Mental Models in the Brain: On Context-Dependent Neural Correlates of Mental Models

Abstract

In this paper, the concept of context-dependent realisation of mental models is introduced and discussed. Literature from neuroscience is discussed showing that different types of mental models can use different types of brain areas. Moreover, it is discussed that the same occurs for the formation and adaptation of mental models and the control of these processes. This makes that it is hard to claim that all mental models use the same brain mechanisms and areas. Instead, the notion of context-dependent realisation is proposed here as a better manner to relate neural correlates to mental models. It is shown in some formal detail how this context-dependent realisation approach can be related to well-known perspectives based on bridge principle realisation and interpretation mapping realisation.

Full text

Cognitive Systems Research 69 (2021) 83–90
Available online 21 June 2021
1389-0417/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Mental models in the brain: On context-dependent neural correlates of
mental models
Jan Treur
Social AI Group, Vrije Universiteit Amsterdam, Netherlands
ARTICLE INFO
Keywords:
Brain
Realisation
Mental model
Neural correlate
ABSTRACT
In this paper, the concept of context-dependent realisation of mental models is introduced and discussed.
Literature from neuroscience is discussed showing that different types of mental models can use different types of
brain areas. Moreover, it is discussed that the same occurs for the formation and adaptation of mental models and
the control of these processes. This makes that it is hard to claim that all mental models use the same brain
mechanisms and areas. Instead, the notion of context-dependent realisation is proposed here as a better manner
to relate neural correlates to mental models. It is shown in some formal detail how this context-dependent
realisation approach can be related to well-known perspectives based on bridge principle realisation and
interpretation mapping realisation.
1. Introduction
Mental models can occur in various forms; e.g., (Craik, 1943; Evans,
2006; Furlough & Gillan, 2018; Gentner & Stevens, 1983; Halford, 1993;
Johnson-Laird, 1983; Treur & van Ments, 2022). They are a kind of
structures or processes in the mind that reect structures or processes in
the world or in other persons. For example, you perceive an impressive
course of events in front of you and after closing your eyes you see a kind
of movie replay in your mind that replays this course of events. Humans
often use some form of mental model to handle situations, for example,
operating a device or machine, or to handle somebody else. All such
examples show the wide variety of mental models.
A natural question to ask, is about neural correlates of mental models
in the brain. How are mental models and their operations encoded as
brain states and processes? However, the concept of mental model and
the processes in which they are involved have a very diverse appearance
in the literature and also the denition and boundaries of the concept
mental model are not very sharp. Nevertheless, it is still fair to assume
that mental models provide a form of conceptualisation and interpre-
tation of what actually goes on in the brain. But that all diverse types of
mental models described in the literature relate in a uniform manner to
the same brain states and processes, is probably asked too much. Note
that for the sake of simplicity, here the word brain is used while in
addition also parts of the body or even in the external world (for
example, drawings or notes on paper or on a screen) may be involved in
the underlying physically embodied processes.
In this paper, rst in Section 2 some literature from neuroscience is
discussed where it is shown that different types of mental models can use
different types of brain areas, for example in relation to different mo-
dalities addressed by a given mental model. Next, in Section 3 from the
perspective of philosophy of mind the concept of context-dependent
realisation of mental states is discussed. It is illustrated for two well-
known cases of multiply realisable concepts: a unied cognitive BDI-
model applied to humans and bacteria and the unied notion of force
in physics with its different types of realisations. Then, in Section 4 it is
discussed how this notion of context-dependent realisation can be
applied to mental models. In Section 5 the approach is formalised via
two well-known perspectives on realisation from philosophy of mind
and philosophy of science: bridge principle realisation and interpreta-
tion mapping realisation. Finally, Section 6 is a discussion.
2. Literature on neural correlates for mental models
In this section it is discussed how in the neuroscientic literature
various neural correlates for mental models are proposed.
2.1. Some literature from neuroscience
In neuroscience literature, a few examples of how mental models
relate to processes in the brain are:
E-mail address: j.treur@vu.nl.
