=Paper=
{{Paper
|id=Vol-2518/paper-CAOS4
|storemode=property
|title=Towards Modeling Conceptual Dependency Primitives with Image Schema Logic
|pdfUrl=https://ceur-ws.org/Vol-2518/paper-CAOS4.pdf
|volume=Vol-2518
|authors=Jamie C. Macbeth,Dagmar Gromann
|dblpUrl=https://dblp.org/rec/conf/jowo/MacbethG19
}}
==Towards Modeling Conceptual Dependency Primitives with Image Schema Logic==
https://ceur-ws.org/Vol-2518/paper-CAOS4.pdf
Towards Modeling
Conceptual Dependency Primitives with
Image Schema Logic
Jamie C. MACBETH a and Dagmar GROMANN b,1
a Smith College, Northampton, MA, 01063, USA
b University of Vienna, Gymnasiumstraße 50, A-1190 Vienna, Austria
Abstract. Conceptual Dependency (CD) primitives and Image Schemas (IS) share
a common goal of grounding symbols of natural language in a representation that
allows for automated semantic interpretation. Both seek to establish a connection
between high-level conceptualizations in natural language and abstract cognitive
building blocks. Some previous approaches have established a CD-IS correspon-
dence. In this paper, we build on this correspondence in order to apply a logic de-
signed for image schemas to selected CD primitives with the goal of formally tak-
ing account of the CD inventory. The logic draws from Region Connection Calcu-
lus (RCC-8), Qualitative Trajectory Calculus (QTC), Cardinal Directions and Lin-
ear Temporal Logic (LTL). One of the primary premises of CD is a minimalist ap-
proach to its inventory of primitives, that is, it seeks to express natural language
contents in an abstract manner with as few primitives as possible. In a formal anal-
ysis of physical primitives of CD we found a potential reduction since some primi-
tives can be expressed as special cases of others.
Keywords. Conceptual Dependency, Formal Modeling, Image Schemas
1. Introduction
Natural language understanding remains to be one of the major challenges of modern Ar-
tificial Intelligence (AI) and cognitive systems. One approach to tackling this challenge
is to map the potentially infinite compositional variety of natural language sequences
onto abstract, unambiguous base forms in a (semi-)formal representation. Conceptual
Dependency (CD) comprises one such framework that performs this function by decom-
posing language into complex combinations of language-independent conceptual primi-
tives [14,15]. CD evolved to reduce the number of conceptual primitives in the system,
generalizing them, increasing levels of decomposition, and reducing chances of multiple
representations of the same concept.
A second major such system is that of Lakoff [7] and Johnson [5] called image
schemas (IS), building on embodied cognition [16]. Sensori-motor experiences with the
1 Corresponding Author: University of Vienna, Gymnasiumstraße 50, A-1190 Vienna, Austria; E-mail:
dagmar.gromann@gmail.com
Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution
4.0 International (CC BY 4.0).
external world form patterns that are believed to shape abstract conceptualizations, such
as reasoning and language, and they are generally described as spatio-temporal relation-
ships. A first important step towards image-schematic computational models is their un-
ambiguous, formal representation. A formalization approach to image schemas, the so-
called Image Schema Logic ISLM , builds on various calculi for modeling their spatial
and temporal dimension, but also movement and dynamic dimension. A correspondence
between CD and IS has been established before [10] and backed with empirical evidence
[2].
Building on this previous correspondence, we evaluate the utilization of ISLM for
modeling CD primitives. Since CD representations lack a level of formality, utilizing a
well-defined logic towards this end can be highly beneficial to check on the CD inventory
for potential redundancies. As a very first experiment, this paper models a selection of
physical primitives that are mapped to a comparable set of image schemas, as established
in previous work [10], with a view to evaluating their correspondence in ISLM . We found
that certain primitives could be removed without loss of CD expressiveness.
