children’s analogy perfor-
mance characterized by both relational complexity and
featural distraction, and how representation of relational
knowledge can help to reduce the demand for this
resource, and thus help to explain a cultural difference in
A computational account of analogy
In an effort to understand the factors behind changes in
children’s analogical reasoning in scene analogy prob-
lems, we modeled results from Richland et al. (2006) and
Richland et al. (2010) in LISA (Learning and Inference
with Schemas and Analogies; Hummel & Holyoak, 1997,
2003). The four counterbalanced versions of an example
problem from these two experimental papers are pro-
vided in Figure 1.
Learning and Inference with Schemas and Analogies
LISA is a neurally inspired computational model of
relational reasoning. LISA uses temporal synchrony to
dynamically bind distributed (i.e. connectionist) repre-
sentations of relational roles to distributed representa-
tions of their fillers in working memory. Importantly,
because LISA dynamically binds representations of
relational roles to their arguments (i.e. because it solves
the binding problem; see Hummel, Holyoak, Green,
Doumas, Devnich, Kittur & Kalar, 2004), LISA’s rep-
resentations support structured (i.e. explicitly relational)
processing. While the explicit structured representations
utilized by LISA can be ‘hand-coded’by the researcher,
they can also be generated from unstructured examples
by using an extension of LISA called DORA (Doumas
et al., 2008).
When LISA ‘thinks about’a proposition, it fires roles
in synchrony with their fillers, and fires separate role-
filler bindings out of synchrony with one another. The
synchronized (and de-synchronized) patterns of activa-
tion serve as the basis for memory retrieval, analogical
mapping and inference, and schema induction (see
Hummel & Holyoak, 1997, 2003). LISA has previously
been used to account for changes in reasoning with age
(Viskontas et al., 2004) and with damage to either the
prefrontal or anterior temporal cortex (Morrison et al.,
LISA represents relational structure using a hierarchy
of distributed and localist codes (see Figure 2 for a
schematic representation of LISA’s architecture as
applied to the proposition chase (cat, mouse)). At the
bottom of the hierarchy, semantic units (small circles in
Figure 2) represent objects and relational roles (i.e.
predicates) in a distributed fashion. For instance, each
role of the chase relation would be represented by
semantic units such as aggressor for the first chase role
(chaser or c1 in Figure 2), victim for the second role
(chased or c2 in Figure 2), and pursuit for both. Simi-
larly, the arguments ‘cat’and ‘mouse’would be repre-
sented by units specifying their meaning (e.g. cat: cat,
pet; mouse: mouse, pest; both: animal). The exact con-
tent of the semantic units is not important to LISA’s
operation; they might be whatever is meaningful to
describe the predicates and objects and more import-
antly whatever is neurally plausible to do so. At the next
Development of analogical reasoning 519
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level of LISA’s hierarchy, localist predicate and object
units (triangles and large circles, respectively, in
Figure 2) represent relational roles and their arguments
and have bi-directional excitatory connections to the
corresponding distributed semantic units. Sub-proposi-
tion (SP) units (rectangles in Figure 2) bind roles to
their arguments, and have bi-directional connections to
the corresponding predicate and object units. In the case
of chase (cat, mouse), one SP would bind ‘cat’to the
first role of chase (i.e. chaser, c1), and another would
bind ‘mouse’to the second role (i.e. chased, c2).At the
top of the hierarchy, proposition units link role-filler
bindings (i.e. SPs) into complete propositions via excit-
atory connections to the corresponding SPs. In addition
to the excitatory connections already mentioned, localist
units also have bi-directional inhibitory connections
between units of the same type. For instance, cat and
mouse would have an inhibitory connection, as would
the two SP units representing the chaser ⁄cat and
chased ⁄mouse role bindings.
