Scaling Understanding up to Mental Spaces 
Eva Mok, John Bryant, Jerome Feldman 
International Computer Science Institute 
1947 Center Street Suite 600, 
Berkeley, CA 94704 
{emok, jbryant, jfeldman}@icsi.berkeley.edu 
 
 
Abstract 
Mental Space Theory (Fauconnier, 1985) en-
compasses a wide variety of complex linguis-
tics phenomena that are largely ignored in to-
day’s natural language processing systems. 
These phenomena include conditionals (e.g. If 
sentences), embedded discourse, and other 
natural language utterances whose interpreta-
tion depends on cognitive partitioning of con-
textual knowledge. A unification-based 
formalism, Embodied Construction Grammar 
(ECG) (Chang et al., 2002a) took initial steps 
to include space as a primitive type, but most 
of the details are yet to be worked out. The 
goal of this paper is to present a scalable com-
putational account of mental spaces based on 
the Neural Theory of Language (NTL) simu-
lation-based understanding framework (Nara-
yanan, 1999; Chang et al., 2002b). We 
introduce a formalization of mental spaces 
based on ECG, and describe how this formal-
ization fits into the NTL framework. We will 
also use English Conditionals as a case study 
to show how mental spaces can be parameter-
ized from language. 
1 Introduction 
There are two dimensions to scalability: improving sys-
tem performance (e.g. speed and size) for a fixed task, 
and expanding the range of tasks that the system can 
handle. Today’s natural language processing (NLP) 
systems are not very scalable in the latter dimension. 
They tend to ignore a wide range of cognitive linguistic 
phenomena, notably those associated with mental 
spaces, which are key to understanding any non-trivial 
piece of natural language. Mental spaces (Fauconnier, 
1985) are partial cognitive structures built up during 
discourse that keep track of entities and relations in dif-
ferent contexts. Hypothetical reasoning, depictions (e.g. 
stories, paintings or movies) and reasoning about other 
minds are but a few examples where new mental spaces 
are required. Mental spaces provide an important parti-
tioning of contextual knowledge that allows scalable 
reasoning in a partitioned large knowledge base. 
However, the literature on Mental Space Theory 
does not address how these cognitive structures are 
specified compositionally, let alone offering formaliza-
tions of mental space representations or computational 
realizations. We thus seek to scale up the complexity of 
natural language understanding (NLU) systems by pro-
posing a computational method of handling mental 
spaces. In this paper we give a brief introduction to 
Mental Space Theory (Section 2), and then explain how 
Mental Space Theory can be incorporated into the exist-
ing Neural Theory of Language (NTL) simulation-based 
understanding framework (Section 3). In this frame-
work, each mental space is a separate thread of simula-
tion. Each thread of simulation comprises a dynamic 
structure combining knowledge, event models and be-
liefs that evolve over time.  
The use of a simulation-based framework imposes 
constraints on how mental spaces are represented, and 
we introduce a formalization of mental spaces based on 
Embodied Construction Grammar (ECG). As a case 
study (Section 4), we will walk through the formaliza-
tion of English Conditionals (Dancygier and Sweetser, 
2004) using mental space analysis. Through this case 
study we illustrate how mental spaces are parameterized 
compositionally by language, and capture this composi-
tionality succinctly using construction grammar. Then 
with these formal tools, we address the issue of infer-
ence in mental spaces (Section 5), which is at the core 
of the scaling up understanding. 
2 Mental Space Theory 
Mental spaces refer to the partial cognitive structures 
built up, usually through discourse, that provide a parti-
tioning of contextual as well as world knowledge. This 
partitioning in turn affects what inferences can be 
drawn. In traditional mental space analysis, certain 
linguistic constructions called space builders may open 
a new mental space or shift focus to an existing space. 
Examples are in this picture…, Nancy thinks…, if it 
rains…, back in the ’50s…(Fauconnier, 1997). Consider 
the following sentence: 
 
(1) In Harry’s painting of Paris, the Eiffel Tower is 
only half-finished.  
 