2. Conceptual Dependency
This section first introduces Conceptual Dependency (CD) and a selected number of
primitives focusing on physical aspects. It then continues to elaborate on previously es-
tablished correspondences between CD and image schemas as a basis for our assumption
that ISLM can be applied to formalizing selected CD primitives.
2.1. Conceptual Dependency Primitives
As a theory of meaning representation, CD was developed as an alternative natural lan-
guage understanding system to formal, linguistic theories at that time [14,15,9]. It intends
to equip computational systems with human-like understanding of language that mirrors
human cognition. It decomposes meaning of natural language into language-agnostic
structures, called conceptual primitives.
2.2. CD Constructs and Syntax
The main well-formed expression in the Conceptual Dependency representation system
is the conceptualization. CD conceptualizations have basic elements that are described
and depicted in Table 1.
CD has numerous primitives used to represent thought, perception, social interac-
tion, and communication (see [15]). However, in this paper, we narrow our focus to its
physical, spatial, and object-defining primitives, whose names and descriptions are given
in Table 2. Example sentences in Table 2 are taken from a previous study on crowd-
sourcing the annotation of natural language sentences with CD primitives [11]. CON-
TAIN is utilized to specify physical objects in conceptualizations, which is why it is also
provided.
Denominations of CD primitives resonate English words, however, the concepts they
identify differ from the lexical definitions of those words. For instance, “ingest” relates
to events of animate beings consuming food or drinks. The CD primitive INGEST is
broader in meaning as it relates to a variety of acts where a substance or object enters
Table 1. Descriptions of the components and constructs of CD conceptualization diagrams as described in
[15]. Examples of full conceptualization diagrams are given in Table 4.
CD Construct Description
PPs Picture producers (PPs) denote physical objects serving in various roles
in a conceptualization. In representing the sentence “Amy took a
breath,”, “Amy” and “breath” (or “air”) are PPs.
ACTs ACTs are conceptual primitives representing things that can be done by
an actor to an object, or events that can happen to an object. PTRANS
and INGEST, described in Table 2, are examples of ACTs.
PP ks +3 ACT One kind of CD conceptualization is an ACT performed by a PP as the
actor. For example, for “Amy took a breath,” could be (partially)
represented by Amy ks +3 INGEST. The double arrow represents the
two-way dependency relationship between the actor and the ACT.
o
ACT o PP A conceptualization can have a PP as an object. The arrow points from
the object PP to the primitive ACT having that PP as an object. For
example, the PP “air” could serve as the object of an INGEST for “Amy
took a breath.”
D / PP1 A conceptualization can have a direction case (also called the
ACT o DIRECTION primitive). Directions are specified as the locations of
o PP2 PPs, with the two PPs indicating the “from” and “to” for primitive acts
involving movement. For example, for “Amy took a breath”, PP1 , the
destination of the movement of air, would be Amy’s lungs.
PP jt *4 PA Picture producers can be described by picture aiders (PAs), “state”
predicates that take the form STATE(VALUE). CONTAIN() is an
example of such a state predicate.
/ PA1
PP jt Picture producers can go through state changes described by a pair of
o PA2
PAs. A state change of a PP is also a type of ACT.
ks +3
JT The result causation connective (indicated by the triple arrow labeled
“r”), which connects two conceptualizations, indicates that one event or
r
act resulted in another.
ks +3
the body of an animate being, such as air, injections, transdermal absorption into the
skin or even single-cell organisms absorbing a molecule through its cell wall. Some
of the primitives have abbreviated names; for example PTRANS is short for “Physical
TRANSfer”.
2.3. Conceptual Dependency and Image Schemas
Image schemas were introduced as abstract spatio-temporal relationships that aim to
bridge the gap between sensorimotor, embodied experiences and high-level conceptual-
izations, such as natural language and reasoning. Image Schemas generalize sensorimo-
tor experiences, by which they abstract away from lexical manifestations of language,
similar to CD. For instance, repeated experiences of objects or people in concave objects,
Table 2. Six physical primitives acts of CD, and the CONTAIN primitive used to specify properties of objects
in conceptualizations
Primitive Description Example/“Target” Sentences
PTRANS A person, object, or thing changes Can be used to represent part of the
physical position or location. conceptualization of “Matthew flew home
from Los Angeles,” as
Matthew ks +3 PTRANS.