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Cognitive Systems Research
journal homepage: www.elsevier.com/locate/cogsys
https://doi.org/10.1016/j.cogsys.2021.06.001
Received 30 April 2021; Accepted 8 June 2021

Cognitive Systems Research 69 (2021) 83–90
84
•for mental models used for singing in (Cohen, Levitin, & Kleber,
2020)
•for relational knowledge in (Garvert, Dolan, & Behrens, 2017)
•for reading orher person’s minds in (Hurley, 2008)
•for learning of linearly ordered sequences in (Van Opstal, Fias,
Peigneux, & Verguts, 2009; Van Opstal, Verguts, Orban, & Fias,
2008)
•for transitive relational reasoning and analogical reasoning in
(Alfred, Connolly, & Cetron, 2020; Holyoak & Monti, 2020; Whi-
taker, Vendetti, Wendelken, & Bunge, 2018)
As a rst example of the latter, in (Alfred et al., 2020) it is reported
that for transitive reasoning, some parts in the brain that relate to spatial
representations are also active during activation of abstract mental
models concerning abstract objects in the context of an abstract linear
order structure (mathematically spoken). Patterns representative of
mental models for such examples of linear order structures were
revealed in both superior parietal lobule and anterior prefrontal cortex.
To get a more general picture, it would be interesting to perform similar
experiments for cases where the examples of mental models used do not
relate to a linear order structure, as conceptually and mathematically
spoken linear order structures are close to the abstract geometric
concept of line and therefore these structures and spatial structures are
not that far apart.
In (Holyoak & Monti, 2020), considering analogical reasoning, the
following is reported indicating that the neural correlates include:
•posterior parietal cortex, implicated in the representation of rst-
order relations
•rostrolateral PFC, apparently central in integrating rst-order re-
lations so as to generate and/or evaluate higher-order relations (e.g.,
A:B::C:D)
•dorsolateral PFC, involved in maintaining relations in working
memory
•ventrolateral PFC, implicated in interference control (e.g., inhibiting
salient information that competes with relevant relations)
Here higher-order relations A:B::C:D describe how a rst-order
relation A:B relates to another rst-order relation C:D, as considered
in analogical reasoning: A relates to B like C relates to D; for example,
‘dress is to closet as milk carton is to refrigerator’ or ‘shoe is to foot like
glove is to hand’. Whitaker et al. (2018) found that a network consisting
of frontal, parietal and occipital regions is active while solving both
analogy problems (like A:B::C:?, for example, ‘shoe is to foot like glove is
to …?’) and semantic problems, and that the development of analogical
reasoning is associated with increased engagement of the left anterior
inferior prefrontal cortex.
2.2. Internal simulation
Another area that addresses brain structures and processes related to
mental models is the area of internal simulation. Internal simulation is a
very central concept for mental models, especially the ones considering
dynamics, as also discussed in (Van Ments & Treur, 2021). It is a means
for prediction of the effects of a considered or prepared action without
executing it. The idea of internal simulation is that in a certain context
(which may cover sensed aspects of the external world, but also internal
aspects such as the own goals), preparation states for actions or bodily
changes are activated, which, by prediction links, in turn activate
certain sensory representation states. The latter states represent the
(predicted) effects of the prepared actions or bodily changes, and can be
activated from the preparation states by internal connections without
actually having executed these actions or bodily changes in the external
world or in the body. The notion of internal simulation has been put
forward, among others, for:
•prediction of effects of one’s own prepared motor actions; e.g.,
(Becker & Fuchs, 1985)
•imagination and conscious thought; e.g., (Hesslow, 2002; Hesslow,
2012)
•predicted body states related to preparations for emotional re-
sponses, forming a basis for feeling the emotion; e.g., (Damasio 1994,
2003; Bechara & Damasio, 2005)
•recognition or reading another person’s mind, for example, the other
person’s emotions; e.g., (Goldman, 2006; Iacoboni, 2008)
As another example, by religious humans a mental God-model is
simulated for inuencing their behaviour as also addressed in (Van
Ments, Treur, & Roelofsma, 2018; Van Ments, Treur, & Roelofsma,
2022). This mental God-model refers to the personal God of the indi-
vidual. As discussed in (Kapogiannis et al., 2009; Kapogiannis, Desh-
pande, Krueger, Thornburg, & Grafman, 2014; Schaap-Jonker, Sizoo,
van Schothorst-van Roekel, & Corveleyn, 2013), this mental God-model
consists of both an emotional part and a cognitive part, and both parts
are dynamically interrelated. The emotional part is unconsciously
developed, highly inuenced by parents and signicant others. The
emotional and the cognitive part that form the mental God-model can be
related to different parts in the brain as studied, for example, by the
above-mentioned (Kapogiannis et al., 2009; Kapogiannis et al., 2014;
Schaap-Jonker et al., 2013). The emotional part involves
•the amygdala, basal ganglia,
•the ventromedial prefrontal cortex, the lateral temporal cortex,
•the dorsal anterior cingulated cortex, and the orbitofrontal cortex.