Harry’s painting creates a new Depiction-Space. The 
Eiffel Tower is the only entity local to this Depiction-
Space, and it maps to the physical Eiffel Tower. How-
ever, only the Eiffel Tower in the Depiction-Space has 
an additional attribute half-finished, and one should not 
be led to think that the real Eiffel Tower is also half-
done. This kind of space-building is traditionally illus-
trated in diagrams similar to Figure 1. 
 
In the mental space literature, the transfer of as-
sumptions between spaces is guided by the presupposi-
tion float principle. The presupposition float principle 
states that any presupposed structure in the parent space 
can float to a child space unless it conflicts with struc-
ture already in that space. In the above example, any 
attributes about the real Eiffel Tower can be assumed in 
the Depiction-Space, as long as they do not depend on it 
being finished. However, this account of assumption 
and inference transfer is incomplete. Specifically, it is 
incorrect to assume that different types of mental spaces 
obey the same presupposition float principle. For exam-
ple, if we are having a conversation right now about 
Harry’s painting, very little of what is currently happen-
ing should transfer into the Depiction-Space. On the 
other hand, if we are having a conversation about our 
plans for tomorrow, our current situation is very rele-
vant to our actions tomorrow, and this information 
should carry over to the future space. The other key 
piece that is missing from the presupposition float ac-
count is how inference is drawn across spaces in gen-
eral. Any computational account of mental spaces must 
address this inference process precisely and supply a 
formalized representation that inference can operate 
with. We will outline such a computational solution in 
the next two sections of this paper.  
3 Simulation-Based Understanding 
A central piece of a scalable computational treatment of 
mental spaces is a robust language understanding 
framework. Our work relies on the NTL simulation-
based understanding paradigm (Narayanan, 1999; 
Chang et al., 2002b), and extends the model in a con-
ceptually straightforward way. The simulation-based 
understanding paradigm stipulates that, in addition to 
constructional analysis of the surface form, language 
understanding requires active simulation. 
The constructional analysis is based on Embodied 
Construction Grammar (Chang et al., 2002a) which con-
tains four primitive types: schemas, constructions, maps 
and mental spaces. Schemas are the basic ECG unit of 
meaning, capturing embodied concepts such as image 
schemas, actions, and events. Constructions are the ba-
sic linguistic unit, pairing meaning schemas with repre-
sentations of linguistic form (words, clauses, etc.).  
Maps and mental spaces are the subject of this paper, 
and will be discussed in detail in the next section. It is 
worth noting that in the ECG formalism, in addition to 
support of an inheritance hierarchy (with the keyword 
subcase of), there is also an evokes relation that makes 
an outside structure accessible to a schema through a 
local name. The evokes relation is neither a subcase-of 
or part-of relation, but is analogous to spreading activa-
tion in the neural sense. 
During analysis, a Semantic Specification (Sem-
Spec) is created from the meaning poles of the construc-
tions, and is essentially a network of schemas with the 
appropriate roles bounded and filled in. Crucially, 
within this network of schemas are executing schemas 
(or X-schemas), which are models of events. They are 
active structures for event-based asynchronous control 
that can capture both sequential flow and concurrency.  
Simulation is a dynamic process which includes 
executing the X-schemas specified in the SemSpec and 
propagating belief updates in a belief network. This 
mechanism is used for metaphor understanding in (Na-
rayanan, 1999), and is being generalized to Coordinated 
Probabilistic Relational Models (CPRM) in current ef-
forts (Narayanan, submitted). The CPRM mechanism is 
discussed in more detail in Section 5.  
Within a simulation-based understanding paradigm, 
each mental space involves a new thread of simulation, 
with its own separate belief network and simulation 
trace. This is necessary for keeping track of possibly 
contradictory beliefs, such as the alternative scenarios 
where it is sunny or rainy tomorrow. Each alternative 
scenario exists within its own mental space, and in 
many situations, there can be a large number of alterna-
tives. However, not only is it computationally expensive 
Parent-Space 
 
