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The representation and manipulation of structured relations is central to human reasoning. Recent work in computational modeling and neuroscience has set the stage for developing more detailed neurocomputational models of these abilities. Several key neural findings appear to dovetail with computational constraints derived from a model of analogical processing, 'Learning and Inference with Schemas and Analogies' (LISA). These include evidence that (i) coherent oscillatory activity in the gamma and theta bands enables long-distance communication between the prefrontal cortex and posterior brain regions where information is stored; (ii) neurons in prefrontal cortex can rapidly learn to represent abstract concepts; (iii) a rostral-caudal abstraction gradient exists in the PFC; and (iv) the inferior frontal gyrus exerts inhibitory control over task-irrelevant information.
Anatomy and connections related to relational reasoning. Areas of the prefrontal cortex (PFC) frequently identified in reasoning studies include the rostrolateral prefrontal cortex (RLPFC; anterior region of the inferior frontal gyrus, approximately Brodmann area 10, sometimes referred to as frontopolar prefrontal cortex), the dorsolateral prefrontal cortex (DLPFC; anterior region of the middle frontal gyrus, approximately Brodmann areas 9/46), and the ventrolateral prefrontal cortex (VLPFC; posterior region of the inferior frontal gyrus, approximately Brodmann areas 47/45/44). The anterior temporal lobe (ATL; located on the anterior lateral surface of the temporal lobe, approximately Brodmann areas 20, 31, 38) is frequently associated with semantic memory (see [72]) and is important for reasoning about semantic relations [24]. The medial temporal lobe (MTL; located on the medial surface of the temporal lobe including the hippocampus and entorhinal cortex, approximately Brodmann areas 27, 28, 34, 35, 36) is critical for episodic memory [73], and thus is important for relational reasoning about specific events. The ATL and MTL are connected to areas in the VLPFC via the uncinate fasiculus (UF). Regions in the parietal lobe, such as areas around and including the precuneus (PC; approximately Brodmann area 7) and the temporal parietal junction (TPJ; approximately Brodmann area 39) have heavy reciprocal connections to the PFC via the superior longitudinal fasciculus (SLF). These areas are frequently associated with tasks requiring relational reasoning about visuospatial entitites. The anterior cingulate cortex (ACC; located on the medial surface of prefrontal cortex approximately, Brodmann areas 24, 32, 33) is frequently active during relational reasoning and has reciprocal connections to the DLPFC.
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Author's personal copy
A
neurocomputational
system
for
relational
reasoning
Barbara
J.
Knowlton
1
,
Robert
G.
Morrison
2
,
John
E.
Hummel
3
and
Keith
J.
Holyoak
1
1
Department
of
Psychology,
University
of
California,
Los
Angeles,
Los
Angeles,
CA
90095,
USA
2
Department
of
Psychology,
Neuroscience
Institute,
Loyola
University
Chicago,
Chicago,
IL
60626,
USA
3
Department
of
Psychology,
University
of
Illinois
at
Urbana-Champaign,
Champaign,
IL
61820,
USA
The
representation
and
manipulation
of
structured
rela-
tions
is
central
to
human
reasoning.
Recent
work
in
computational
modeling
and
neuroscience
has
set
the
stage
for
developing
more
detailed
neurocomputational
models
of
these
abilities.
Several
key
neural
findings
appear
to
dovetail
with
computational
constraints
de-
rived
from
a
model
of
analogical
processing,
‘Learning
and
Inference
with
Schemas
and
Analogies’
(LISA).
These
include
evidence
that
(i)
coherent
oscillatory
activity
in
the
gamma
and
theta
bands
enables
long-distance
commu-
nication
between
the
prefrontal
cortex
and
posterior
brain
regions
where
information
is
stored;
(ii)
neurons
in
prefrontal
cortex
can
rapidly
learn
to
represent
abstract
concepts;
(iii)
a
rostral-caudal
abstraction
gradient
exists
in
the
PFC;
and
(iv)
the
inferior
frontal
gyrus
exerts
inhibi-
tory
control
over
task-irrelevant
information.
How
is
thinking
realized
in
the
human
brain?
One
of
the
deepest
puzzles
for
cognitive
neuroscience
is
to
explain
how
the
most
distinctively
human
types
of
think-
ing
and
reasoning
are
realized
in
the
brain.
Humans
can
grasp
analogies
between
disparate
situations,
infer
hidden
causes
of
observed
events,
apply
general
rules
to
novel
situations,
and
learn
new
abstractions
from
experience
[1–
3].
Such
intellectual
abilities,
which
exceed
those
of
any
other
extant
primate
species
(perhaps
in
a
qualitative
manner
[4])
are
difficult
to
capture
in
any
computational
model,
but
pose
particular
challenges
for
those
that
aim
for
neural
fidelity.
How
does
the
brain
organize
neurons,
which
are
basically
simple
computing
devices,
so
as
to
achieve
the
kinds
of
complexity
manifested
in
human
thinking
and
reasoning?
Research
over
the
past
decade
and
a
half
has
begun
to
address
this
challenge.
Cognitive
neuropsychological
and
neuroimaging
studies
have
implicated
various
subregions
of
the
prefrontal
cortex
(PFC;
Figure
1)
as
critical
parts
of
a
larger
network
supporting
higher
cognition
(for
reviews,
see
[5–9]).
The
most
anterior
lateral
portion
of
the
PFC,
generally
termed
frontopolar
or
rostrolateral
(RLPFC),
is
activated
by
tasks
that
require
integration
of
multiple
relations,
processing
relatively
abstract
concepts,
or
nego-
tiating
hierarchical
goal
structures
[10–22].
More
dorsal
and
inferior
areas
of
the
PFC
have
also
been
implicated
in
the
systematic
control
of
representations
necessary
for
these
processes
[10,13,20,23–25].
Over
roughly
the
same
time
period,
a
number
of
compu-
tational
models
[26–30]
have
attempted
to
explain
aspects
of
human
thinking
and
reasoning
within
neural
systems,
differing
in
their
architectures
and
domains
of
application
(Table
1).
A
substantial
gap
remains,
however,
between
current
theories
of
PFC
function
and
computational
mod-
els
capable
of
actually
performing
tasks
involving
thinking
Opinion
Glossary
Active
memory:
information
in
a
state
of
current
readiness
for
use
in
processing
(including
the
active
portion
of
LTM),
typically
over
a
time
span
of
around
20
seconds.