A complete analog (i.e. situation, story or event) is
represented by the collection of semantic, predicate,
object, SP and proposition units that collectively code the
propositions in that analog. For instance, Figure 3 shows
a representation for a 1-Relation with Distractor scene
analogy problem shown in Figure 1b. This representa-
tion includes both an analog in the driver and two
competitive recipient analogs. Analogs in the driver and
recipient do not share object, predicate, SP or proposi-
tion units; however, all analogs in LISA’s long-term
memory are connected to the same set of semantic units.
Thus, the distributed semantic units permit the localist
(i.e. proposition, SP, predicate, and object) units in one
analog to communicate with the units in other analogs.
For the purposes of memory retrieval and analog-
ical mapping (Hummel & Holyoak, 1997) as well as
Figure 1 Counterbalanced versions of the ‘chase’ Scene Analogy Problems (Richland, Morrison & Holyoak, 2006): (a) 1-Relation ⁄
No Distractor, (b) 1-Relation ⁄Distractor, (c) 2-Relation ⁄No Distractor, (d) 2-Relation ⁄Distractor.
520 Robert G. Morrison et al.
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analogical inference and schema induction (Hummel &
Holyoak, 2003), analogs are divided into two mutually
exclusive sets: a driver and one or more recipients. The
driver controls the sequence of events: propositions in
the driver become active (i.e. enter working memory) one
at a time. When a proposition enters working memory,
the binding of its roles to their arguments is represented
by synchrony of firing: All the units under a given SP fire
in synchrony with one another, and separate SPs fire out
of synchrony with one another. The result on the
semantic units is a set of mutually desynchronized pat-
terns of activation (see Figure 4bi): one pattern for each
active SP (i.e. role binding) in the driver. In the case of
chase (cat, mouse), the semantic units of ‘cat’(e.g. cat,
pet, animal) would fire in synchrony with the features of
the first role of chase (i.e. chaser, c1), while the semantic
units representing ‘mouse’(e.g. mouse, pest, animal) fires
in synchrony with the second role (i.e. chased, c2). This
oscillatory pattern of systematic SP activation and
deactivation results from the inhibitory connections
between SPs and is intrinsic to LISA’s operation.
In order to represent the proposition chase (mouse,
cat), LISA activates exactly the same semantic units, but
their synchrony relations are reversed (‘mouse’fires in
synchrony with the chaser (i.e. c1), and ‘cat’fires with
chased (i.e. c2)). The resulting patterns of activation on
the semantic units drive the activation of the localist
units representing the relational structure in the various
recipient analogs, and serve as the basis for analogical
mapping, inference, schema induction, and the other
functions LISA performs (Hummel & Holyoak, 1997,
2003). Each set of SPs from a given analog is referred to
as a working-memory phase set. For LISA to completely
‘think about’an analog, all of the SPs making up the
propositions for that analog must time-share in the
working-memory phase set.
The final component of the LISA architecture is a set
of mapping connections between units of the same type
(e.g. object to object, predicate to predicate, etc.) in the
driver and the various recipient analogs (see Figure 5).
These connections grow (via Hebbian learning) whenever
corresponding units in the driver and recipient fire at the
same time. They permit LISA to learn the correspon-
dences (i.e. mappings) between analogous units in sepa-
rate analogs. They also permit correspondences learned
early in mapping to influence the correspondences
Inhibition in working memory in LISA
In addition to providing an account of human relational
reasoning, LISA also serves as a model of working
memory. When a proposition is fired, one of its role
bindings (SPs) enters the focus of attention in working
memory. Likewise, all of the units connected either
directly or indirectly in long-term memory receive acti-
vation. The various SPs timeshare the limited-capacity
chases (cat, mouse)
Predicate & object unit
Figure 2 LISA architecture for proposition chases (cat, mouse)
showing the hierarchical arrangement of localist (i.e. proposi-
tion, SP, predicate, object) and distributed (i.e. semantic) units.
Figure 3 LISA rapidly learns what in the recipient goes with what in the driver by using a Hebbian learning algorithm to track what
units of the same type are firing at the same time. These ‘mapping connections’ are the basis for analogical mapping and inference.