painting         Eiffel Tower 
Depiction-Space 
 
                       Eiffel Tower 
                      (half-finished) 
Figure 1. The painting opens a Depiction- 
Space where the Eiffel Tower is half-finished. 
to create a new thread of simulation, but cognitive ca-
pacity also constrains the number of concurrently open 
spaces. We need both a cognitively plausible and com-
putationally feasible theory of how mental spaces are 
manipulated.  
The insight in addressing this problem is that at any 
given level of granularity, not all spaces need to be 
opened at the same time. Harry’s painting, in example 
(1), may be represented at different granularity depend-
ing on the context. If it is discussed simply as a wall-
hanging, the Depiction-Space need not be expanded and 
the painting should be treated schematically as an ob-
ject. However, once the contents of the painting are un-
der discussion (e.g., the trip to Paris during which the 
painting was done), inference in a separate mental space 
is required, and the Depiction-Space needs to be built.  
As illustrated by this example, the simulation proc-
ess dictates the actual building of mental spaces. The 
analysis process is responsible for supplying all the nec-
essary parameterization of the spaces and their corre-
sponding maps in case they need to be built. As a result, 
each potential space-builder is represented at two levels 
of granularity – as an object in its schematic form and as 
a full mental space.  
 
Formalizing this idea in ECG, mental spaces are 
represented in two ways: as a compressed mental space 
and an uncompressed version. In the ECG notation in 
Figure 2, the Compressed-Mental-Space is just a 
schema, and Mental-Space is of the space primitive 
type. In each version there is pointer to its counterpart, 
ums and cms respectively. The role parent-space points 
to the parent of this space. The uncompressed mental 
space contains the list of alternatives and the local-
content. Alternatives are scenarios that are different and 
cannot co-exist, such as the different activities one 
might be doing tomorrow at noon. Local-content 
at noon. Local-content provides the local semantics of 
mental spaces, maintaining a list of predications that are 
true in this space, ceteris paribus. Each predication con-
tains a role local-to that denotes the space to which it 
belongs. The predication is then automatically added to 
the local-content of the space when this role is assigned. 
Figure 3 shows an example of the Cause-Effect schema 
with the cause, effect, and local-to role.  
In the next section, we will demonstrate the use of 
the above formalization with a case study on conditional 
sentences in English. In Section 5, we will discuss how 
this representation supports the needed inference.  
4 Case Study: English Conditionals 
One of the most common classes of space-building 
expressions is the predictive conditional. Predictive 
conditionals are sentences like  
 
(2) If it rains tomorrow, the game will be cancelled.  
 
They are space-builders, setting up a primary condi-
tional space and an alternative space
1
 (Dancygier and 
Sweetser, 2004). As shown in Figure 4, in the primary 
conditional space for tomorrow, it rains, and therefore 
the game is cancelled. In the alternative space, it does 
not rain, and the game is not cancelled.  
This case study will focus on predictive conditionals 
in English. An English predictive conditional is charac-
terized by tense backshifting in the if clause, i.e., the use 
of the present tense for a future event. On the meaning 
side, the condition and the conclusion are related by 
some causal or enablement relationship. 
In this section we will gradually build up to the Con-
ditional-Prediction construction by introducing the rele-
vant schemas and smaller constructions. It is important 
to stress how construction grammar succinctly captures 
how mental spaces can be parameterized in a composi-
tional way. The larger constructions supply information 
about the spaces that is not contained in any of its 
smaller constituents. Through compositionality, the 
grammar becomes much more scalable in handling a 
wide range of linguistic variations.  
                                                           
1
 Readers interested in the mental space analysis of other types 
of English conditionals should refer to (Dancygier and Sweetser, 
2004), as well a technical report for the formalization (Bryant and 
Mok, 2003).  
SCHEMA Compressed-Mental-Space    
ROLES 
 ums: Mental-Space 
 parent-space: Mental-Space 
 status 
CONSTRAINTS 
 self ↔ ums.cms 
SPACE Mental-Space 
 ROLES 
  cms: Compressed-Mental-Space 
  parent: Mental-Space 
  alternatives: Mental-Space 
  local-content 
 CONSTRAINTS 
  parent ↔ cms.parent-space 
Figure 2. ECG notation for Compressed
and Uncompressed Mental Spaces 
 
