=Paper=
{{Paper
|id=Vol-2518/paper-CAOS5
|storemode=property
|title=Linking Image Schemas with Affordances: An Ontological Approach
|pdfUrl=https://ceur-ws.org/Vol-2518/paper-CAOS5.pdf
|volume=Vol-2518
|authors=Fumiaki Toyoshima,Adrien Barton
|dblpUrl=https://dblp.org/rec/conf/jowo/ToyoshimaB19
}}
==Linking Image Schemas with Affordances: An Ontological Approach==
https://ceur-ws.org/Vol-2518/paper-CAOS5.pdf
Linking Image Schemas with Affordances:
An Ontological Approach
Fumiaki TOYOSHIMAa,1 and Adrien BARTONb,2
a
Graduate School of Advanced Science and Technology, JAIST, Nomi, Japan
b
Institut de Recherche en Informatique de Toulouse, CNRS, Toulouse, France
Abstract. Affordances and image schemas are two building blocks of cognitive and
behavioral modeling. In this paper, we present initial steps towards an extension of
our dispositional view of affordances and effectivities to image schemas. In
particular, we consider image schemas as mental patterns that are, in most cases,
about classes of affordances and effectivities.
Keywords. image schema, affordance, disposition, agency, cognition
1. Introduction
According to Kutz et al. [1], affordances and image schemas are the twin pillars on which
a successful theory of cognition is built; and they have been intensively investigated in
various fields for the last few decades. How affordances and image schemas are entwined
has been less carefully investigated, though. Indeed, for instance, Kuhn [2] develops an
image-schematic and algebraic account of affordances, which has been widely applied
as in Cunha et al’s [3] visual representation of concepts. However, an analysis of
ontological nature of affordances, image schemas, and their relations is still lacking. We
provided in former work a dispositional formalization [4, 5] of affordances and
effectivities. This paper will provide an ontological analysis of some relation between
image schemas on one hand, and affordances and effectivities on the other hand.
The remainder of the paper is structured as follows. After preliminaries on our
general ontological framework, Section 2 synthetizes how we formalized affordances
and effectivities in former work [5], and analyzes the connection of image schema with
so-called “family-directed” affordances and effectivities. Section 3 discusses a few
points, including how image schemas can be applied beyond their domain of origin, how
our framework accounts for the dual nature (static and dynamic) of image schemas, and
how image schemas might be combined. Section 4 concludes the paper with some
remarks on future directions of research.
1
Corresponding Author: Fumiaki Toyoshima, Graduate School of Advanced Science and Technology, Japan
Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, 923-1292, Japan; E-mail:
toyo.fumming@gmail.com, fumiakit@buffalo.edu.
2
Corresponding Author: Adrien Barton, IRIT, avenue de l'étudiant, 31400 Toulouse, France; E-mail:
adrien.barton@irit.fr.
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution
4.0 International (CC BY 4.0).
2. From Affordances to Image Schemas
2.1. Preliminaries
For the sake of anchoring our work in a general ontological background, we postulate
some basic categories and relations that are relatively widespread in upper ontologies.
Entities fall into two kinds: universals (aka types, classes) and particulars (aka tokens,
instances). Particulars (e.g., Mary) bear the instance-of relation to universals (e.g.,
Human). Particulars (resp. universals) fall into two categories: continuants (aka
endurants) and occurrents (aka perdurants). Continuants exist fully at each time when
they exist; whereas occurrents (including processes) extend through time and have
temporal parts. Note that discussion on occurrents in formal ontology is complicated by
significantly diverse usages of the term “process” (as well as the terms “event” and
“state”, which we will not discuss for simplicity). In this paper the term “process” refers
to occurrents in which continuants can participate (such as the process of an organism
sleeping). Continuants can be further divided into independent continuants (including
objects) and dependent continuants (properties such as qualities or dispositions, which
can be seen as tropes). Independent continuants, especially objects (e.g., stones), can be
bearers of dependent continuants (e.g., hardness).