Here the mapping connections from various object units in several recipient analogs are shown to the cat object unit in the driver.
Development of analogical reasoning 521
!2010 Blackwell Publishing Ltd.
focus of attention; however, recently activated units
remain in active memory – their activation decaying over
time if they are not brought back into the focus of
attention. This conception of working memory is similar
to that developed by Cowan (1995), Fuster (2008) and
Kane and Engle (2002), where working memory involves
neurons in prefrontal cortex activating neurons in pos-
terior cortex representing information in long-term
memory. As detailed below, the systematic activation and
dynamic binding of information stored in long-term
memory in LISA’s working memory is critically depen-
dent on inhibition, a cognitive function frequently asso-
ciated with the prefrontal cortex (e.g. Morrison et al.,
2004; Perret, 1974; Shimamura, 2000) and frequently
cited as important in human development (e.g. Bjork-
lund & Harnishferger, 1990; Diamond, 2002, Hasher &
Zacks, 1988, Viskontas et al., 2004).
Of particular importance to the present simulations,
inhibition plays a role in the selection of items to enter
working memory because selection is a competitive
process: Propositions in the driver compete to enter
working memory on the basis of several factors, includ-
ing their pragmatic centrality, or importance, support
from other propositions that have recently fired, and the
recency with which they themselves have fired. Reduced
driver inhibition results in reduced competition and more
random selection of SPs to fire. The selection of which
SPs are chosen to fire, and in what order, can have
substantial effects on LISA’s ability to find a structurally
consistent mapping between analogs. It follows that
reduced driver inhibition, resulting in more random
selection of propositions into working memory, can
likewise affect LISA’s ability to discover a structurally
The role of inhibition in the activity of a recipient
analog is directly analogous to its role in the activity in
the driver. Recipient inhibition causes units in the
recipient to compete to respond to the semantic patterns
generated by activity in the driver. If LISA’s capacity to
inhibit units in the recipient is compromised, then the
result is a loss of competition, with many units in the
recipient responding to any given pattern generated by
the driver. The resulting chaos hampers (in the limit,
completely destroys) LISA’s ability to discover which
units in the recipient map to which in the driver. In short,
inhibition determines LISA’s working memory capacity
(see Hummel & Holyoak, 2003, Appendix A; Hummel &
Holyoak, 2005), controls its ability to select items for
placement into working memory, and also regulates its
ability to control the spread of activation in the various
recipient analogs. As such, inhibition in LISA is critical
for the model’s ability to favor relational similarity over
featural similarity. This conception is also highly com-
plementary to that presented by Zelazo and colleagues
Prop: chase1 (cat, mouse)
chr1 + c
c1 (c, m)
chd + m
Prop: chase2 (dog, cat)
chr1 + c
c1 (c, m)
chr2 + d
c2 (d, c)
chd2 + c
chr + d
cc (d, c, m)
Prop: chase-chain (dog, cat, mouse)
(i) (ii) (iii)
WM phaseset WM phaseset WM phaseset
chase1 (cat, mouse)
chase1 (cat, mouse)chase2 (dog, cat)
chase-chain (dog, cat, mouse)
Figure 4 (a) LISA representations for the driver of scene analogy problems showing (i) a 1-Relation problem, (ii) a 2-Relation
problem represented with two propositions, and (iii) a 2-Relation problem where the relations have been chunked into a single three-
place proposition. (b) Firing diagrams for the three representations showing the various ‘phases’ of firing to fully capture the relational
structure in each type of problem. Note that chunking the 2-Relation problem (iii) results in a smaller (i.e. shorter) WM phase
set relative to the unchunked 2-Relation problem (ii) and that both 2-Relation representations have a larger WM phase set than
the 1-Relation problem (i).
522 Robert G. Morrison et al.
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(1998, 2003) who describe the need to inhibit one rule
(relational structure) in the service of another.