Analogical
mapping:
the
process
of
identifying
systematic
correspondences
between
elements
of
two
situations
(analogs)
based
on
relational
structure.
Cross-frequency
coupling:
interactions
between
different
frequency
bands,
such
as
theta
and
gamma,
which
aid
in
integrating
neural
activity
across
different
spatial
and
temporal
scales.
Driver:
in
LISA,
an
analog
that
is
currently
in
active
memory
and
serves
as
a
generator
of
spreading
activation.
Phase
set:
in
LISA,
the
set
of
mutually
desynchronized
role
bindings
represented
by
neuronal
oscillations.
The
phase
set
corresponds
to
the
current
focus
of
attention
and
is
the
most
significant
bottleneck
for
reasoning
with
relations.
The
phase
set
is
equivalent
to
working
memory
(WM)
for
relations.
Proposition:
a
predicate
instantiated
by
binding
its
role(s)
to
particular
arguments
(objects
or
other
propositions).
A
proposition
is
the
smallest
unit
of
representation
that
can
have
a
truth
value:
intuitively,
a
‘complete
thought’.
In
LISA,
a
proposition
is
represented
by
a
hierarchy
of
structure
units.
Proxy
unit:
a
transient
representation
of
a
structure
unit,
formed
in
prefrontal
cortex
in
order
to
support
structured
reasoning,
such
as
an
analogical
comparison.
Recipient:
in
LISA,
an
analog
that
is
currently
receiving
activation
from
the
driver.
There
may
be
multiple
recipients
in
long-term
memory
(during
retrieval)
or
a
single
recipient
in
active
memory
(during
mapping,
inference,
and
schema
induction).
Role-based
relational
reasoning:
reasoning
that
depends
on
the
active
representation
and
manipulation
of
concepts
involving
roles
and
role
binding
(see
‘proposition’).
Role
binding:
the
binding
of
a
single
argument
(object
or
proposition)
to
a
single
role
associated
with
a
predicate.
Schema:
a
relatively
abstract
relational
structure
representing
a
category
or
class
of
situations
(e.g.,
a
schema
for
a
type
of
problem).
In
LISA,
schemas
can
be
formed
as
a
consequence
of
comparing
two
or
more
relatively
specific
analogs.
Semantic
unit:
a
unit
that
represents
a
simple
element
of
meaning,
associated
with
neurons
in
posterior
cortex.
In
LISA,
semantic
units
are
the
sole
conduits
for
the
transmission
of
activation
between
distinct
analogs.
Spike-timing-dependent
plasticity:
a
phenomenon
based
on
evidence
that
if
a
neuron
is
being
driven
at
a
high
rate,
as
occurs
in
the
high
gamma
band,
the
inputs
driving
it
will
be
strengthened.
It
provides
a
neural
mechanism
by
which
the
kind
of
synchronous
activity
that
in
the
LISA
model
supports
dynamic
representations
will
also
lead
to
synaptic
strengthening.
Structure
unit:
in
LISA,
a
unit
representing
a
component
of
a
proposition
within
an
analog:
P
(proposition),
RB
(role
binding),
O
(object),
and
R
(role);
or
a
correspondence
between
elements
of
two
analogs
(M).
Such
units
may
be
associated
with
neurons
in
posterior
cortex
(when
stored
in
LTM),
but
must
also
be
associated
with
dynamically
recruited
neurons
in
prefrontal
cortex
(see
‘proxy
unit’).
Corresponding
author:
Knowlton,
B.J.
(knowlton@psych.ucla.edu).
1364-6613/$
see
front
matter
ß
2012
Published
by
Elsevier
Ltd.
http://dx.doi.org/10.1016/j.tics.2012.06.002
Trends
in
Cognitive
Sciences,
July
2012,
Vol.
16,
No.
7
373
Author's personal copy
and
reasoning.
Functional
theories
often
highlight
very
general
concepts
such
as
‘abstraction’
and
‘relational
inte-
gration’,
which
though
potentially
helpful
remain
ill-de-
fined
in
the
absence
of
computational
instantiations.
Here
we
attempt
to
build
an
initial
bridge
across
this
gap.
Focusing
on
computational
mechanisms
instantiated
in
a
leading
model
of
relational
reasoning,
‘Learning
and
Inference
with
Schemas
and
Analogies’
(LISA;
[27,31]),
we
review
the
neural
literature
to
construct
more
specific
hypotheses
about
how
these
mechanisms
may
be
realized
in
the
human
brain.
Even
though
our
focus
is
on
the
LISA
model,
we
will
also
note
connections
with
other
neurocom-
putational
models.
Our
opinion
article
reveals
a
remark-
able
convergence
between
constraints
on
models
of
human
reasoning
derived
from
computational
analyses,
behavior-
al
experiments,
and
neurophysiological
investigations.
Al-
though
necessarily
preliminary,
we
hope
that
this
effort
will
help
the
development
of
more
detailed
neural
models
of
high-level
cognition.
Role-based
relational
reasoning
in
LISA
The
LISA
model
provides
a
computational
account
of
role-
based
relational
reasoning:
inferences
that
depend
on
the
roles
that
entities
play,
not
just
on
perceptual
similarity.
For
example,
knowing
that
Sam
is
an
enemy
of
Brian,
and
Dylan
is
a
friend
of
Sam,
a
person
might
conjecture
that
Dylan
may
also
be
an
enemy
of
Brian
(Figure
2).
This
‘mutual
support’
schema
may
have
itself
been
acquired
through
analogical
reasoning,
by
comparing
specific
cases
that
share
a
common
relational
structure.
LISA
codes
an
analog
by
binding
distributed
repre-
sentations
of
roles
to
distributed
representations
of
their
fillers
(coded
on
separate
pools
of
semantic
units;
Figure
2).
Semantic
units
are
assumed
to
be
coded
by
neurons
in
posterior
regions.
For
each
individual
analog,
a
hierarchy
of
localist
structure
units
represents
objects
(O),
relational
roles
(R),
individual
role
bindings
(RB),
and
complete
propositions
(P).
Structure
units
may
be
coded
in
long-term
memory
(LTM),
but
in
order
to
be
made
available
for
active
comparisons,
they
require
a
transient
form
(proxy
units)
in
active
memory
[32].