SCHEMA Cause-Effect 
 ROLES 
  Cause: Predication 
  Effect: Predication 
  local-to: Mental-Space 
Figure 3. Cause-Effect is a predication 
that contains a pointer to a Mental-Space 
4.1  Conditions 
The condition, often preceding the conclusion in a con-
ditional statement, sets up or locates the space in which 
the conclusion is to be placed. Therefore the Condi-
tional-Schema, given below, is a subcase of the Com-
pressed-Mental-Space. In addition to the inherited roles, 
the Conditional-Schema has roles for a condition, a 
premise, and a conclusion. The condition role stands for 
the condition P as expressed, and premise can be P or 
~P, depending on the conjunction.  Finally, epistemic-
stance is the degree of commitment that the speaker is 
making towards the condition happening, as indicated 
by the choice of verb tense. For example, a sentence 
such as If you got me a cup of coffee, I’d be grateful 
forever (Dancygier and Sweetser, 2004) has a negative 
epistemic stance. The speaker makes a low commitment 
(by using the past tense got) so as to not sound pre-
sumptuous, even though she may think that the ad-
dressee will very likely bring her coffee. On the other 
hand, a counterfactual such as If I’d’ve known you were 
coming, I’d’ve stayed home has a very negative epis-
temic stance. The speaker, in this case, implies that he 
did not know the addressee was coming. 
4.2 The If construction 
The abstract construction Conditional-Conjunction is a 
supertype of lexical constructions If and other condi-
tionals conjunctions. Each conjunction leads to a differ-
ent way of parameterizing the spaces, therefore a 
Conditional-Conjunction does not have meaning on its 
own. Instead, it EVOKES two copies of the Conditional-
Schema, one as primary and one as alternative.  
Given the Conditional-Conjunction and the Condi-
tional-Schemas it evokes, the If construction only needs 
to hook up the correct premise and set the epistemic-
stance to neutral. The condition itself is not filled in 
until a larger construction uses the Conditional-
Conjunction as a constituent.  
4.3  The Condition Construction 
The Condition construction forms a Subordinate-Clause 
from a Conditional-Conjunction and a Clause, such as If 
it rains tomorrow from our game cancellation example 
in (2). The most important aspect of this construction is 
that it identifies its meaning pole (a Conditional-
Schema) with the Conditional-Schema that is evoked by 
the Conditional-Conjunction, thereby preserving all the 
constraints on the premise, epistemic-stance and status 
that the conjunction sets up.  
SCHEMA Conditional-Schema 
 SUBCASE OF Compressed-Mental-Space 
 ROLES 
  epistemic-stance 
  condition: Predication  
  premise: Predication    
  conclusion: Predication 
  ums: Conditional-Space 
 CONSTRAINTS 
  epistemic-stance ↔ ums.epistemic-stance   
  premise ↔ ums.premise 
  conclusion ↔ ums.conclusion 
SPACE Conditional-Space 
 SUBCASE OF Mental-Space 
 ROLES 
  cms: Conditional-Schema 
  epistemic-stance 
  premise: Predication 
  conclusion: Predication 
 CONSTRAINTS 
  premise.local-to ← self 
  conclusion.local-to  � self 
 
Figure 5. Conditional-Space has roles for 
premise, conclusion and epistemic-stance 
lexical CONSTRUCTION If 
 SUBCASE OF Conditional-Conjunction 
 FORM: Word 
  self.f.orth  � "if" 
 MEANING 
  cs.premise ↔ cs.condition 
  cs.epistemic-stance  � neutral 
CONSTRUCTION Conditional-Conjunction 
 MEANING 
  EVOKES Conditional-Schema AS cs 
  EVOKES Conditional-Schema AS alt 
Figure 6. Conditional-Conjunctions evokes 
two Conditional-Schemas. The If construction 
identifies the  premise with the condition in the 
primary space 
If it rains tomorrow, the game will be cancelled. 
Base-Space 
 
It rains tomorrow 
↓ 
The game is cancelled 
It does not rain tomorrow 
↓ 
The game is not cancelled 
Alternative Space 
neutral neutral 
backshifting 
Figure 4. A predictive conditional sets up 
two spaces 
In addition, it also fills in the content of the condition 
role with the meaning of the Clause. It sets the parent-
space to the current focus-space.  
4.4  Predictions 
Predictions are not space builders in and of themselves. 
Instead, they are simply events that are marked as fu-
ture. The Prediction-Schema is therefore not a subcase 
of Compressed-Mental-Space. It includes a predicted-
event, which is a predication of category Event (denoted 
through the evokes statement and the binding), and a 
basis-of-prediction. A predicted event also has an asso-
ciated probability of happening, which may be supplied 
linguistically (through hedges like perhaps or proba-
bly). This probability directly affects what inferences we 
draw based on the prediction, and is captured by the 
likelihood-of-predicted-event role. 
 