These parts of the brain are involved in assigning emotional signif-
icance to behaviour and events and to control of cognition and emotion.
Moreover, the cognitive part of the mental God-model involves
•the lateral prefrontal cortex, the medial prefrontal cortex,
•the lateral parietal cortex, the medial parietal cortex,
•and the medial temporal lobe
These all are brain circuits that more in general are responsible for
the processing of more complex linguistic and symbolic input. For the
case of mental God-models considered here, the above indicated com-
bination of brain parts enable the formation of the personal mental God-
model of the individual.
All such types of internal simulation use internal connections or
causal pathways from an action preparation state to some type of sen-
sory representation state for the (predicted) effect of this action (without
actually executing the action). Such relations and processes are often
part of mental models. For example, Damasio calls such pathways (in
particular, to generate feelings) as-if body loops (Damasio, 1994; Dam-
asio, 2003; Bechara & Damasio, 2005), while Hesslow (2002) refers to
them (considering a more general context) as ‘simulation of behaviour
and perception’ or simulated perception-behaviour chains. For both types
of causal pathways, see Fig. 1. In the latter case the emphasis is on longer
chains, as every sensory action effect representation can trigger prepa-
ration for a new action, which in turn can trigger a new predicted sen-
sory action effect representation, and so on. These chains are proposed
by Hesslow (2002) as the neural basis for conscious thought.
Such structures of pathways for internal simulation are realisations
in the brain of mental models that are executed. In case these mental
models relate to processes in someone else’s mind, these chains refer to
the mind of the other person, like in ‘simulating minds’ by which
mindreading can be achieved in combination with mirroring (Goldman,
2006; Iacoboni, 2008) or in Theory of Mind. In Fig. 1 two original pic-
tures of as-if body loops (Damasio, 1994; Damasio, 2003; Bechara &
Damasio, 2005) and of simulated perception-behaviour chains (Hes-
slow, 2012) illustrate the idea of internal simulation in some more
detail.
J. Treur

Cognitive Systems Research 69 (2021) 83–90
85
Viewed from a higher abstraction level, all these different types of
processes in the brain serve as some form of internal simulation. How-
ever, in these different cases, different brain states, pathways and areas
are used. For example, mental models involving emotions and feeling
states associated to some considered action or belief (i.e., mental models
involving an emotional context), will use parts and pathways of the
brain that are not the same as mental models that do not involve such
emotions and feeling states (i.e., mental models involving a non-
emotional context).
Right picture, adopted from (Hesslow, 2012): (a) Stimulus S
1
causes
perceptual activity s
1
, which causes preparatory response r
1
and overt
response R
1
. This R
1
causes predictable new stimulus S
2
, which causes
new sensory activity, etc. (b) Preparatory response r
1
elicits, via internal
association mechanisms, perceptual activity s
2
before overt behaviour
occurs and causes new stimulus.
The notion of internal simulation can be viewed as an abstraction
that unies these different types of brain processes. More in general, the
neural circuits to internally simulate processes from the externall world
will be different from the circuits used when simulating mental pro-
cesses of other persons. Such simulations will usually apply the same
brain structures as those involved in perceiving the processes in reality;
for example, perceiving the own or someone else’s body states uses brain
areas that are different from brain areas used when perceiving states of
the physical world.
2.3. Neural correlates for adaptation and control for mental models
From the above it seems that most research on the neuroscience of
mental models focuses on the use of mental models and not on their
formation, adaptation or control as discussed, for example, in (Van
Ments & Treur, 2021). For the latter types of processes, still other parts
and pathways in the brain may be used. For formation and adaptation of
mental models, the extensive neuroscience literature on plasticity may be
relevant, such as (Hebb, 1949; Chandra & Barkai, 2018; Daoudal &
Debanne, 2003; Debanne, Inglebert, & Russier, 2019; Sj¨
ostr¨
om, Rancz,
Roth, & Hausser, 2008) to name just a few. For control, probably some
parts of the prefrontal cortex concerning executive functions and
cognitive control may be involved, but also literature on the more
detailed neuroscience of metaplasticity for control of plasticity such as
(Abraham & Bear, 1996; Magerl, Hansen, Treede, & Klein, 2018) may be
relevant. So, there are still some challenges left to be explored for the
area of neural correlates for mental model handling.