2.2. Affordances, Effectivities and Image Schemas
The term “affordance” was coined by Gibson [6] to pin down precisely the interaction
between animals and the environment: “The affordances of the environment are what it
offers the animal, what it provides or furnishes, either for good or ill” [6, p. 119]. For
instance, a gap affords hiding when it is of a certain size relative to the size of a person
and a stair affords climbing when it is a certain proportion of a person’s leg length. Our
recent conceptualization of affordances [4, 5] builds upon both Turvey’s [7] dispositional
view of affordances and a state-of-the-art formal-ontological characterization of
dispositions [8, 9]. A disposition is a property that is linked to a realization, namely to a
specific possible behavior of an independent continuant (typically an object) that is the
bearer of the disposition. To be realized in a process, a disposition needs to be triggered
by some other process. Typical examples include fragility (the disposition of a glass to
break when pressed with a certain force) and solubility (the disposition of salt to dissolve
when put in a certain solvent). The crux of Turvey’s argument is that: “An affordance is
a particular kind of disposition, one whose complement is a dispositional property of an
organism” [7, p. 179]. He also calls this complement an “effectivity”. For instance, the
affordance of the stairs is their disposition to move an organism upward and its
complement is the disposition (effectivity) of an organism to move upward when using
stairs.
Image schemas, on which we put a primary focus in this paper, are used in a number
of different domains, ranging from cognitive linguistics and developmental psychology
to artificial intelligence. They are usually attributed originally to Lakoff [10] and Johnson
[11]. Roughly speaking, image schemas are mental patterns or “conceptual building
blocks” that are extracted from the sensory and motile experiences.3 They are presumed
3
For instance, Johnson [11, p. xiv] initially defines image schemas as follows: “An image schema is a
recurring, dynamic pattern of our perceptual interactions and motor programs that gives coherence and
structure to our experience.” Oakley [12, p. 215] explains image schemas from the viewpoint of cognitive
to be learnt during the early infancy [14]; and a complete understanding of them requires
considering carefully prelinguistic conceptual development [13]. Image schemas are
derived from embodied experiences deriving themselves from sensorimotor inputs,
which are multimodal. Quite often, image schemas are nonetheless associated practically
to generic spatiotemporal relationships that are learnt from the repetitive interactions
with the environment (and the objects therein), especially in formal studies.4
One of the most intensively studied image schemas is CONTAINMENT: broadly,
the recognition that objects can be inside other objects or (container-shaped) sites. 5
CONTAINMENT is most basically defined as the relationship between an inside, an
outside, and the border between them [11]. Seen dynamically, however,
CONTAINMENT could be characterized in terms of more “fine-grained” image
schemas INTO and OUT OF [13]. Other paradigmatic examples of image schemas
include SUPPORT (which denotes a relationship between two objects in which one
provides support to the other), PATH (which represents movement of objects from one
point to another), and LINK (an enforced connection between objects where the linked
object reacts to the stimuli of the other).
2.3. The Connection between Image Schemas and Effectivities
As has been already alluded to in [5], Galton [17, p. 1] would serve as a useful starting
point for the extension of our dispositional construal of affordances to image schemas:
“Examples of image schemas include CONTAINER and PATH: the link with
affordances is obvious, since to be a container is precisely to afford containment, while
to be a path is to afford passage. Thus at least in many cases image schemas may be
characterized in terms of the affordances of actual exemplars of those schemas.”
We agree with Galton that there is a strong connection between image schemas and
affordances. We will characterize image schemas in terms of what we call “family-
directed” affordances and effectivities. To explain what those are, we need to remind our
model [5] of Turvey’s [7] idea of affordances and effectivities as reciprocal dispositions.
2.3.1. Categorical Bases and Reciprocal Dispositions
First, let us introduce the notion of “categorical basis” of a disposition as a quality (or a
sum of qualities) of the disposition bearer that underlies this disposition. The categorical
basis of glass0’s fragility is the sum of individual qualities of glass0 that make it fragile,
and the categorical basis of its electrical resistivity is the sum of its individual qualities
that make it electrically resistive [8,9].6
Let us now turn to the notion of reciprocal dispositions. Classical examples of
reciprocal dispositions include a key and a lock such that the former opens the latter:
key1 has the disposition d1 to open lock2, and lock2 has the disposition d2 to be opened
linguistics: “an image schema is a condensed redescription of perceptual experience for the purpose of mapping
spatial structure onto conceptual structure.” Mandler and Cánovas [13, p. 526] also critically state: “Image
schemas are generally viewed as redescriptions of perceptual events, or even more broadly as generalizations
over perceived similarities.”