4.5 The Prediction Construction 
The Prediction construction is a Clause that evokes a 
Prediction-Schema in its meaning, such as the game will 
be cancelled. The meaning pole of a Clause is a Predica-
tion. The nature of prediction requires that the time ref-
erence be future with respect to the viewpoint-space, in 
this case, today. The meaning of the Prediction construc-
tion is itself the predicted-event. 
 
4.6 Conditional Statements 
Conditional-Statement is a very general construction 
that puts a Condition and a Clause together, in unre-
stricted order. The most important thing to notice is that 
this larger construction finally fills in the conclusion of 
the Condition with the meaning pole of the statement. 
 
4.7 Predictive Conditionals 
To a first approximation, a Conditional-Prediction is just 
a special case of the Conditional-Statement where the 
statement has to be a Prediction. However, extra care 
has to be taken to ensure that the alternative spaces and 
cause-effect relations between the premises and conclu-
sions are set up correctly. 
Recall that the Conditional-Conjunction EVOKES two 
Conditional-Schemas, which are either partially filled in 
or not filled in at all. Intuitively, the goal of this con-
struction is to completely fill out these two schemas 
(and their respective spaces), and put a Cause-Effect 
relation between the premise and conclusion in the local-
content of each space.  
A role alt is created with type Conditional-Schema to 
capture the fact that there is an alternative space param-
eterized by this construction. alt is then identified with 
the alternative Conditional-Schema evoked in the Condi-
tional-Conjunction. This allows the unused alternative 
Conditional-Schema in the If construction to be filled in.  
The complete filling out of both Conditional-
Schemas are done by identifying the premise in the al-
ternative schema with the negation of the premise in the 
Figure 7. The Condition construction fills 
in the content of the condition role 
CONSTRUCTION Condition 
 SUBCASE OF Subordinate-Clause 
 CONSTRUCTIONAL 
  conj: Conditional-Conjunction  
  cl: Clause 
 FORM 
  conj meets cl 
 MEANING: Conditional-Schema 
  self.m ↔ conj.m.cs 
  self.m.condition ↔ cl.m 
  self.m.parent-space ↔ focus-space 
 
SCHEMA Prediction-Schema 
 EVOKES Event AS e 
 ROLES 
  predicted-event: Predication 
  likelihood-of-predicted-event 
  basis-of-prediction: Predication 
 CONSTRAINTS 
  predicted-event.category ↔ e 
  predicted-event.time-location  � future 
 
Figure 8. Predictions are not space-
builders by themselves.  
CONSTRUCTION Conditional-Statement 
 CONSTRUCTIONAL 
  cond: Condition 
  statement: Clause 
 MEANING 
  cond.conclusion ↔ statement.m 
 
Figure 10. The Conditional-Statement
construction puts together a Condition and a 
Clause 
CONSTRUCTION Prediction 
 SUBCASE OF Clause 
 CONSTRUCTIONAL 
  time-reference  � relative-future (viewpoint- 
              space) 
 MEANING:  
  EVOKES Prediction-Schema AS ps 
  ps.predicted-event ↔ self.m 
 