3. Context-dependent realisation of mental states
As discussed above, proposed neural correlates for mental models
show a diversity of occurrences. This does not t well to a maybe
preferred option that there is one universal mechanism in the brain that
realises all mental models. Perhaps it is asked too much to assume that
there is one xed architecture in the brain that realises all types of
mental models. This suggests that other options may be considered that
t better. Within philosophy of mind, from a wider context a similar
issue is addressed: the issue of multiple realisability of mental states; e.
g., (Kim, 1996). Here an interesting option to address this issue is dis-
cussed, namely the perspective based on context-dependent realisation.
This looks like a more promising perspective than assuming that one
universal brain structure can be found as a correlate for handling all
types of mental models.
3.1. Context-dependent multiple realisation of mental states
According to this alternative perspective, instead of a one-to-one
correspondence of all types of mental models to one specic type of
brain structure, a more realistic approach is by relating mental models to
brain areas in a more pluriform and context- sensitive manner. In
particular, the notion of context-dependent multiple realisation as sug-
gested by Kim (1996), pp. 233–236, can provide a useful way of inter-
pretation of the situation. Here, roughly spoken, depending on the
context a mental state can relate to different types of brain states and
processes (multiple context-specic realisations can exist), and within
each context the specic causal relations for these brain states should be
in accordance with the relations assumed for the considered mental
states. A context is here, for example, the physical makeup of an or-
ganism. These makeups usually differ for different species and in-
dividuals, but at a more abstract level still the same mental concepts can
be used to describe them in a unied manner. More details about this
perspective of context-dependent realisation (and how this can be used
more generally to clarify how mental relations or laws and neurological
relations or laws relate to each other) can be found in (Treur, 2008;
Treur, 2011).
Based on context-dependent realisation, the mental states and their
assumed causal relations form a unied high-level description of a
number of different specic brain states and their specic causal re-
lations. For example, suppose mental states M and M′are considered
with an assumed causal relation M → M′; see Fig. 2. Then, for example,
in two different contexts C
1
and C
2
two different types of realisations
may be considered, one in context C
1
where M is realised by brain state
B
1
and M′by brain state B′
1
and another one in context C
2
where M is
realised by brain state B
2
and M′by brain state B′
2
. Then, for a faithful
realisation it is required that causal relations B
1
→ B′
1
within context C
1
and B
2
→ B′
2
within context C
2
exist between these brain states. In this
case, at a higher, more abstract level of description the causal relation M
→ M′unies these specic causal relations B
1
→ B′
1
and B
2
→ B′
2
within
the two different contexts, as shown in Fig. 2. In Sections 3.2 and 3.3
some examples of multiple realisation are presented; in Section 5 a
formalisation is addressed.
Fig. 1. Left picture, adopted from (Bechara & Damasio, 2005): Simple diagrams illustrating the Body Loop and As-If Body Loop chain of physiologic events. In both
Body Loop and As-If Body Loop panels, the brain is represented by the top black perimeter and the body by the bottom one. Depicted are among others, the primary
(SI) and the secondary somatosensory (SII) cortices, the ventromedial pre-frontal (VM) cortex, and the periaqueductal gray (PAG).
J. Treur

Cognitive Systems Research 69 (2021) 83–90
86
3.2. An illustration from biology: Multiple realisation of behavioural
choice
One illustration, borrowed from the work described in (Jonker,
Snoep, Treur, Westerhoff, & Wijngaards, 2002; Jonker, Snoep, Treur,
Westerhoff, & Wijngaards, 2008) is the following (see Fig. 3). Here the
left-hand side describes a causal network for how an E. coli bacterium
determines what food it uses as intake (according to the literature in
biochemistry) and the right-hand side describes a causal network for
how a human is assumed to do that (according to the socalled BDI-
model). The horizontal dashed double arrows show how the states for
DNA, mRNA, active enzyme and ux of an E. coli correspond to states for
desire, intention, readiness, and action, respectively for a human.