MOVE A person, object, or thing moves a part Used to represent “Kevin crossed his
of its body or part of itself. arms,” as Kevin ks +3 MOVE with “arms”
as the object.
EXPEL A change in spatial relationship between Can be used to represent part of the
two picture producers (PP1 and PP2) conceptualization of a sentence such as
beginning with PP1 being on the inside “Michelle threw up her lunch,” as
of PP2, and ending with PP1 being on Michelle ks +3 EXPEL.
the outside of PP2.
INGEST A change in spatial relationship between Can be used to represent part of the
two picture producers (PP1 and PP2) conceptualization of a sentence such as
beginning with PP1 being on the outside “Amy took a deep breath,” as
of PP2, and ending with PP1 being on Amy ks +3 INGEST.
the inside of PP2.
CONTAIN Denotes containment relations for Can be used to represent part of the
objects in CD conceptualizations as a conceptualization of a phrase like “a frog
Picture Aider (PA). in a box” as frog jt *4 CONTAIN(box).
such as water in a glass, a tissue in a box, a person in a room, reinforce our basic pattern
of the image schema C ONTAINMENT, that is, something with an inside, an outside, a
boundary, and a container where becoming contained at some moment in time requires
motion.
First correspondences between CD primitives and image schemas were established
on a theoretical basis with annotations of natural language examples by three experts
[10] and are depicted in Table 3. This mapping has been experimentally reinforced by
replicating a crowdsourcing-based annotation project of CD primitives [11] for image
schemas, uitilizing the same dataset of linguistic sequences for both experiments [2]. It
has to be noted that several distinct physical primitives can be expressed by identical
(combinations of) image schemas. This repetition in image-schematic mapping moti-
vated our assumption that more complex physical primitives, such as INGEST and EX-
PEL that map to three image schemas, might be expressible as a combination of less
complex primitives, such as PTRANS and CONTAIN. It seemed only natural to utilize
an existing, closely related logic to formally analyze this assumption.
A second major motivator for our choice of logic was the existing modeling of dy-
namic aspects of C ONTAINMENT [3], one of the central image schemas in our map-
ping to CD primitives, which generally occurs in combination with movement along
a S OURCE PATH G OAL. As such it provides an excellent basis for formally analyzing
complex physical primitives and the feasibility of expressing more complex primitives
with simpler ones, thereby reducing the number of required primitives to model meaning
underlying natural language sequences.
Table 3. Mappings between the physical primitive acts, the PP, and CONTAIN primitives of CD, and the
related image schemas and spatial primitives.
CD Primitive Related Image Schema(s) Related Spatial Primitives
PTRANS S OURCE PATH G OAL S OURCE, G OAL, PATH, M OVE,
D IRECTION
MOVE S OURCE PATH G OAL, S OURCE, G OAL, PATH, M OVE,
PART-W HOLE D IRECTION, PARTS, W HOLE,
INGEST S OURCE PATH G OAL, I N, B OUNDARY, C ONTAINER,
C ONTAINMENT, F ORCE S OURCE, G OAL, PATH, M OVE,
D IRECTION
EXPEL S OURCE PATH G OAL, O UT, B OUNDARY, C ONTAINER,
C ONTAINMENT, F ORCE S OURCE, G OAL, PATH, M OVE,
D IRECTION
PP O BJECT
CONTAIN C ONTAINMENT C ONTAINER, I N, O UT, B OUNDARY
3. Formalization Language
We rely on a previously introduced formal language for image schema modeling called
ISLM [4] and refer the interested reader to this reference for a full account. In this paper,
we will limit our description to an overall summary of specific crucial elements of the
logic that draws from existing calculi, required to model the selected CD primitives. The
logic is a combined one of RCC-8, cardinal directions, QTC, and LTL with 3d Euclidean
space for the spatial domain briefly touched upon in this chapter.