To test whether LISA’s architecture could explain the
major trends identified in children’s developmental
pathways of analogical reasoning, we used LISA to
simulate children’s performance on scene analogy prob-
lems (Richland et al., 2006). These problems had been
created to examine the relative effects of distraction from
object-based features (relational shift) and relational
complexity when prerequisite knowledge was likely and
effectively held constant across conditions. These prob-
lems were tested with English and Chinese (Cantonese)
speaking children to reflect the variety of developmental
trends across cultures.
Scene analogy problems
Richland et al. (2006) developed a set of scene analogy
problems to investigate relational complexity and fea-
tural distraction within a single analogical reasoning task
based on a paradigm originated by Markman and
Gentner (1993). The relations and the objects used to
represent them were familiar to preschool age children
(see Richland et al., 2006, Experiment 2).
Figure 1 depicts an example of each of the four
counterbalanced versions that were created for each of
the 20 picture sets. Each set of problems factorially
varied (1) the number of instances of the relevant relation
that needed to be mapped (1-Relation or 2-Relation),
and (2) the presence of an object in the target scene that
was either featurally similar (Distractor) or dissimilar
(No-Distractor) to the object to be mapped in the source
scene. 2-Relation problems were created by having one
object that was not involved in the principal relation (dog
in Figure 1a and 1b) in the 1-Relation problems partic-
ipate in the principal relation for the 2-Relation version
(chase (dog, cat)). Distractor and No-Distractor versions
were created by having an extra object in the same pic-
ture that was either similar (sitting cat in Figure 1b and
1d) or dissimilar (sandbox in Figure 1a and 1c) to the
item to be mapped in the source picture (running cat).
Children were asked to indicate which object in the target
picture corresponded to the indicated object in the
source picture (the running boy in the example in
United States children
In a series of experiments with children from the United
States (US), Richland et al. (2006) found reliable effects
of both relational complexity and featural distraction on
children’s analogical reasoning ability (see Figure 6).
Specifically, 3–4-year-olds showed strong effects of both
distraction and relational complexity that interacted to
reveal the highest accuracy in the 1-Relation ⁄No-Dis-
tractor condition and the lowest accuracy in the
2-Relation ⁄Distractor condition. This pattern was simi-
lar for the 6–7-year-olds, with main effects of both
relational complexity and distraction. In contrast, the
13–14-year-olds showed a main effect of relational
chases (cat, mouse)
c2c1 b g
chases (boy, girl)
s2s1 c y
sits-on (cat, yard)
Figure 5 Mapping connections in LISA. Temporal
synchrony results in the growth of mapping connections
(via Hebbian learning) in LISA between like types of units in
the driver and recipient. These mapping connections are the
basis of analogical mappings, which in this case allow LISA
to ‘decide’ that the boy in the recipient goes with the cat in
Mean relational responses
Figure 6 Experimental results from several experiments
(Richland et al., 2006, Experiment 1; Richland et al., 2010)
using the scene analogy problems with children.
Development of analogical reasoning 523
!2010 Blackwell Publishing Ltd.
complexity but no effect of distraction. In a second
experiment, Richland et al. (2006) demonstrated that
these effects in young children were not due to problems
in identifying the relevant relations.
Error data confirmed that these patterns in accuracy
showed corresponding developmental effects of both
relational complexity and object similarity distraction.