Similar correspondences can be made for the other nodes in the two
networks as indicated by the longer dashed double arrows. This example
shows how the BDI-model (originally meant for human mental processes
and behaviour) can also be used as a more general unied description of
mental processes, unifying processes in different types of organisms with
different physical makeups where the general unied model gets its
different context-dependent realisations.
The perspective discussed above is just one example of a form of
unication: different types of processes are comparable, and we can, for
example, compare the processes underlying human intelligence and
behaviour to the processes underlying bacterial behaviour, as described
from a wider perspective in (Jonker et al., 2002; Jonker et al., 2008;
Westerhoff, He, Murabito, Cr´
emazy, & Barberis, 2014a; Westerhoff,
Brooks, Simeonidis, García-Contreras, He, Boogerd, Jackson, Gon-
charuk, & Kolodkin, 2014b). For example:
‘We have become accustomed to associating brain activity – partic-
ularly activity of the human brain – with a phenomenon we call
“intelligence.” Yet, four billion years of evolution could have selected
networks with topologies and dynamics that confer traits analogous
to this intelligence, even though they were outside the intercellular
networks of the brain. Here, we explore how macromolecular net-
works in microbes confer intelligent characteristics, such as memory,
anticipation, adaptation and reection and we review current un-
derstanding of how network organization reects the type of intel-
ligence required for the environments in which they were selected.
We propose that, if we were to leave terms such as “human” and
“brain” out of the dening features of “intelligence,” all forms of life
– from microbes to humans – exhibit some or all characteristics
consistent with “intelligence”. (Westerhoff et al., 2014b), p. 1.
This quote emphasizes that not only in the human brain, but even in
the smallest life forms many if not all aspects of intelligence as usually
attributed to humans are realised in a variety of different manners using
different types of mechanisms and causal relations underlying them.
3.3. An illustration from physics: Multiple realisation of force
Context-dependent multiple realisation can also be found in other
domains, for example, for the notion of force within physics, as
described by Nagel (1961, pp. 186-192); see also (Treur, 2007). Force is
a general concept that unies multiple occurrences of specic forces in
different contexts. Depending on the context dened by a considered
world conguration, one type of realisation of a force is by gravitation,
but other types are forces realised by electrical charges, by magnetic
objects, or by deformation caused by collisions, or gas temperature, for
example. All these different types of realised forces (1) are generated
through different mechanisms based on different types of causal re-
lations (Nagel calls these ‘force functions’), but (2) in a unied manner
have exactly the same effect on the acceleration a of an object with mass
m according to the wellknown law F =ma which relates force F to ac-
celeration a. The successfulness of this law illustrates within this phys-
ical domain the power of the idea of a unied concept with multiple
realisations.
4. Context-dependent realisation of mental models
Now, returning to mental models, suppose as part of a mental model
a relation M → M′is assumed. If the idea of context-dependent realisa-
tion discussed in Section 2 is applied to mental models, then similar to
the above mental concepts M and M′and their causal relation, this idea
can be applied to any mental model relation M → M′; then the left hand
picture shown in Fig. 4 is obtained for such a mental model relation.
Here contexts such as C
1
and C
2
may depend on the type of species or
person and the type of mental model that is considered. This means that
as within the given mental model, M and M′relate according to M → M′,
and M corresponds to B
1
and M′to B′
1
within context C
1
, for a faithful
realisation there should be a relation B
1
→ B′
1
within that context, and
similarly a relation B
2
→ B′
2
for context C
2
and B
2
and B′
2
.
Note that here it is assumed that the relations within a mental model
can be of any type of relation, causal or not. Then they have to corre-
spond accordingly to certain types of relations in the brain. If in the
mental model the relations considered are meant as causal relations,
then the corresponding relations in the brain can also be taken as causal
Fig. 2. A causal relation M → M
′between mental states and its multiple real-
isation for two different contexts in the brain, for context C
1
by causal relation
B
1
→ B′
1
and for context C
2
by causal relation B
2
→ B′
2
.