3.1. Spatial Dimension
Building on previous work, such as [1], ISLM utilizes Region Connection Calculus
(RCC-8) [12] for basic topological relations, in which two objects can be disconnected
(DC) or partially overlapping (PO). Also, one object can be a proper part of another ob-
ject (PP), a tangential proper part of another object (TPP), or a non-tangential proper part
of another object (NTPP). Thereby, it is possible to denote the (lack of) contact between
two objects. To model directionality, Ligozat’s [8] cardinal directions are applied in the
mode of a fixed observer outside the model, which results in six binary predicates: Left,
Right, FrontOf, Behind, Above, and Below.
3.2. Movement Dimension
To deal with the dynamic aspects of movement, the logic relies on Qualitative Trajec-
tory Calculus (QTC) [17] and selects three possible movements of objects in relation to
each other from its variant QTCB1D : object O1 moves towards O2 (O1 O2 ), object O1
moves away from O2 (O1 ←- O2 ), and object O1 is at rest with respect to O2 ’s position
(O1 |◦ O2 ).
3.3. Temporal Dimension
To simplify the complexity of modeling time in cognitive theories, ISLM relies on a linear
temporal logic (LTL) over the reals [6,13]. The syntax is as follows:
ϕ ::= p | > | ¬ϕ | ϕ ∧ ϕ | ϕUϕ
This allows us to express Fϕ (at some time in the future, ϕ) defined as >Uϕ, and Gϕ
(at all times in the future, ϕ) defined as ¬F¬ϕ.
4. A Comparison of Requirements
One of the most crucial aspects of CD is that it requires a PP, a picture producer, to be
a physical object. Image schemas, in contrast, have no such requirement, even though it
might be counterintuitive to model image schemas without any relation to objects [3].
A dependency between a PP and some primitive ACT is established, which might be a
mental operation [15]. For instance, to “eat” means to take something inside, to INGEST
it. This ACT requires a clear direction to the inside of the object. CD originally was
highly diagrammatic as depicted with the visual representation of the DIRECTION case
in Table 1, which states that some object on the left hand side is moved from a previous
location on the lower right hand side of the diagram to a new location on the upper right
hand side of the diagram.
Requirements specific to INGEST and EXPEL ACTs are the movement of a PP in
a specific DIRECTION with the entailed change of location. In contrast to other types
of movement, this CD primitive involves a relation to CONTAIN, either as leaving or
entering a container. However, this relation is not explicitly established in CD. In the
example diagrams in Table 2, the PP “frog” becomes CONTAINed in a PP “box”. Please
keep in mind that PP here refers to picture-producer. Depending on which ACT applies,
the DIRECTION is to the inside or outside. This is highly similar to the image schema
C ONTAINMENT, which subsumes both directions. For DIRECTION, there is the addi-
tional requirement that it might only connect locations, whereas CONTAIN would be
considered a state, which cannot be mixed. There is no required relation between CON-
TAIN and DIRECTION, and it is not necessary that the latter coincide with a container
in either location, start or end.
CD also explicitly distinguishes objects (animate or inanimate) and persons (per
definition animate) which is not the case for image schemas. Both of these are mapped to
the image schema O BJECT, which could be equalled to PP. As such, some requirements
for INGEST and EXPEL are similar to those of the image schema C ONTAINMENT, as
the PP that ACTs as CONTAINer can have one opening (putting food into your mouth),
two openings (breathing through the nose), or several openings (transdermal absorption
into the skin) through which objects or persons can go.