Figure 9. The Prediction construction 
makes itself the predicted-event in the 
Prediction-Schema 
primary schema, and like-wise for the conclusion. The 
epistemic-stance of the alternative schema is set to the 
opposite of that in the primary. For example, the oppo-
site of a neutral stance is neutral, and the opposite of a 
negative stance is a positive stance. 
So far, the only things in the local-content of both 
spaces are the premise and conclusion, which are just 
predications without any relations between them. The 
next two sections assert a Cause-Effect relation between 
the respective premise and conclusion, and place that in 
the local-content. It also adds the other space to its list 
of alternatives. 
Finally, the last statement identifies the primary 
cause-effect with ce1 of the predicted-event (in the 
Event schema), thereby filling in the cause of the pre-
dicted-event.   
4.8 Example 
With the Conditional-Prediction construction and the 
smaller constructions in hand, along with the related 
schemas and spaces, we now return to example (2) in 
the beginning of this section: If it rains tomorrow, the 
game will be cancelled.  
Figure 12 shows the schemas and mental spaces that 
result from the analysis of this sentence. The first half of 
the sentence, If it rains tomorrow, is an instance of the 
Condition construction. The Conditional-Conjunction If 
evokes a primary and an alternative Conditional-
Schema, and partially fills out the primary one. Specifi-
cally, the If construction sets the epistemic-stance to 
neutral, and identifies the premise with the condition. 
The Condition construction then fills in the condition 
role with the meaning of the Clause it rains tomorrow. 
For simplicity, the actual schemas for representing a 
rain event are omitted from the diagram.  
The second half of the sentence, the game will be 
cancelled, is an instance of the Prediction construction. 
The basic job that the Prediction construction performs 
is to fill in the predicted-event with the actual predic-
tion, i.e., game cancellation tomorrow. 
At this point, given a Condition with if and a Predic-
tion, an instance of the Conditional-Prediction construc-
tion is formed, and the diagram in Figure 12 is 
completed. The predicted-event is filled into the conclu-
sion in the primary Conditional-Schema. The alternative 
Conditional-Schema, previously untouched by If, now 
gets the negated premise and conclusion. A primary 
Cause-Effect (ce-Primary) is evoked and placed into the 
local-content of the primary Conditional-Space, and 
likewise for the alternative space. The two spaces are 
then linked as alternatives. 
5 Inference and Scalability 
As we discussed in Section 3, the ECG simulation se-
mantics approach to NLU involves both dynamic simu-
lations and extensive belief propagation. This approach 
leads to systems that are scalable in semantic depth. For 
such systems to be practical, we also need them to be 
scalable in size. In recent work, (Narayanan, submitted) 
has shown how the dynamic simulations and belief 
propagation techniques can be tightly coupled in a 
highly scalable formalism called CPRM, Coordinated 
Probabilistic Relation Models.  
This same formalism also provides the tools for a 
systematic treatment of inference across mental spaces, 
which correspond to separate threads of simulation. 
Returning to example (2) in the last section, If it rains 
tomorrow, the game will be cancelled, we can now 
make additional inference about the hypothetical sce-
nario and the actions of the participants involved. One 
can ask, what if the game is cancelled and the partici-
pants need to plan for other activities? How will these 
activities affect their actions today? 
The CPRM mechanism elegantly handles the trans-
fer of assumptions and inferences needed to answer 
such questions. While the varying types of mental 
spaces have different rules of inference, all of the cou-
plings are of only two different types, both of which are 
handled nicely by CPRM. Any two mental spaces will 
be related either by some shared assumptions, some 
Figure 11. The Conditional-Prediction
construction fills out the parameterization of 
both the primary and alternative spaces 
CONSTRUCTION Conditional-Prediction 
 SUBCASE OF Conditional-Statement 
 CONSTRUCTIONAL 
  statement: Prediction 
  statement.time-reference  � relative-future  
             (condition.time-reference) 
 MEANING: 
  EVOKES Cause-Effect AS ce-primary 
  EVOKES Cause-Effect AS ce-alternative    
 
  alt: Conditional-Schema 
  alt ↔ cond.conj.alt  
  alt.premise ↔ not(cond.premise) 
  alt.conclusion ↔ not(cond.conclusion) 
  alt.epistemic-stance  � opposite  
     (cond.epistemic-stance) 
 
  ce-primary.cause ↔ cond.premise 
  ce-primary.effect ↔ cond.conclusion 
  ce-primary.local-to  � cond.msp 
  alt.msp.local-to  � cond.msp.alternatives 
 
  ce-alternative.cause ↔ not(cond.premise) 
  ce-alternative.effect ↔ not(cond.conclusion)  
  ce-alternative  � alt.msp 
  alt.msp.alternatives  � cond.msp 
 