DNA
mRNA
active enzyme
flux
desire
intention
readiness
action
ENVIRONMENT ENVIRONMENT
reporter
su
bstance
s
receptor
beliefs
activation protein/repressor
phosphorylated transcription factor
(co)factor
prod
uct
inhibitor
substrate
primary
reason
additional
reason
enabling conditions
Fig. 3. Multiple realisations of a general unied BDI-model for mental processes in an E. coli bacterium (left hand side) and in a human (right hand side) and their
mutual correspondence relations (horizontal dashed double arrows).
J. Treur

Cognitive Systems Research 69 (2021) 83–90
87
relations. This causality can still be of many different forms, for example,
varying from a description of successive relational or analogical
reasoning steps to algorithmic steps in an algorithmic skill or any (other)
type of causality underlying dynamical systems.
As a mental model can also be assumed to relate to actual relations in
the world (e.g., see Van Ments & Treur, 2021), at the same time the
right-hand picture in Fig. 4 applies, where relation W → W′in the world
corresponds to relation M → M′in the mental model. Then the
assumption that the mental model relations M → M′correspond to re-
lations W → W′in the world plus the assumption that mental model
relations M → M′correspond to (for example) relations B
2
→ B′
2
between
states in the brain within context C
2
imply by transitivity of
′correspondence′that these relations B
2
→ B′
2
in the brain also corre-
spond to the relations W → W′in the world (see the dashed arrows be-
tween the left and right picture in Fig. 4). That means that the brain
processes simulate the world processes according to similar relations,
which is in line with (Craik, 1943). In his book (Craik, 1943) he de-
scribes a mental model as a small-scale model that is carried by an or-
ganism within its head and used to try out alternatives of actions before
executing them as follows:
‘… it is a physical working model which works in the same way as the
process it parallels…Thus, the model need not resemble the real
object pictorially; Kelvins’ tide-predictor, which consists of a number
of pulleys on levers, does not resemble a tide in appearance, but it
works in the same way in certain essential respects…’ (Craik, 1943,
p. 51).
‘If the organism carries a “small-scale model” of external reality and
of its own possible actions within its head, it is able to try out various
alternatives, conclude which is the best of them, react to future sit-
uations before they arise, utilise the knowledge of past events in
dealing with the present and future, and in every way to react in a
much fuller, safer, and more competent manner to the emergencies
which face it.’ (Craik, 1943, p. 61)
He emphasizes that such internal models work in a way similar to
how the real world works.
In Fig. 4, for the sake of simplicity and explanation only one mental
model relation is considered. As in general a mental model involves a
whole network of such relations, a more realistic picture is shown in
Fig. 5.
Here for a faithful realisation, all relations in the mental model
network have to correspond to similar relations in the brain and for a
Fig. 4. Left picture: a mental model relation M → M
′and its multiple realisation for two different contexts in the brain, for context C
1
by B
1
→ B′
1
and for context C
2
by B
2
→ B′
2
. Right picture: the same mental model relation M → M′and its correspondence to a relation W → W′in the world. Dashed arrows between left and right
picture: relation W → W′in the world is simulated in the brain by relation B
2
→ B′
2
(within context C
2
).
Fig. 5. A mental model for context C realised in the brain and its correspondence to the world.
J. Treur

Cognitive Systems Research 69 (2021) 83–90
88
faithful representation of the world all relations in the mental model
network have to correspond to similar relations in the world. As a result,
the corresponding network in the brain will faithfully simulate the world
processes.
Note that the perspective based on context-specic realisation allows
to maintain a very general notion of mental model unifying all types of
mental models, also those that use very different brain processes. But
within that general notion of mental model, as a form of classication
still specic types of mental models can be considered, for example types
of mental models that do share a common structure for their realisation
in the brain. In a sense, this provides the best of two worlds: (1) there is
one universal notion of mental model with general knowledge and
theory covering a very wide variety of cases, and (2) under the umbrella
of this general notion of mental model, still a number of very specic
types of mental models can be studied as well with more specic
knowledge and theories in addition. In Section 3 a few specic results on
neural correlates of different types of mental models will be discussed
that might be considered to provide some evidence in favour of this
perspective of context-specic realisations.