Increasing the level of relational complexity raised the
number of relational errors in the youngest children the
most, with decreasing numbers with age. Adding a fea-
tural distractor led to greater object similarity errors in
the youngest children in contrast to the oldest children
who showed no effect. Interestingly, when children
solved problems with both a featural distractor and two
levels of relational complexity, featural errors, as
opposed to relational complexity errors, were the most
Children from Hong Kong
As a follow-up to our study with US children, we inves-
tigated whether 3–4-year-old native Cantonese speakers
from Hong Kong (HK) showed the same pattern as US
children (Richland et al., 2010). Based on their different
relational knowledge base as well as their different
experience with reasoning about relations, we believed
Chinese children would perform differently than the US
children on the scene analogy problems. Adult studies
have shown cultural differences in normative patterns for
drawing relational inferences (see D’Andrade, 1995;
Hansen, 1983; Ji, Peng & Nisbett, 2000; Nisbett, 2003)
such that Chinese and Japanese reasoners may be more
attuned to relational correspondences than US partici-
pants. These differences also appear in cross-cultural
variations in children’s socialization and linguistic rou-
tines, with Asian caregivers using more action-oriented
language and referential verbs in play and caregiving than
relatively object-focused US caregivers (e.g. Korean: Au,
Dapretto & Song, 1994; Gopnik, Choi & Baumberger,
1996; Japanese: Fernald & Morikawa, 1993; Ogura, Dale,
Yamashita & Murase, 2006; Chinese: (Mandarin) Tardif,
1996; Tardif, Gelman & Xu, 1999; Tardif, Shatz &
Naigles, 1997; (Cantonese) Leung, 1998). Chinese
children themselves may additionally show a higher rel-
ative rate of verb usage in Mandarin (Tardif, 1996; 2006;
Tardif et al., 1997; Tardif et al., 1999) and Cantonese (Tse,
Chen & Li, 2005) than US children of comparable ages
who show a more pronounced noun bias (see Gentner,
1981, 1982; Gentner & Boroditsky, 2001).
These children’s greater experience with relational
language and socialization suggests that they may have a
greater expertise in representing relational information.
Thus, we hypothesized that children from Hong Kong
(HK) may tend to construct a somewhat different, and
potentially more expert, representation of 2-relation
problems than US children. There was no theoretical
reason to expect differences in processing capacity
(Hedden, Park, Nisbett, Ji, Jing & Jiao, 2000) or baseline
knowledge of the task since it was a novel task for
everyone with simple relations (for more information see
Richland et al., 2010).
Data were collected with 61 3- and 4-year-old children
who were native Cantonese speakers. Participants were
sampled from Chinese preschools with similar demo-
graphics to the previously tested US population. Like the
US children, children from HK showed a similar effect of
distraction, favoring the featurally similar distractor to
the relationally similar choice when it was present in the
Distractor condition (see dashed line in Figure 6).
However, the HK sample showed no decline in perfor-
mance for 2-Relation problems relative to US children,
and outperformed US children on the 2-Relation prob-
lems. This was true for both the 3-year-olds and 4-year-
olds when examined separately. This reinforced our
contention that these children may have a more expert,
or at least a different, representation of the relational
knowledge (verbs) needed to solve these multi-relation
scene analogy problems. In order to ensure that the
linguistic translation of the task could not have explained
the differences, an additional control condition was
run with 3- and 4-year-old US children using a back-
translation of the Cantonese version, and the results
replicated the prior US children’s data (Richland et al.,
2010). The Chinese sample again outperformed the US
sample on 2-Relation problems.
Simulating United States children’s analogical reasoning
We simulated children’s performance in the scene anal-
ogy problems to demonstrate that a systematic change in
inhibition levels in LISA could account for age-related
distraction and relational complexity performance
changes in analogical reasoning. To model the scene
analogy problems, we constructed LISA representations
of the four problem types. 1-Relation problems were
represented by a single, 2-place predicate (e.g. chase1
(cat, mouse); see Figure 4ai). For 2-Relation problems we
represented both target relations explicitly as two,
2-place predicates (e.g. chase2 (dog, cat) and chase1 (cat,
mouse); see Figure 4aii).
As such, both relations were
represented in LISA’s working memory together. Thus,
the 2-relation phase set (i.e. the number of SPs and their
attached Predicate and Object units that must fire inde-
pendently to represent the full relational structure in
working memory; see Figure 4bi & 4bii) was double that
of the 1-Relation phase set. In LISA, units of the same
type in the driver and recipient inhibit one another (i.e.