  ce-primary ↔ assertion.ps.predicted- 
      event.ce1 
 
influence links, or both. Since the CPRM formalism is 
inherently nested, it is straightforward to have shared 
spaces. For example, if several people are watching a 
game and are talking about it, the progress of the game 
is a (dynamic) shared space that is common ground for 
all the speakers. 
Influence links are the central primitive in all belief 
networks, including CPRM. These encode the effect of 
one attribute on the conditional probabilities of another 
attribute. In the mental space context, we employ ex-
plicit influence links to encode the dependencies of one 
space on attributes of another space. In the game cancel-
lation example, the participants can choose to further 
plan for the scenario where it does rain. They might 
pick a backup plan, for example going to the theater. If 
this backup plan requires some resource (e.g. a discount 
card), there should be an influence link back to the pre-
sent plan suggesting that the discount card be brought 
along. 
More generally, each particular kind of mental space 
relation will have its own types of shared knowledge 
and influence links. Some of these can be evoked by 
particular constructions. For example: Harry never 
agrees with Bob would set up dependency links between 
our models of the minds of these two individuals. It 
should be feasible to use these mechanisms to formalize 
the informal insights in the Cognitive Linguistics litera-
ture and therefore significantly extend the range of 
NLU. 
6 Conclusion 
In this paper we have provided a computational realiza-
tion of mental spaces. Within a simulation-based under-
standing framework, a mental space corresponds to a 
new thread of simulation, implementable using the Co-
ordinated Probabilistic Relational Model formalism. 
Cognitive and computational constraints demand that 
each mental space be represented at two levels of granu-
larity: as a schema (compressed-mental-space) and as a 
full space. The analyzer, using constructions like the 
ones shown in the case study, creates a Semantic Speci-
fication parameterizing the compressed and uncom-
pressed versions of each mental space. Simulation 
determines the correct level of granularity to operate on, 
and builds new mental spaces only when it is necessary 
to perform inference in the new space. Once a new men-
tal space is built, shared spaces and influence links be-
tween any two mental spaces can be defined to allow 
the transfer of inference between the spaces. 
Our proposed formalization of mental spaces allows 
systems to be scalable in both size and semantic depth: 
(i) Our formalization makes explicit how mental spaces 
partition contextual knowledge into manageable chunks, 
Parent-Space 
 
Local-content 
alternatives 
neutral neutral 
epistemic-stance: neutral 
condition 
alt: Conditional-Schema 
parent-space: 
ums 
conclusion: Game will not be cancelled 
premise: It doesn't rain tomorrow 
~1 
status 
~2 
epistemic-stance: neutral 
condition: It rains tomorrow 
cond: Conditional-Schema 
parent-space: Focus-Space (Base) 
ums 
conclusion: Game will be cancelled 
premise: It rains tomorrow 
status 
1 
1 
2 
predicted-event: Game will be cancelled 
Prediction-Schema 
basis-of-prediction 
likelihood-of-prediction 
2 
alt.ums 
 
Local-content: 
 
 
 
 
 
 
conclusion: Game will not be  
                 cancelled 
premise: It doesn’t rain tomorrow 
~1 
~2 
ce-Alternative 
cause 
effect 
~1 
~2 
cond.ums 
 
Local-content: 
 
 
 
 
 
 
 
conclusion: Game will be cancelled 
premise: It rains tomorrow 
1 
2 
ce-Primary 
cause 
effect 
1 
2 
Figure 12. If it rains tomorrow, the game will be cancelled. 
thereby providing significant computational advantage. 
(ii) By using Embodied Construction Grammar, our 
formalization provides a compositional approach to 
parameterizing mental spaces. Compositionality has the 
advantage of allowing a small grammar to handle a 
large degree of linguistic variation. (iii) During simula-
tion, new threads of simulation are built only as needed, 
obeying cognitive capacity constraints as well as mak-
ing mental spaces computationally tractable. (iv) CPRM 
provides a tightly coupled, scalable inference mecha-
nism that handles the couplings between mental spaces. 
Our proposed mental space formalism thus provides a 
precise and scalable means for handling a rich body of 
complex linguistics phenomena beyond the reach of 
current NLU systems. 
 
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