5. Context-dependent realisation from different perspectives
Based on the notion context-dependent realisation as introduced in
(Treur, 2008), a set of contexts can be identied and realisations of
mental models can be related to these contexts. Assuming that contexts
are dened in a sufciently ne-grained manner, within one context the
realisation is unique. Then contexts can be seen as a form of parame-
terisation of the realisations. For mental models, for example, these
contexts may be based on different types of sensory representations. For
a context-dependent realisation approach, a (neurological) background
base theory T is assumed with a set of contexts C, such that each
particular context is formally described by a context S ∈C. The contexts
S are assumed to be descriptions in the language of T and consistent with
T. The contexts S ∈C can be used to distinguish the different realisations
that are possible for mental models. This means that for a given mental
model a context S can be found such that all relations of the mental
model can be related to realisers within this context S. Below it is shown
how this context-dependency can be addressed for two wellknown
general approaches to realisation, namely bridge principle realisation
(Nagel, 1961) and realisation by an interpretation mapping; e.g.,
(Bickle, 1992) and (Hodges, 1993), pp. 201–263. Here a xed (neuro-
logical) background theory T is assumed. It will be assumed as a general
setting that a mental model is dened by a set of relations R(a
1
, …, a
k
)
between basic concepts a
i
. For example, in Fig. 4, such a relation R is
denoted by an arrow; for the example mental model depicted in Fig. 5, in
the R-notation the relations are R(M
1
, M
2
), R(M
1
, M
3
), R(M
2
, M
5
), and so
on.
5.1. Context-dependent bridge principle realisation
For the bridge principle realisation approach, for a given relation R
(a
1
, …, a
k
) the set of realisers that exists within a context S ∈C, is
expressed by context-dependent biconditional bridge principles para-
meterised by context S ∈C, specied by
a1↔b1,S,…,ak↔bk,S
In Fig. 5, these correspond to the blue dashed double arrows, so they
can be specied by:
M1↔B1M2↔B2M3↔B3
M4↔B4M5↔B5M6↔B6
Given such a specication, context-dependent bridge principle realisa-
tion within context S for the relations R(a
1
, …, a
k
) dening a given mental
model can be formulated in two equivalent manners by (where ⊧ is a
symbol for logical entailment):
(i) R(a1,…,ak)⇒T∪S∪ {a1↔b1,S,…,ak↔bk,S}⊧R(a1,…,ak)
(ii) R(a1,…,ak)⇒T∪S⊧R(b1,S,…,bk,S)
Note that context-dependent bridge principle realisation implies
unique realisers (up to equivalence) per context S: from a ↔ b
S
and a ↔
b′
S
it follows that b
S
and b′
S
cannot be non-equivalent in S. So to obtain
context-dependent bridge principle realisation in cases of multiple
realisation, the contexts are dened with a grain-size such that per
context a unique realisation exists.
5.2. Context-dependent interpretation mapping realisation
A context-dependent interpretation mapping is a multi-mapping of
concepts parameterised by contexts: a multi-mapping φ
S
(S ∈C) from
mental model concepts to concepts of the background (neurological)
theory parameterised by contexts S ∈C. For example, in Fig. 5, following
the blue dashed double arrows, such a mapping can be dened by:
φS(M1) = B1φS(M2) = B2φS(M3) = B3
φS(M4)=B4φS(M5) = B5φS(M6) = B6
These mappings are assumed compositional in the sense that for any
mental model relation R(a
1
, …, a
k
) it is assumed
φS(R(a1,…,ak))=R(φS(a1),…,φS(ak))
Such a multi-mapping is a context-dependent interpretation mapping
realisation when it satises the property that for any context S ∈C for any
relation R(a
1
, …, a
k
) in a given mental model, the relation φ
S
(R(a
1
, …,
a
k
)) is entailed by S:
R(a1,…,ak)⇒T∪S⊧φS(R(a1,…,ak))
5.3. Relating bridge principle realisation and interpretation mapping
realisation
In this section it is shown how context-dependent bridge principle
realisation can be translated into context-dependent realisation based on
an interpretation mapping and vice versa.
5.3.1. From interpretation mapping realisation to bridge principle
realisation
Suppose a context-dependent interpretation mapping realisation φ
S
is given for some S ∈C. For each basic concept a
i
of a mental model,
specify the bridge principle
ai↔bi,S with bi,S=φS(ai)
If R(a
1
, …, a
k
) is mental model relation involving concepts a
1
, …, a
k
,
then
T∪S⊧φS(R(a1,…,ak))
By compositionality of mapping φ
S
it follows that
T∪S⊧R(φS(a1),…,φS(ak))
Therefore it follows
T∪S⊧R(b1,S,…,bk,S)
This shows that the criterion for context-dependent bridge principle
realisation within context S is fullled.