Dur-
ing
mapping,
the
emerging
correspondences
are
also
coded
by
proxy
units,
called
M
(mapping)
units,
that
connect
structure
units
of
a
given
type
across
the
two
analogs
(e.g.,
P
units
to
P
units).
These
explicit
learned
correspondences
allow
LISA
to
assess
the
overall
simi-
larity
between
two
analogs
[33]
and
to
generate
sensible
PC
TPJ
ACC
MTL
ATL
UF
DLPFC
RLPFC
VLPFC
SLF
TRENDS in Cognitive Sciences
Figure
1.
Anatomy
and
connections
related
to
relational
reasoning.
Areas
of
the
prefrontal
cortex
(PFC)
frequently
identified
in
reasoning
studies
include
the
rostrolateral
prefrontal
cortex
(RLPFC;
anterior
region
of
the
inferior
frontal
gyrus,
approximately
Brodmann
area
10,
sometimes
referred
to
as
frontopolar
prefrontal
cortex),
the
dorsolateral
prefrontal
cortex
(DLPFC;
anterior
region
of
the
middle
frontal
gyrus,
approximately
Brodmann
areas
9/46),
and
the
ventrolateral
prefrontal
cortex
(VLPFC;
posterior
region
of
the
inferior
frontal
gyrus,
approximately
Brodmann
areas
47/45/44).
The
anterior
temporal
lobe
(ATL;
located
on
the
anterior
lateral
surface
of
the
temporal
lobe,
approximately
Brodmann
areas
20,
31,
38)
is
frequently
associated
with
semantic
memory
(see
[72])
and
is
important
for
reasoning
about
semantic
relations
[24].
The
medial
temporal
lobe
(MTL;
located
on
the
medial
surface
of
the
temporal
lobe
including
the
hippocampus
and
entorhinal
cortex,
approximately
Brodmann
areas
27,
28,
34,
35,
36)
is
critical
for
episodic
memory
[73],
and
thus
is
important
for
relational
reasoning
about
specific
events.
The
ATL
and
MTL
are
connected
to
areas
in
the
VLPFC
via
the
uncinate
fasiculus
(UF).
Regions
in
the
parietal
lobe,
such
as
areas
around
and
including
the
precuneus
(PC;
approximately
Brodmann
area
7)
and
the
temporal
parietal
junction
(TPJ;
approximately
Brodmann
area
39)
have
heavy
reciprocal
connections
to
the
PFC
via
the
superior
longitudinal
fasciculus
(SLF).
These
areas
are
frequently
associated
with
tasks
requiring
relational
reasoning
about
visuospatial
entitites.
The
anterior
cingulate
cortex
(ACC;
located
on
the
medial
surface
of
prefrontal
cortex
approximately,
Brodmann
areas
24,
32,
33)
is
frequently
active
during
relational
reasoning
and
has
reciprocal
connections
to
the
DLPFC.
Table
1.
Major
neurocomputational
models
of
human
thinking
Model
Architecture
Domain(s)
of
Application
Unique
Characteristics
SMRITI
[28] Localist
connectionist
network
using
binding
by
synchrony
Episodic
memory
encoding,
storage,
binding
and
retrieval
Corresponds
to
known
architecture
of
hippocampus
LISA
[27,31] Distributed
connectionist
network
using
binding
by
synchrony
Relational
reasoning
Integrates
dynamic
binding
in
WM
with
static
binding
in
LTM,
enabling
symbolic
processing
to
arise
from
a
neural
architecture
STAR-2
[26] Connectionist
network
using
tensor
products
to
code
bindings
Relational
reasoning
Tensor
rank
(number
of
basis
vectors
that
together
define
the
tensor)
corresponds
to
relational
complexity,
predicting
difficulty
of
reasoning
tasks
ACT-R
with
neural
modules
[30]
Production
system
integrated
with
modules
for
perception,
motor
responses,
spatial
representation,
memory
retrieval,
and
goal
maintenance
Solving
algebraic
equations
and
related
laboratory
tasks
Provides
a
macro-level
mapping
between
information-processing
modules
and
brain
areas,
coupled
with
an
analysis
of
the
time
course
of
activation
for
each
module
SAL
(Synthesis
of
ACT-R
and
Leabra)
[29]
Production
system
with
declarative
memory
(ACT-R);
subsymbolic
processes
realized
by
a
connectionist
network
based
on
a
point-
neuron
activation
function
(Leabra)
Spatial
navigation
and
search
Integration
of
symbolic
control
processes
with
subsymbolic
representations
and
learning
mechanisms,
using
a
neurally-
constrained
architecture
Opinion Trends
in
Cognitive
Sciences
July
2012,
Vol.
16,
No.
7
374
Author's personal copy
structured
inferences
based
on
correspondences
between
elements
of
the
two
analogs.
LISA
exploits
dynamic
binding
coded
by
neural
synchro-
ny
[34]
to
impose
a
hierarchical
temporal
structure
on
knowledge
representations
within
working
memory
(WM).
A
small
number
of
role
bindings
in
one
analog
(the
driver)
can
enter
the
phase
set
the
set
of
mutually
desynchronized
role
bindings.
The
phase
set
corresponds
to
the
current
focus
of
attention,
and
is
the
most
significant
bottleneck
in
the
system.
Each
individual
phase
(the
smal-
lest
unit
of
WM)
corresponds
to
one
role
binding
(i.e.,
an
RB
unit
and
its
constituents).
The
size
of
the
phase
set
is
determined
by
the
number
of
role-filler
bindings
(phases)
that
can
be
simultaneously
active
but
mutually
out
of
synchrony.
The
maximum
number
is
proportional
to
the
length
of
time
between
successive
peaks
in
a
phase
(the
period
of
the
oscillation)
divided
by
the
duration
of
each
phase
(at
the
level
of
small
populations
of
neurons)
and/or
temporal
precision
(at
the
level
of
individual
spikes)
[35].
Binding
may
be
accomplished
by
synchrony
in
the
>30
Hz
(gamma)
range,
with
a
neuron
or
population
of
neurons
generating
one
spike
(or
burst)
approximately
every
25
ms,
implying
WM
capacity
of
approximately
4-6
role
bindings
(roughly
2-3
propositions).
This
value
is
consistent
with
estimates
of
WM
capacity
based
on
behavioral
evidence
(e.g.,
[36])
and
may
have
roots
in
the
mechanisms
by
which
information
is
processed
throughout
the
brain,
including
lower-level
posterior
cortex
[37].