4
For example, Kuhn [2] characterizes image schemas merely as “patterns abstracting from spatio-
temporal experiences.”
5
For details on CONTAINMENT, see Davis, Marcus and Frazier-Logue [15] in artificial intelligence;
and also Bennett and Cialone [16] in formal ontology. Note that (canonical) image schemas are normally
written in upper case letters in the relevant literature, and we adhere to this convention in this paper.
6
Particulars and relations will be hereafter written in bold, and classes in italic.
by key1. Those two dispositions have something in common: they can be triggered by
instances of the same class of process, namely key1_pivoting_in_ lock, and they can be
realized by instances of the same class of process, namely lock2_opening. We say that d1
and d2 are reciprocal dispositions; and affordances and effectivities are reciprocal
dispositions in this sense of the term. For instance, the affordance a0 of gap0 to be
contained in gap0 and the effectivity e0 of John enabling him to be contained in gap0 are
reciprocal dispositions: they both can be triggered by the process of John entering into
gap0 and be realized by the process (or state – we will not analyze this distinction here)
of John being contained in gap0.
2.3.2. Individual-directed and Family-directed Affordances and Effectivities
We can introduce dispositions that are closely related to but differ from d1 and d2. Let Q1
be the universal of properties that characterize a key that can open a lock similar to lock2,
and Q2 be the universal of properties that characterize a lock that can be opened by a key
similar to key1, such that q1 instance_of Q1 and q2 instance_of Q2, where q1 and q2 are
categorical bases of d1 and d2, respectively. Let Key1 be the class of keys which have a
property instance of Q1 (hence key1 instance_of Key1); and let Lock2 be the class of locks
that have a property instance of Q2 (hence lock2 instance_of Lock2). Then, we can define
the following dispositions:
• the disposition d1’ of key1 to open locks instances of Lock2.
• the disposition d2’ of lock2 to be opened by keys instances of Key1.
Although they are similar to some extent, d1 and d1’ are not identical: contrarily to d1,
d1’ does not depend existentially on lock2 – that is, d1’ could continue to exist even if
lock2 ceased to. Similarly, d2 and d2’ are not identical: contrarily to d2, d2’ does not
depend existentially on key1. Dispositions like d1’ and d2’ reflect more general properties
of key1 and lock2, and therefore might be more relevant entities than d1 and d2.
This strategy can be adapted to affordances and effectivities, since we have defined
them as reciprocal dispositions. We have called the affordance a0 of gap0 to contain John,
and the effectivity e0 of John to be contained in gap0 “individual-directed” affordances
and effectivities, respectively [5]. Such dispositions are in line with Turvey’s [7] analysis
of affordances and effectivities, as they depend existentially on each other. However,
more relevant dispositions might be the affordance a1 provided by gap0 to contain any
member of a general class Material object1 (the class of material objects with the
appropriate dimensions to be contained in gap0) and the effectivity e1 of John to be
contained in any member of a general class Gap1 (the class of gaps with the appropriate
dimensions to contain John). We call such dispositions “family-directed” (abbreviated
as “F-D”) affordances and effectivities.
Because of their general character, F-D affordances and effectivities seem to be
especially relevant for all fields using the notions of affordances and effectivities.
Moreover, as explained in [5], individual-directed affordances and effectivities are
vulnerable to “Cambridge change”: a0 depends existentially on John, although John is
external to a0’s bearer gap0. Similarly, e0 depends existentially on gap0, although gap0 is
external to e0’s bearer John. On the other hand, a1 and e1 would not be affected by
changes external to their bearers. And as we will see, F-D affordances and effectivities
are also more relevant to image schemas.
2.3.3. What Image Schemas are about
We will propose that (at least) most image schemas are closely related to special kinds
of affordances and effectivities. First, we must make clear that image schemas are not
identical to affordances and effectivities. As a matter of fact, according to classical views
like Turvey’s [7], affordances and effectivities are – at least partly – “out of the mind”
of the agent. For example, a1 inheres in gap0, and has as categorical basis physical
qualities of gap0 (or maybe qualities of the material in which gap0 is carved). Similarly,
e1 inheres in John, and has as categorical basis physical qualities of John such as his
height. Independently of the existence of agents, any site has a disposition (an
affordance) to contain objects of appropriate dimensions, and any material object has a
disposition (an effectivity) to be contained in sites of appropriate dimensions.