In the original CD version, MOVE is restricted to the movement of body parts,
which over time has been broadened to denote also the movement of parts of PPs. In
contrast, the general motion entailing a change of location is modeled as PTRANS. For
instance, “John placed his hand over his mouth” falls into the former category of primi-
tives, whereas “John went home” requires the latter. The change of location for INGEST
and EXPEL ACTs is from the inside to the outside or vice versa. This type of movement
requires a PP, a DIRECTION, and an instrument, which is not further specified by CD. In
the interpretation of this paper we consider the instrument either as a second PP utilized
to cause the movement (e.g. a vehicle) or a PATH serving as the basis for the movement.
General requirements in CD foresee modifications of primitives to account for tenses
in language. This corresponds to past, future, negation, start of transition, end of tran-
sition, conditional, continuous, interrogative, timeless, and present [15]. For the sake of
simplicity, we will limit those cases to the ones introduced in Section 3.3.
5. Modeling CD Primitives in ISLM
As the most central element of CD primitives, we need to first establish an equivalence
between picture-producers and O BJECTs based on previous findings presented in Sec-
tion 2.3, which we will refer to as O BJECTs in this section since PP will here refer
to RCC proper part from now on. Such O BJECTs can change their locations, which in
line with ISLM we model using QTC (see Section 3.2) M OVEMENT A LONG PATH and
which corresponds to PTRANS.
On PATH Toward(O1 , O2 ) :=
(O1 O2 ∧ DC(O1 , O2 ))
In order to model the MOVE CD primitive, which represents animate actors moving
parts of their bodies (e.g. arms or legs, or diaphragm muscles to represent a sentence like
“Amy took a breath”), we need to take into consideration that a body part of an animate
actor is a proper part of their body. For the sake of simplicity, we utilize PP(O1 , O2 ),
where object O1 is a proper part of object O2 and can be a tangential proper part (T PP)
or a non-tangential proper part (NT PP). This allows us to model MOVE as a special case
of M OVEMENT A LONG PATH. It requires three objects, since it concerns the body part
(O1 ), a body (O2 ), and an object that the body part moves toward (O3 ). In special cases,
it is possible that O3 coincides with O2 when the body part is moved towards the body or
represents another PP of the body, such as “John placed his hand over his mouth”, where
PP(O1 , O2 ) ∧ PP(O3 , O2 ).
Move Toward(O1 , O2 , O3 ) :=
PP(O1 , O2 ) ∧
On PATH Toward(O1 , O3 )
In the cases of PTRANS and MOVE, the inverse movement of one object away from
another is also possible, which would be modeled by replacing with ←- .
On PATH From(O1 , O2 ) :=
(O1 ←- O2 ∧ DC(O1 , O2 ))
This implicitly allows us to include the CD primitive DIRECTION, which is a re-
quirement for both PTRANS and MOVE. Again here it is possible that the third object
is a proper part of the body as well.
Move From(O1 , O2 , O3 ) :=
PP(O1 , O2 ) ∧
On PATH From(O1 , O3 )
One central basic primitive is CONTAIN, which as a state in CD can be modeled
utilizing the static representation of C ONTAINMENT in ISLM as suggested by Hedblom
et al. [3]. Like Hedblom et al, we augment ISLM with predicates opening of(op, O) to
represent op is an opening of O, inside of(in, O) representing that in is the inside of O,
and outside of(out, O) representing that out is on the outside of O.
Contained Inside(O1 , O2 ) :=
inside of(in, O2 ) ∧ PP(O1 , in)
In order to become contained, an object needs to cross the opening of the con-
tainer. For instance, when breathing the air might pass into the body through the open-
ing “mouth”. The definition below shows a close relation between several primitives.
It utilizes On PATH Toward, utilized to model PTRANS above, and Contained Inside,
utilized to model CONTAIN, above.
Crossing Opening(O1 , O2 , opening) :=
opening of(opening, O2 ) ∧
(DC(O1 , O2 ) ∧ On PATH Toward(O1 , opening)) ∧
F(PO(O1 , opening))
Crossing Opening is one important modeling component for INGEST, which is sim-
ilar to the inward directed movement of a C ONTAINMENT image schema and equivalent
to the Going I N in the ISLM implementation of dynamic C ONTAINMENT [3]. The fact
that this modeling reuses the modeling of PTRANS and CONTAIN establishes a direct
connection to INGEST.