Because
of
the
strong
capacity
limit
on
its
phase
set,
LISA’s
processing
is
necessarily
highly
sequential,
Supported + Sam
Supports + Dylan
Supports + Dylan
Supported + Sam
Time
Supported + Sam
Supports + Dylan
Semantic + units
Structure units
e1 e2 s1 s2 SB
D
e2+B
s2+S
S1+D
e2+B
e (S, B) s (D, S)
Enemy-of (Sam, Brian)
Semantic units Semantic units
Structure units
Enemy-of (Sam, Brian) Supports (Dylan, Sam) Enemy-of (Dylan, Brian)
e1 e1 e2
e1+S e1+S
RB units
P units
e2+B e2+B E1+D e2+B
e (D, B)
s (D, S)e (S, B)
S1+D s1+R s2+S
e2+B
e (R, B)
s (R, S)
e (S, B)
(a) (b)
(d)(c)
Enemy-of (Sam, Brian) Supports (Dylan, Sam) Enemy-of (Dylan, Brian)
E1+D
s2+S
e2 s1 s1 s2
s2 S
SBD
B
D
R & O units
Structure units
Supports (Dylan, Sam) Enemy-of (Ralph, Brian)
e (D, B)
e1+S E1+D
TRENDS in Cognitive Sciences
Figure
2.
Representation
of
propositions
in
the
LISA
model.
(a)
A
pool
of
semantic
units
(bottom),
which
are
connected
to
localist
structure
units
that
capture
bindings
at
successive
levels
of
generality:
individual
roles
and
objects,
bindings
of
objects
to
roles,
and
bindings
of
role/filler
combinations
into
propositions.
(b)
In
a
single
phase
of
the
dynamic
form
of
binding,
one
role
binding
of
one
proposition
becomes
active,
along
with
its
constituent
O
and
R
units
and
associated
semantic
units.
(c)
In
a
subsequent
phase,
a
different
role
binding
and
its
constituents
are
activated
in
synchrony
with
each
other
(and
out
of
synchrony
with
the
first
role
binding).
(d)
The
overall
pattern
in
which
structure
units
for
the
proposition
fire
across
a
series
of
temporal
phases.
Input
Analog
retrieval
Mapping
Analogical
inference
Schema
induction
Guided
pattern
recognition
Hebbian
learning
Self-
supervised
learning
Intersection
discovery
TRENDS in Cognitive Sciences
Figure
3.
Operations
on
LISA’s
knowledge
representations
at
major
stages
of
relational
reasoning
and
learning.
Opinion Trends
in
Cognitive
Sciences
July
2012,
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16,
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7
375
Author's personal copy
constituting
a
form
of
guided
pattern
recognition
(Figure
3).
At
any
given
moment,
one
analog
(the
driver)
is
the
focus
of
attention.
As
one
or
more
driver
propositions
enter
the
phase
set,
synchronized
patterns
of
activation
are
generated
on
the
semantic
units
(one
pattern
per
RB).
In
turn,
these
patterns
activate
propositions
in
one
or
more
recipient
analogs
in
LTM
(during
retrieval),
or
a
single
recipient
in
active
memory
(during
mapping,
infer-
ence
and
schema
induction).
LISA
provides
a
natural
account
of
the
loss
of
relational
reasoning
in
populations
with
forms
of
brain
damage,
such
as
patients
suffering
from
either
frontal-lobe
or
temporal-
lobe
variants
of
Frontotemporal
Lobar
Degeneration
[24].
The
model
has
also
been
used
to
simulate
changes
in
relational
reasoning
during
cognitive
development
[38–
40]
and
normal
aging
[41].
In
the
remainder
of
this
article
we
review
several
key
neural
findings
that
appear
to
correspond
to
computational
constraints
that
arise
in
LISA.
Role
of
oscillatory
activity
in
reasoning
LISA
fundamentally
depends
on
the
representation
of
information
in
a
temporal
structure.
RB
units
must
be
activated
in
synchrony
with
O
and
P
units
(and
their
associated
semantic
units)
to
form
dynamic
representa-
tions,
while
these
different
representational
complexes
must
be
kept
out
of
synchrony
with
each
other
to
maintain
distinct,
non-overlapping
role-filler
bindings
(Figure
4a,
b).
Temporal
structure
in
the
form
of
oscillatory
activity
is
in
fact
prominent
in
the
brain
[42],
although
no
direct
evi-
dence
yet
connects
such
activity
to
the
coding
of
proposi-
tions.
Rhythmic
neural
activity,
as
reflected
in
the
firing
of
groups
of
neurons,
can
be
detected
throughout
the
central
nervous
system,
both
in
local
interactions
within
a
neural
ensemble,
and
across
brain
regions
through
long-distance
connections
between
populations
of
neurons
[43].
Oscillations
can
arise
from
the
intrinsic
circuit
proper-
ties
of
the
central
nervous
system,
as
neurons
tend
to
be
interconnected
with
numerous
excitatory
and
inhibitory
neurons,
resulting
in
entrainment
of
firing
of
an
ensemble
of
neurons
at
a
specific
frequency.
These
oscillations
may
reflect
the
firing
rates
of
individual
neurons,
such
as
those
that
show
bursts
of
firing
in
the
gamma
band.
Slower
oscillations,
such
as
firing
in
the
theta
band
(4–8
Hz),
generally
do
not
arise
from
a
group
of
individual
neurons
firing
at
that
frequency;
rather,
summed
over
a
large
group
of
neurons,
peaks
of
firing
will
be
apparent
at
this
lower
frequency
due
to
slower
feedback
modulation.
In
LISA,
the
smallest
unit
of
WM
is
essentially
defined
as
the
synchronous
firing
of
representational
units.
Impor-
tantly,
LISA
uses
phase
to
maintain
the
separation
of
multiple
role-filler
bindings.
Behavioral
experiments
using
a
priming
paradigm
suggest
that
synchrony
underlies
the
representations
of
perceptual
relations
for
humans
[44].
Likewise,
a
recent
EEG
study
suggests
that
phase
syn-
chrony
within
the
fronto-parietal
network
can
bind
object
properties
together
in
WM
[45].