5.3.2. From bridge principle realisation to interpretation mapping
realisation
For a translation the other way around, assume for context-
dependent bridge principle realisation, for some S ∈C bridge principles
ai↔bi,S
are given for the basic concepts a
i
of a mental model such that the
bridge principle realisation criterion for context S and bridge principles
J. Treur

Cognitive Systems Research 69 (2021) 83–90
89
a
i
↔ b
i,S
is fullled:
R(a1,…,ak)⇒T∪S⊧R(b1,S,…,bk,S)
Dene the mapping φ
S
for each basic expression a
i
, based on the
given bridge principle a
i
↔ b
i,S
, by
φS(ai)= bi,S
For R(a
1
, …, a
k
) extend this by compositionality
φS(R(a1,…,ak) ) = R(φS(a1),…,φS(ak))
For this mapping φ
S
, from R(a
1
, …, a
k
) by the bridge principle
realisation criterion it follows:
R(a1,…,ak)⇒T∪S⊧R(φS(a1),…,φS(ak))⇒T∪S⊧φS(R(a1,…,ak))
Therefore, the criterion for a context-dependent interpretation
mapping realisation is fullled. Note that the translations from context-
dependent bridge principle realisation to context-dependent interpre-
tation mapping realisation and from context-dependent interpretation
mapping realisation to context-dependent bridge principle realisation as
given are each other’s inverse.
6. Discussion
In this paper, the use of the concept of context-dependent realisation
of mental states from philosophy of mind for mental models was dis-
cussed. This concept was illustrated for two wellknown cases of multiply
realisable concepts: a unied cognitive BDI-model applied to humans
and bacteria and the unied notion of force in physics with its different
types of realisations. As the core of this paper, it was discussed how this
idea of context-dependent realisation can be applied to mental models.
Some literature from neuroscience was discussed where it is shown
that different types of mental models can use different types of brain
areas. For example, some types of mental models address spatial or
linearly ordered structures and turn out to make use of brain areas that
typically relate to the processing of spatial information; e.g., (Alfred
et al., 2020). Other examples of mental models may concern emotions of
other persons; these mental models turn out to make use of brain parts
typically involved in emotions and feelings; e.g., (Damasio, 1994;
Iacoboni, 2008). Moreover, it was discussed that this diversity applies
also to the formation and adaptation of mental models and the control of
these processes. This makes that the notion of context-dependent real-
isation can be a suitable manner to relate neural correlates to mental
models in a pluriform manner. This has been worked out more formally
in Section 5.
More specically, these observations suggest a perspective on
context-dependent neural correlates of mental models where this
context-dependency actually concerns the type of content of the mental
model: what it represents. It might be regretted that in this way these
neural correlates do not concern one universal mechanism in the brain
that handles all mental models. However, in the paper it has been shown
that the notion of context-dependent realisation from Philosophy of
Mind (Kim, 1996) still provides a neat foundational description of this
more pluriform perspective. In addition, it has been discussed that also
in other scientic disciplines this perspective occurs; for example, not
only for mental states in general as put forward by Kim (1996), but
within physics the notion of force F used in the very successful law F =
ma relating force to acceleration a, also has multiple context-dependent
realisations by essentially different (physical) mechanisms such as
gravitation, electrical charge, magnetic inuence, deformation by
collision, gas temperature, … (Nagel, 1961). Therefore, the topic of
mental models is in good scientic company concerning this perspective
of context-dependent realisation.
Finally, this idea has some relation to the historical Simulation-
Theory versus Theory-Theory discussion for understanding each
other’s minds; e.g., (Goldman, 2006), pp. 10–22. From a Theory-Theory
perspective it may be tempting to look for one universal (‘reasoning’)
mechanism in the brain to reason with all theories (mental models) of
others’ minds. But from a Simulation-Theory perspective, it makes more
sense that brain areas for various types of modalities are used for in-
ternal simulation of theories (mental models) of others’ minds, and these
modalities correspond to the modalities for the content of the mental
model at hand. In that sense the proposed perspective on context-
dependent neural correlates for mental models may relate more to the
Simulation-Theory perspective than to the Theory-Theory perspective.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
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