To make this relation between primitives more explicit, we show the CD diagram
on the left and the ISLM definition on the right in Table 4. As can be seen in the ISLM
modeling and the CD diagram, INGEST can be treated as a composition of PTRANS
and CONTAIN, if the DIRECTION is modeled as in ISLM . It could be argued that the
explicit Crossing Opening is missing in this case, however, in the CD diagram, this is
also missing for INGEST. Thus, ISLM not only facilitates the detection of CD primitive
interrelations but also fosters a higher precision in their definitions.
In Table 5, we perform the same modeling exercise for the CD primitive EXPEL,
which equally can be viewed as a composition of PTRANS, CONTAIN, and DIREC-
Table 4. Correspondence of INGEST with PTRANS, CONTAIN and DIRECTION through ISLM on the sen-
tence “Amy took a deep breath.”
CD Diagram ISLM
air
o
/ inside(Amy) Going I N(air, Amy, mouth) :=
D Crossing Opening(air, Amy, mouth) ∧
Amy ks +3 INGEST o
F(Contained Inside(air, Amy))
o outside(Amy)
air
o
/ inside(Amy)
D
Amy ks JT
+3 PTRANS o
o outside(Amy)
Going I N(air, Amy, mouth) :=
Crossing Opening(air, Amy, mouth) ∧
r F(Contained Inside(air, Amy))
/ CONTAIN(Amy)
air jt
o
TION with the only difference of a change of direction in CD. As can be seen in Ta-
ble 5, the same ISLM elements are being used for Going O UT as for Going I N with the
addition of the final state being outside.
In the previously established correspondences between CD primitives and image-
schematic constructs, INGEST and EXPEL were mapped to C ONTAINMENT and
S OURCE PATH G OAL. With ISLM we could now show that in fact these two are spe-
cific cases of C ONTAINMENT, which in order to be dynamic requires movement along
a PATH, a CONTAIN relation and a DIRECTION. Since these are other CD primitives,
INGEST and EXPEL can be modelled utilizing compositions of PTRANS, CONTAIN,
and DIRECTION, which further reduces the CD inventory.
6. Conclusion
In this paper, we evaluated the formal modeling of Conceptual Dependency primitives,
with the objective of allowing for a more fine-grained comparison and detection of poten-
tial redundancies. Since a previous correspondence to image schemas was established,
we decided to utilize the well-defined Image Schema Logic ISLM , which turned out to be
well applicable to the modeling of CD primitives. This modeling exercise allowed us to
establish an equivalence between INGEST and EXPEL with the only difference of their
DIRECTION, and also show that both could be modeled as a composition of PTRANS,
CONTAIN, and DIRECTION, which means they could be considered redundant. Since
this was only a first experiment on a limited set of primitives, in the future we want to
extend the formalization the full CD repository, which might bring further equivalences
among primitives but also to image schemas to the light.
Table 5. Correspondency of EXPEL with PTRANS, CONTAIN, and DIRECTION through ISLM on the sen-
tence “Michelle threw up her lunch.”
CD Diagram ISLM
lunch Going O UT(lunch, Michelle, mouth) :=
Contained Inside(lunch, Michelle)∧
o
/ outside(Michelle) F(Crossing Opening
D
Michelle ks +3 EXPEL o (lunch, Michelle, mouth)∧
o inside(Michelle)
F(outside of(lunch, Michelle)))
lunch
Going O UT(lunch, Michelle, mouth) :=
o
/ outside(Michelle) Contained Inside(lunch, Michelle)∧
D
ks +3 PTRANS o
Michelle JT F(Crossing Opening
o inside(Michelle) (lunch, Michelle, mouth)∧
r / F(outside of(lunch, Michelle)))
lunch jt
o CONTAIN(Michelle)
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