Electrophysiological
stud-
ies
in
nonhuman
primates
have
revealed
a
link
between
WM
and
the
synchronous
firing
of
neural
ensembles.
For
example,
pairs
of
neurons
have
been
shown
to
fire
in
synchrony
in
a
task-dependent
manner,
consistent
with
the
hypothesis
that
synchronous
firing
dynamically
repre-
sents
the
representations
needed
in
WM
to
perform
the
current
task
[46].
The
fact
that
neural
assemblies
can
Spike rate
Spike rate
Time
Excitatory connection
Key:
(2) rb1 rb2
M
Time
M
o4
o3
o1
o2
(1)
(2)
Inhibitory connection
(a) (c) (d)
(b)
p (rb1, rb2)
TRENDS in Cognitive Sciences
Figure
4.
Oscillatory
inhibition
and
cross-frequency
coupling
in
LISA.
(a)
Oscillatory
inhibition
is
central
to
LISA’s
ability
to
exploit
temporal
synchrony
to
discover
relational
mappings
in
WM.
Role-binding
(RB)
units
for
a
single
proposition
[e.g,
p
(rb1,
rb2)]
are
kept
out
of
phase
by
pools
of
inhibitory
neurons
that
inhibit
competing
RBs
(e.g.,
rb1
and
rb2)
(1),
and
also
apply
inhibition
to
an
RB
after
it
fires
(2).
(b)
Thus,
‘tonic’
excitation
from
a
single
proposition
unit
in
the
driver
[e.g,
p
(rb1,
rb2)]
causes
all
attached
RB
units
(e.g.,
rb1
and
rb2
here)
to
fire
out
of
phase
with
each
other,
while
allowing
each
RB
an
opportunity
to
fire
as
determined
by
accumulating
mapping
evidence
(via
the
mapping
connections).
Oscillatory
inhibition
is
critical
for
determining
LISA’s
intrinsically
limited
WM
capacity.
(c-d)
By
using
temporal
synchrony
as
a
binding
mechanism,
LISA
is
able
to
utilize
cross-frequency
coupling
in
conjunction
with
spike-timing-dependent
plasticity
to
rapidly
learn
relational
mappings
(i.e.,
M
units
representing
correspondences
between
objects
in
the
driver
and
the
recipient)
via
Hebbian
learning.
In
this
example,
semantic
units
represented
by
populations
of
neurons
in
posterior
cortex
(blue
units
in
panel
(c)
fire
relatively
slowly
[slower
blue
wave
in
panel
(d)],
sending
activation
to
populations
of
neurons
representing
object1
[red
o1
unit
in
panel
(c)].
These
neurons
fire
at
a
much
higher
collective
frequency
[faster
red
waves
in
panel
(d)].
In
LISA,
similar
types
of
units
in
the
driver
and
recipient
are
connected
via
mapping
units
[represented
here
by
the
dotted
lines
in
panel
(c)].
Synchronous
rapid
firing
of
the
populations
of
neurons
representing
o1
and
o3
result
in
rapid
changes
to
the
mapping
units
via
spike-timing-dependent
plasticity.
Thus,
LISA
quickly
learns
that
o1
and
o3
are
firing
at
the
same
time,
and
hence
correspond
relationally.
A
similar
correspondence
exists
between
o2
and
o4
[orange
units
in
panel
(c)],
which
fire
out
of
synchrony
with
o1
and
o3
given
their
different
roles
in
their
respective
propositions.
Opinion Trends
in
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Sciences
July
2012,
Vol.
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7
376
Author's personal copy
rapidly
shift
between
different
patterns
of
synchrony
depending
on
the
information
being
held
in
WM
indicates
that
the
method
of
representing
propositions
in
LISA
is
neurally
credible.
LISA
also
depends
on
long-distance
communication
between
prefrontal
regions
and
posterior
regions
of
the
cortex,
where
semantic
information
is
stored.
In
order
for
prefrontal
RB
units
to
be
activated
by
semantic
informa-
tion,
there
must
be
a
means
by
which
oscillatory
activity
in
the
temporal
lobes
engages
circuits
in
PFC
that
represent
this
information.
In
the
brain,
synchrony
in
lower
frequen-
cy
bands,
including
theta,
is
detectable
between
sites
separated
by
several
millimeters,
suggesting
that
entrain-
ment
of
neural
activity
across
brain
regions
occurs
at
lower
frequency
oscillations
[47–49].
In
contrast,
synchronous
activity
within
local
neural
circuits
tends
to
be
higher
frequency,
in
the
gamma
range.
Within
the
PFC,
local
circuits
will
require
inhibition
to
maintain
the
phase
rela-
tionships
of
different
role-filler
bindings.
Studies
of
learning
and
memory
have
shown
that
brain
oscillatory
activity
is
relevant
to
behavior.
For
example,
successful
memory
formation
is
associated
with
the
tighter
coupling
of
the
firing
of
individual
neurons
to
the
theta
frequency
[50].
In
addition,
stimulation
during
theta
peaks
is
particularly
effective
in
inducing
long-term
potentiation
in
the
hippocampus,
whereas
blocking
theta
prevents
the
induction
of
long-term
potentiation
[51,52].
It
thus
appears
that
neural
oscillations
provide
support
for
neural
plastic-
ity.
Reasoning
similarly
requires
the
rapid
formation
of
new
representations.
In
LISA,
M
units
are
formed
between
structure
units
in
the
driver
and
recipient
to
capture
correspondences
between
them.
This
type
of
rapid
learning
of
connections
has
been
observed
in
PFC,
based
on
single-
unit
recordings
with
non-human
primates
[53,54].
It
appears
that,
in
addition
to
plasticity
being
related
to
the
phase
of
the
theta
cycle,
high
gamma
frequency
itself
can
directly
enhance
neural
plasticity
through
a
Hebbian
learning
mechanism
[55].
When
neuronal
circuits
fire
at
this
high
rate,
inputs
to
a
neuron
arrive
shortly
before
the
neuron
fires,
which
thus
becomes
depolarized.
In
Hebbian
plasticity,
synaptic
inputs
that
are
active
when
the
neuron
is
depolarized
are
strengthened.
Thus,
if
the
neuron
is
driven
at
a
high
rate,
as
occurs
in
the
high
gamma
band,
the
inputs
driving
it
will
be
strengthened.