SPs inhibit other SPs, Ps inhibit other Ps, etc.). In fact, it
is this inhibition that allows the various SPs in the phase
set to have an opportunity to timeshare in working
memory. To simulate each age group we changed the
While we hand-coded these representations to clearly embody our
hypothesis in this study, they could have been generated using DORA
(Doumas et al., 2008) from unstructured examples of chasing between
objects. See Doumas, Morrison and Richland (2010).
524 Robert G. Morrison et al.
!2010 Blackwell Publishing Ltd.
inhibition level between corresponding units in the driver
and the recipient. Younger age groups were assigned
lower mean inhibition levels.
Each simulation run consisted of firing three phase sets
in LISA’s working memory, ‘randomly’assigned by
LISA. On each simulation an inhibition level for units in
the recipient was sampled from a normal distribution
with the means listed in Figure 7 and an SD of .1. The
inhibition between corresponding units in the driver and
recipient were set to the inhibition level. We ran 40
simulations of each problem type for each age group.
When LISA failed to determine a stable mapping after
firing three phase sets, an answer was selected based on
n;wij> maxðwkj Þ
is the mapping weight from recipient unit ito
driver unit j, max(w
) is the maximum mapping weight
into all other recipient units k, where kis the same type
to driver unit j, max(mapWeight) was the highest
mapping weight into any recipient object unit and driver
unit j, and nis the number of object units in the recipient,
and the probability, P
, of selecting any recipient unit i,
was given by:
where jis all units of the same type as iin the recipient
(including unit i).
The simulation results along with the experimental
results from Richland et al. (2006) are presented in
Figure 7. LISA’s performance mirrored experimental
results for each age group across conditions, accounting
for a large portion of the variance in the experimental
= 0.97) with just a single parameter change.
Specifically, LISA simulations showed: (1) a main effect of
age, (2) an effect for both relational complexity and dis-
traction for 3–4-year-olds, (3) a smaller effect for both
relational complexity and distraction for 6–7-year-olds
than for 3–4-year-olds, and finally (4) a mild effect for
relational complexity, but no effect for distraction for
Lowering the inhibition between units in LISA’s driver
and recipient produced patterns of behavior that very
closely resembled the age-related differences in analogical
ability exhibited by human children. When there is less
inhibition in the driver, LISA’s working-memory effi-
ciency is decreased because units that had just been
active are more likely to fire again immediately (because
of their high level of activation), thus firing is less sys-
tematic. When there is less inhibition between units in the
recipient, there is decreased competition between these
units to respond to patterns of activation in the driver.
With less competition, more recipient units became
active simultaneously, which impeded LISA’s ability to
find the accurate mapping between source and target
items (i.e. as each role and filler in the driver activated
more numerous roles and fillers in the recipient, it was
more difficult for LISA to determine which recipient
units the active driver units corresponded to).
Lastly, as in the experimental results, when LISA did
not select the correct analogical mapping in the distrac-
tor conditions, the model preferentially chose the fea-
turally similar distractor object. This was due to the
distractor object in the recipient (e.g. sitting cat) sharing
the most semantic units with the indicated object in the
driver (e.g. running cat) and thus the distractor was the
most likely object to be active via spreading activation.
Interestingly, decreasing inhibition levels captured the
effects of both distraction and relational complexity and
the interaction between them mimicking the exact pat-
tern observed in human children. While distraction and
relational complexity effects are sometimes thought of as
distinct effects, these simulations suggest that there may
be a single underlying neural cause of these patterns of
results, that is, limited inhibition between units.