This
phenome-
non,
termed
‘spike-timing-dependent
plasticity’
[56],
implies
that
there
is
a
neural
mechanism
by
which
the
kind
of
synchronous
activity
postulated
by
LISA
will
also
lead
to
synaptic
strengthening.
Such
increases
in
synaptic
strength
may
underlie
the
strengthening
of
M
units
during
the
mapping
process.
The
facilitatory
influences
of
theta-
and
gamma-band
activity
on
neural
plasticity
appear
to
be
related
[47,48].
Through
cross-frequency
coupling
(see
[57]),
the
phase
of
the
low
frequency
theta
wave
modulates
the
power
of
the
gamma
band,
such
that
the
amplitude
of
EEG
measured
in
the
gamma
band
is
greatest
at
a
specific
point
in
the
theta
wave
(Figure
4c,
d).
The
theta
wave
may
serve
to
entrain
bursts
at
gamma
frequency
by
shifting
the
probability
of
spike
timing.
By
this
mechanism,
long-dis-
tance
communication
across
regions
in
the
form
of
theta
activity
could
modulate
the
timing
of
gamma
bursts.
It
follows
that
information
in
regions
of
posterior
cortex
responsible
for
representing
semantic
information
may
influence
local
gamma
activity
in
the
PFC
via
theta
fre-
quency
firing.
Additional
evidence
supports
the
hypothesis
that
the
phase
of
neuronal
oscillations
in
the
PFC
codes
the
repre-
sentation
of
specific
items
in
WM.
Simultaneous
recording
of
single
units
and
the
local-field
potential
in
monkeys
have
demonstrated
that
spikes
in
response
to
a
specific
stimulus
occur
at
a
characteristic
point
in
a
32-Hz
cycle,
correspond-
ing
to
the
gamma
band.
When
the
monkey’s
task
was
to
keep
more
than
one
item
in
mind
at
a
time,
spikes
corre-
sponding
to
the
second
item
occurred
at
a
different
point
in
the
wave
[58].
Interestingly,
spike
synchronization
was
also
observed
at
approximately
3
Hz,
at
the
lower
end
of
the
theta
band.
The
fact
that
both
theta
and
gamma
band
oscillations
are
synchronized
in
the
PFC
is
consistent
with
the
possibility
that
cross-frequency
coupling
is
a
means
to
coordinate
activity
in
distant
regions
with
the
rapid
oscil-
lations
that
support
local
processing.
The
finding
that
phase-specific
spiking
in
the
gamma
phase
is
related
to
segregation
of
information
in
WM
is
consistent
with
LISA’s
mechanism
for
representing
propositions
via
temporal
asynchrony
of
role
bindings.
Proxy
units
in
prefrontal
cortex
In
LISA,
when
propositions
enter
active
memory,
proxy
units
(the
transient
form
of
structure
units)
are
rapidly
formed
in
PFC.
These
proxy
units
that
code
individual
analogs
in
turn
connect
to
M
units
that
represent
corre-
spondences
between
the
elements
of
two
analogs.
The
rapid
learning
required
by
these
units
could
be
supported
by
the
spike-timing-dependent
plasticity
that
can
occur
during
high
gamma-band
activity
synchronized
to
the
theta
rhythm
[56].
The
rapid
changing
of
weights
on
these
units
makes
them
suitable
to
dynamically
represent
dif-
ferent
stimuli
depending
on
the
information
being
pro-
cessed
at
the
moment.
Neurons
with
the
properties
ascribed
to
proxy
units
have
been
identified
in
the
primate
lateral
PFC
[53,54,59].
About
a
third
of
neurons
in
the
lateral
PFC
respond
to
categories
of
stimuli,
which
means
that
the
neuron
will
increase
firing
rate
when
presented
with
members
of
a
particular
category
(e.g.,
dogs).
Impor-
tantly,
these
neurons
fire
based
on
the
conceptual
proper-
ties
of
the
stimuli,
and
not
simply
on
the
basis
of
their
visual
features.
Unlike
neurons
in
inferotemporal
cortex,
neurons
in
lateral
PFC
respect
the
sharp
boundaries
be-
tween
categories.
These
neurons
respond
similarly
to
typi-
cal
and
atypical
members
of
a
category,
which
suggests
that
they
are
sensitive
to
the
rules
defining
the
concept
itself.
This
property
is
necessary
for
the
proxy
units
in
LISA,
in
that
they
must
be
able
to
represent
high-level
propositions
that
are
abstract.
Furthermore,
neurons
in
the
PFC
appear
to
also
be
able
to
code
abstract
relational
rules.
Cromer
et
al.
[54]
had
monkeys
perform
two
different
tasks:
one
in
which
they
had
to
respond
to
matching
stimuli
and
another
in
which
they
had
to
respond
if
the
stimuli
did
not
match
[13].
The
most
common
type
of
neuron
recorded
in
the
prefrontal
cortex
(41%
of
all
those
recorded)
responded
selectively
to
the
current
rule,
regardless
of
the
stimuli
that
were
pres-
ent.
These
neurons
thus
appear
to
represent
the
relation
Opinion Trends
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7
377
Author's personal copy
between
stimuli
and
a
rule
governing
the
current
task
not
the
stimuli
themselves
a
major
requirement
for
the
proxy
units
posited
by
LISA.
Although
neurons
responding
to
abstract
rules
could
be
found
in
all
regions
of
the
PFC,
the
majority
were
located
in
the
lateral
subregion.
The
apparent
flexibility
of
these
neurons
is
another
property
that
makes
them
suitable
as
instantiations
of
the
proxy
units
postulated
by
LISA.
Individual
neurons
do
not
simply
respond
to
one
type
of
stimulus;
rather,
in
the
context
of
different
tasks,
they
respond
to
different
catego-
ries
[54].
A
neuron’s
response
to
the
same
stimulus
can
vary
on
a
trial-by-trial
basis
depending
on
the
task
per-
formed
[60].
This
flexibility
stands
in
stark
contrast
to
the
firing
properties
of
inferotemporal
neurons,
in
which
firing
to
a
complex
visual
stimulus
is
relatively
static
[61].
Al-
though
caution
is
warranted
in
extrapolating
from
studies
of
monkeys
to
more
complex
human
reasoning,
such
find-
ings
suggest
that
PFC
neurons
may
act
as
representational
elements
for
very
different
propositions
depending
on
the
task
context.
Such
dynamic
repurposing
of
neurons
is
consistent
with
the
flexible
role
played
by
proxy
units
in
the
LISA
model.
Proxy
units
are
formed
rapidly
to
represent
propositions
during
reasoning.
Spike-timing-dependent
plasticity
resulting
from
fast
gamma-band
activity
in
prefrontal
neurons
can
support
the
kind
of
rapid
changes
in
response
properties
that
are
necessary
for
proxy
units.
Importantly,
synaptic
strength
can
be
rapidly
decreased,
as
well
as
increased,
based
on
the
timing
of
presynaptic
firing
and
post-synaptic
depolarization.
Long-term
depression
of
syn-
aptic
strength
allows
neurons
to
be
returned
to
a
pool
from
which
they
can
be
recruited
for
the
representation
of
new
propositions.
Moreover,
the
shift
from
long-term
potentia-
tion
to
long-term
depression
occurs
as
the
result
of
a
shift
in
spike
timing
on
the
order
of
milliseconds
[62].
These
findings
suggest
that
spike-timing-dependent
plasticity
can
support
the
rapid
binding
and
unbinding
that
is
fun-
damental
to
the
LISA
model.
Rostral-caudal
abstraction
gradient
in
PFC
Recently,
an
effort
has
been
made
to
understand
the
sub-
regions
in
PFC
in
terms
of
a
hierarchy
of
action.
Badre
and
D’Esposito
[6]
have
argued
that
more
caudal
regions
of
the
PFC
are
involved
in
generating
specific
stimulus-response
motor
actions,
whereas
progressively
more
rostral
regions
become
more
involved
when
actions
must
be
based
on
more
abstract
information
(e.g.,
a
plan
based
on
the
integration
of
multiple
subgoals)
[6].
For
example,
although
caudal
regions
of
the
PFC
are
sufficient
to
subserve
the
act
of
picking
up
a
cup
from
which
to
drink,
more
rostral
regions
would
become
engaged
in
the
act
of
deciding
what
to
drink
in
order
to
satisfy
more
abstract
goals
(e.g.,
trying
to
be
healthy).
Similarly,
Christoff
et
al.
[16]
have
shown
that
a
set
to
process
more
abstract
concepts
selectively
activates
RLPFC.
In
LISA,
the
highest
level
of
hierarchical
organization
is
reflected
in
the
M
units,
which
form
rapid
associations
between
elements
of
propositions
in
the
analogs
being
com-
pared.
These
mapping
units
represent
very
abstract
infor-
mation,
specifically,
shared
relational
roles
that
can
make
otherwise
dissimilar
propositions
analogous.
Moreover,
the
very
process
of
identifying
relational
commonalities
can
trigger
the
acquisition
of
more
abstract
schemas
for
classes
of
situations.
The
LISA
architecture
is
thus
based
on
repre-
sentations
at
successive
levels
of
abstraction,
an
overall
structure
that
appears
to
be
reflected
in
the
organization
of
the
PFC.
The
role
of
inhibition
in
reasoning
The
nervous
system
is
characterized
by
the
interplay
of
excitation
and
inhibition.
At
the
circuit
level,
the
tight
coupling
of
inhibitory
interneurons
and
excitatory
neurons
results
in
oscillatory
activity
that
allows
for
temporal
coding
of
information
in
LISA’s
WM.
As
discussed
above,
circuit-level
inhibition
is
required
to
maintain
role-filler
bindings
mutually
out
of
synchrony,
and
thus
distinct
in
WM
(Figure
4a,
b).
In
addition,
inhibition
plays
a
role
in
reducing
interference
from
competing
semantic
concepts
during
analogical
reasoning
(e.g.,
[24,25,34,40]).
Activation
of
propositions
in
the
driver
analog
will
trigger
activation
in
related
semantic
units,
which
in
turn
will
activate
candidate
recipient
propositions.
The
most
active
recipient
propositions
will
eventually
enter
WM
and
be
available
for
analogical
mapping.
However,
if
task-irrelevant
propositions
are
activated
in
the
driver,
these
may
bias
the
system
to
find
suboptimal
correspondences.
LISA
postulates
top-down
inhibition
of
propositions
tagged
as
low
in
goal-relevance,
which
helps
prevent
these
propositions
from
entering
the
phase
set.
This
selectivity
increases
the
efficiency
of
the
mapping
process
by
enhancing
the
signal-to-noise
ratio
favoring
goal-relevant
matches.
Regions
in
the
PFC
exhibit
similar
properties
by
selectively
inhibiting
semantic
representations
in
posterior
regions
of
cortex.
The
PFC
has
many
reciprocal
connections
with
posterior
cortical
regions,
including
in
particular
tem-
poral
and
posterior
parietal
lobes
(see
[63]),
and
thus
is
able
to
influence
processing
in
these
regions.
The
primary
evi-
dence
for
the
role
of
the
PFC
in
inhibition
is
that
a
major
consequence
of
prefrontal
lesions
is
behavioral
disinhibi-
tion.
Patients
with
damage
to
the
prefrontal
cortex
often
fail
to
inhibit
inappropriate
behaviors
and
have
difficulty
main-
taining
cognitive
control.
By
one
view,
the
main
role
of
the
prefrontal
cortex
is
the
dynamic
filtering
of
activations
in
posterior
cortical
regions
to
facilitate
behavior
directed
towards
a
goal
[64].
Different
subregions
appear
to
support
inhibition
in
different
domains.
In
particular,
damage
to
the
right
inferior
prefrontal
cortex
impairs
ability
to
inhibit
a
prepotent
response
in
cognitive
tasks
whereas
damage
to
orbitofrontal
regions
results
in
social
and
emotional
disin-
hibition
[65].
Behavioral
studies
have
shown
that
the
presence
of
irrelevant
relations
in
analogs
can
impact
relational
rea-
soning,
suggesting
the
inhibition
is
a
necessary
component
of
analogical
reasoning
[24,25,38,40,41,66].
Neuroimaging
studies
have
produced
even
more
direct
evidence
of
the
engagement
of
prefrontal
inhibitory
control
during
analog-
ical
reasoning.
In
a
number
of
studies,
activity
was
ob-
served
in
the
inferior
frontal
gyrus
while
subjects
were
solving
analogy
problems
[23,67].
This
same
region
has
been
shown
to
be
active
in
a
number
of
tasks
of
inhibitory
control
or
semantic
competition
(see
[65]).