Simulating Hong Kong children’s analogical reasoning
HK 3–4-year-old children performed better on 2-relation,
No-Distractor problems than US children (Richland et
al., 2010). One explanation for this might be that HK
3–4-year-olds had greater working-memory capacity than
US children and this allowed them to more efficiently
process the more relationally complex problem. While
some early evidence seemed to suggest differences in
working-memory capacity between Western and Eastern
Mean relational responses
LISA inhibit = 0.6
LISA inhibit = 0.75
LISA inhibit = 0.9
Experimental vs. LISA simulation
Figure 7 Comparison of experimental and LISA simulation
results. Change in performance of the scene analogy problems
by US children is well ﬁt by progressively increasing inhibition
in LISA to simulate older children.
Development of analogical reasoning 525
!2010 Blackwell Publishing Ltd.
children, these differences have typically been explained
in terms of differences in phonetics in very limited situ-
ations (see Baddeley, 1996). An alternative explanation is
that HK children utilized a more efficient relational
representation that minimized processing demands, thus
allowing for greater success on two-relation problems in
spite of similar processing capacity to US children of the
same age. This may have been facilitated by their greater
experience with representing relations and producing
verb phrases. At this point we are not prepared to try and
differentiate between potential causes for a child’s
increased ability to represent relations, but the difference
in a child's mental representations could explain his/her
seemingly greater ability to solve complex, multi-relation
analogies. Relational representation should not impact
susceptibility to object distraction, however, since in these
stimuli the object distractor was not a part of the rela-
tional group in the stimuli. Thus, we hypothesized that
the 3–4-year-old Cantonese speakers would continue to
show decrements in performance related to the object
To test this hypothesis, we modeled 2-relations prob-
lems in LISA using a single three-place proposition (i.e.
chase (dog, cat, mouse)) instead of the two binary
propositions (i.e. chase1 (dog, cat); chase2 (cat, mouse))
we used in modeling US children’s performance (see
Figure 4aiii). In LISA, this change in representation
results in only three role-bindings needing to be fired out
of synchrony as opposed to the four role-bindings
necessary for two binary propositions. Thus, the
demands on LISA’s working memory are lower and,
correspondingly, inhibition is less critical. Experimental
results for 3–4-year-old children from both countries and
the simulation results for both representations run at a
low inhibition parameter setting (i.e. 0.6) are shown in
Figure 8. While a two-binary relational representation
scheme better fits US children’s performance, a single-
ternary relational representation scheme better fits HK
In this paper we have presented simulations in LISA that
support the hypothesis that maturation of inhibitory
control in working memory is critical for the develop-
ment of adult-like analogical reasoning. Specifically, we
demonstrated that simple changes in inhibition levels in
LISA (i.e. inhibition between elements of competing
relational representations in working memory) could
account for both relational complexity and featural
distraction effects in children’s analogical reasoning
performance from age 3 to 14 (Richland et al., 2006).
This account is consistent with previous simulations of
results from frontal patients (Morrison et al., 2004) and
older adults (Viskontas et al., 2004) whose analogical
reasoning performance also suffered under increases in
relational complexity and featural or relational distrac-
tion. Given that inhibition is critical for maintaining
systematic patterns of temporal synchrony (and asyn-
chrony) in LISA, this result is also consistent with recent
evidence suggesting that task-related neural synchrony as
measured via EEG increases during childhood and
adolescence (Uhlhaas, Pipa, Lima, Melloni, Neuensch-
´& Singer, 2009).
Second, we presented simulations in LISA that dem-
onstrate how relational knowledge acquisition and
inhibitory control in working memory can interact dur-
ing development. Specifically, we demonstrated that a
knowledge representation change from two, 2-place
predicates into one, 3-place predicate reduces the
demands of processing a ‘2-relation’scene analogy
problem in LISA. This simulation thereby offers an
explanation why Hong Kong children perform better on
2-Relation analogy problems than United States children
while still showing object featural-distraction effects at
the lower inhibition levels used to model 3–4-year-olds. It
is important to note that an explanation solely based on
relational knowledge acquisition is inadequate to explain
these experimental results because both relational com-
plexity and object featural distraction did not improve in
the Hong Kong children together.