Cho
et
al.
(2010)
found
direct
evidence
for
the
involvement
of
this
region
in
Opinion Trends
in
Cognitive
Sciences
July
2012,
Vol.
16,
No.
7
378
Author's personal copy
inhibitory
control
during
analogy,
showing
that
activity
in
a
region
of
right
inferior
frontal
gyrus
increased
when
the
amount
of
interfering
information
increased
[13].
Similar-
ly,
using
recordings
of
scalp
EEG,
Sweis
et
al.
(2012)
found
that
when
participants
needed
to
ignore
a
distracting
relation
while
solving
a
visual
analogy,
right
PFC
was
modulated
at
late
stages
of
processing,
and
the
degree
of
modulation
interacted
with
the
reasoner’s
WM
capacity
[20].
The
inferior
frontal
gyrus
thus
may
be
the
anatomical
source
of
the
active
inhibition
of
competing
units
postulat-
ed
by
the
LISA
model.
Further
directions
Many
open
questions
remain
(Box
1).
Although
we
have
focused
on
implications
of
neural
evidence
for
the
LISA
model,
these
findings
have
implications
for
other
neurocom-
putational
models.
Moreover,
aspects
of
several
of
these
models
might
be
integrated
to
broaden
coverage
of
high-
level
human
cognition.
LISA
and
SMRITI
[28]
both
use
patterns
of
neural
timing
to
encode
binding
information,
and
can
be
viewed
as
complementary
(LISA
focusing
on
prefrontal
functions
and
reflective
reasoning,
SMRITI
focus-
ing
on
hippocampal
functions).
The
macro-level
neural
mod-
ules
postulated
by
ACT-R
[30]
are
compatible
with
LISA;
ACT-R
can
be
viewed
as
a
model
of
the
control
structure
within
which
human
relational
reasoning
may
operate.
There
is
reason
to
hope
that
advances
in
neuroimaging
techniques
[68],
combined
with
refined
methods
for
ana-
lyzing
temporal
patterns
of
neural
activity,
will
make
it
possible
to
directly
test
some
of
the
hypotheses
we
have
laid
out
concerning
the
neural
basis
of
relational
reason-
ing.
In
addition,
the
general
LISA
architecture
may
be
extended
to
incorporate
additional
factors
related
to
PFC
function.
For
example,
in
order
to
capture
information
processing
in
the
PFC
more
fully,
the
LISA
model
would
need
to
incorporate
the
influences
of
neuromodulators.
Monoamine
neurotransmitters,
including
dopamine,
nor-
epinephrine
and
serotonin,
each
have
complex
neuromo-
dulatory
roles.
Depending
on
the
conditions,
these
compounds
have
very
large
inhibitory
or
excitatory
effects
on
neural
transmission
within
the
PFC;
moreover,
their
effects
often
seem
to
interact
with
one
another
[69].
A
large
number
of
psychiatric
conditions
that
affect
cognition
in-
volve
monoamine
dysregulation,
and
a
suitably
expanded
LISA
model
could
aid
in
understanding
these
disorders
at
the
circuit
level.
It
is
likely
that
some
individual
differences
in
reasoning
ability
may
be
explained
by
polymorphisms
in
genes
that
code
for
monoamine
receptors
(e.g.,
[70]).
In
addition,
the
cognitive
monitoring
and
evaluative
func-
tions
of
the
anterior
cingulate
cortex
may
impact
PFC
processing
via
connections
with
neurons
in
the
locus
coer-
ruleus
that
are
the
source
of
cortical
noradrenergic
modu-
lation
[71].
Thus,
elaborating
the
LISA
model
to
incorporate
neuromodulatory
effects
could
lead
to
further
advances
in
understanding
the
conditions
that
lead
to
optimal
(and
suboptimal)
reasoning
in
the
human
brain.
Acknowledgements
Preparation
of
this
paper
was
supported
by
the
Intelligence
Advanced
Research
Projects
Activity
(IARPA)
via
Department
of
the
Interior
(DOI)
contract
number
D10PC20022.
The
U.S.
Government
is
authorized
to
reproduce
and
distribute
reprints
for
governmental
purposes
notwithstanding
any
copyright
annotation
thereon.
The
views
and
conclusions
contained
hereon
are
those
of
the
authors
and
should
not
be
interpreted
as
necessarily
representing
the
official
policies
or
endorsements,
either
expressed
or
implied,
of
IARPA,
DOI,
or
the
U.S.
Government.
Additional
support
was
provided
by
the
American
Federation
of
Aging
Research
and
Arthur
Gilbert
Foundation,
the
Illinois
Department
of
Public
Health,
the
Loyola
University
Chicago
Dean
of
Arts
and
Sciences
and
the
Graduate
School
(to
R.G.M.).
We
thank
Krishna
Bharani
for
help
in
preparing
the
manuscript,
and
Paul
Kogut
and
the
rest
of
the
Lockheed
Martin
FRAMES
team
for
many
helpful
discussions.
Two
anonymous
reviewers
provided
valuable
comments
on
an
earlier
draft.
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Box
1.
Questions
for
future
research
Recent
work
in
the
cognitive
neuroscience
of
thinking
and
in
computational
modeling
has
raised
new
hypotheses
about
how
thinking
is
realized
in
the
human
brain.
Some
current
questions
are:
Can
direct
evidence
be
obtained
to
support
the
possible
role
of
oscillatory
neural
activity
in
coding
propositions
in
human
PFC?
Can
computational
models
employing
oscillatory
algorithms
such
as
cross-cortical
coupling
be
used
to
predict
the
brain’s
complex
network
dynamics
during
relational
reasoning
as
measured
via
electrophysiology?
How
are
the
various
types
of
inhibition
necessary
for
a
model
such
as
LISA
implemented
in
the
brain
throughout
the
time
course
of
relational
reasoning?
What
functions
does
the
RLPFC
support
in
relational
reasoning
at
a
computational
level
and
how
do
these
relate
to
its
functions
in
other
tasks?
What
is
the
relationship
between
dynamic
role
binding
in
the
PFC
and
the
binding
operations
subserved
by
the
hippocampus
and
medial
temporal
cortex?
What
roles
do
neurotransmitters
play
in
relational
reasoning
and
can
their
effects
be
mapped
onto
components
of
a
computational
model?
What
learning
processes