These simulations in LISA are based on a number of
assumptions about the basic cognitive abilities of young
Mean relational responses
2 × 2 LISA, inhibit = 0.6
1 × 3 LISA, inhibit = 0.6
Experimental vs. LISA simulation:
1 (role) × 3 (filler) & 2 (role) × 2 (filler)
representation in LISA
Figure 8 Comparison of experimental and LISA simulation
results. US 3–4-year-old children’s performance on 2-Relation
problems is better fit in LISA by using a representation con-
sisting of two binary (i.e. 2 (role) ·2 (filler)) propositions, while
HK 3–4-year-old children’s performance is better fit in LISA by
using a representation consisting of one ternary (i.e. 1 (role) ·3
526 Robert G. Morrison et al.
!2010 Blackwell Publishing Ltd.
children. Specifically, we assume that young children are
capable of learning and mapping explicit relations
(e.g. Chen et al., 1997; Gentner & Rattermann, 1991;
Goswami, 1992, 2001). We also assume that their working
memory ⁄executive functions are limited – an assumption
that been been supported by many experimental studies
(see Diamond, 2002; Fuster, 2008). They also avoid the
issue of how children discover relations and how they
recognize these relations in a particular scene. The solu-
tion to the problem of relation discovery has recently been
offered by Doumas et al. (2008) in a model that generates
relational knowledge structures in the form used by LISA
from real-world unstructured examples. The second issue,
how reasoners decide which relations to attend to, is an
ongoing topic of study. In these simulations we simply
represent the relations which children describe when
asked what is going on in the scene. These include the
relational and featural knowledge structures.
It is our contention that both relational knowledge
acquisition and inhibitory control in working memory
can shape an individual’s analogical reasoning perfor-
mance. We suggest that the development of analogical
reasoning in children can be conceptualized as an equi-
librium between these two factors. In particular, as
children age, their knowledge about relations advances
while their working-memory capacity as modulated by
inhibitory control also improves. At a given time during
development, the child is able to perform an analogical
task based on both their level of relational knowledge
and their working-memory resources. Specifically, the
equilibrium operates such that greater relational knowl-
edge can impose fewer processing demands while less
knowledge imposes higher demands. Thus, Hong Kong
children given the same working-memory resources can
better solve relationally complex problems. More gener-
ally, as relational knowledge increases in a domain, the
demands on working memory decline, allowing for more
complex reasoning at any given age. This pattern in
cognitive development builds on an understanding of
working-memory effects in expertise (e.g. Chase &
Simon, 1973) where advanced relational knowledge can
decrease processing demands and thereby allow experts
to accomplish cognitive tasks which novices cannot.
We believe that to truly understand the development of
relational reasoning in children, future experimental and
computational studies must take into account both
advances in relational knowledge and changes in inhib-
itory control in working memory. In particular, we posit
that better understanding of how these two aspects of
development interact is essential to clarifying the devel-
opmental course of relational reasoning.
The authors wish to thank John Hummel and Keith
Holyoak for helpful discussions and Professor Denis
Mareschal and several anonymous reviewers for com-
ments on earlier versions of the manuscript. Generous
support for the authors was provided by the North-
western University Mechanisms of Aging and Dementia
Training Grant funded by the National Institute of
Aging (2T32AG020506: RGM), the Loyola University
Chicago Dean of Arts and Sciences (RGM), the Office of
Naval Research (SBIR OSD03-DH07: RGM; and
N000140810186: LER), the Indiana University Devel-
opmental Training Grant funded by the National Insti-
tute of Child Mental Health (LAAD), and the National
Academy of Education ⁄Spencer Foundation (LER).
Preliminary versions of these simulations were presented
at the Twenty-Ninth Annual Conference of the Cognitive
Science Society, Vancouver, Canada, the 7th Biannual
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Received: 21 January 2010
Accepted: 9 June 2010
Development of analogical reasoning 529
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