On the other hand, image schemas are arguably “in the mind” of the agent: they are
mental patterns, and thus should be seen as inhering in the cognitive system of an agent,
or maybe being a part of it (we will not take any further position here on the nature of
mental patterns, though). Therefore, image schemas cannot be identified with
affordances or effectivities.
Despite this, image schemas are strongly related with affordances and effectivities.
More specifically, image schemas are related to family-directed affordances and
effectivities rather than to individual-directed ones, because they are general mental
patterns that are extracted from individual sensorimotor experience.7 Granted that a gap
is a kind of container, for instance, John’s image schema CONTAINMENT should be
construed in connection with FD-affordance a1 or FD-effectivity e1 (rather than in
connection with individual-directed affordance a0 or effectivity e0). Actually,
CONTAINMENT should be understood in connection with classes of such family-
directed affordances and effectivities, such as the class A1 (of which a1 is an instance) of
gaps’ affordances to contain material objects that can fit in them, and the class of material
objects’ effectivities E1 (of which e1 is an instance) to be contained in gaps in which they
can fit.
However, the existence of affordances and effectivities does not require an organism
to have a corresponding image schema: gap0 has an affordance a1 and John has an
effectivity e1 whether he (or any other agent) has a corresponding image schema or not.
As we said, image schemas are mental patterns. As such, there is arguably an
intentional dimension of image schemas: they are about something. A natural proposal
is that many image schemas are about classes of affordances and effectivities. For
example, John’s CONTAINS image schema would be about 8 the class of F-D
affordances of sites (such as gaps) to contain objects, whereas his IS CONTAINED
image schema would be about the class of F-D effectivities of material objects to be
contained in sites.
It is not clear, however, that all image schemas are about classes of affordances or
effectivities. Consider for example the image schema THING [13], that is involved in
recognizing so-called “ordinary material objects” such as stones, people, and tables. This
image schema might be about e.g. Material object or Independent continuant, rather than
being about classes of F-D affordances or effectivities. Some bundle views of objects
7
Kuhn [2] states: “Image schemas generalize over concepts (e.g., the CONTAINMENT schema abstracts
container behavior from concepts like cups, boxes, or rooms)”.
8
See [23,24] for the usage of the is_about relation in formal ontology. See also [25,26] for careful
consideration of the nature of aboutness.
might interpret material objects as bundle of dispositions9 ; in such a framework, even
image schemas such as THING might be about a class of effectivities. We do not take
position here on the validity of such frameworks, and leave as an open question whether
all image schemas are about classes of affordances and effectivities, or only most of
them.10
3. Discussion
3.1. Applying Image Schema beyond the Realm of Material Objects
An agent’s image schemas enable him to organize his perceptions, but they can then be
used to fulfill a variety of purposes. That is, even if an image schema is about a class of
affordances or effectivities (which are dispositions inhering in material objects), this
image schema might then be used to conceptualize other, non-material entities. For
example, Lakoff and Núñez [29] attempt to explain mathematics based on image
schemas (e.g., the natural numbers by the image schema PATH). Such considerations
might enlighten some discussions about constructivist interpretations of mathematics
[30].
3.2. Representing Formally the Aboutness of Image Schemas
As we argued, many (if not all) image schemas are about classes of dispositions, namely
F-D affordances or effectivities. Note that Web Ontology Language (OWL) [31] does
not enable to represent relations of aboutness between a particular (such as John’s
CONTAINS image schema) and a class of dispositions (such as the class of F-D
affordances of sites to contain material objects). A variety of technical workarounds
might enable to represent such relation, such as punning [32] or referent tracking
formalism [33].
3.3. The Static and Dynamic Nature of Image Schemas
One of Tseng’s [34] features of image schemas is that they are static and dynamic,
although they may sound contradictory: “Image schemas can be experienced as states of
being or as a process. For example, the PATH schema can be experienced in a dynamic
way --- the process of moving from one place to another. Or it can be realized “as a static
thing”, the road, track or passage that has been traversed” [34, p. 143].11 Our view of
image schemas as being (in at least many cases) about dispositions solves this paradox.
As a matter of fact, dispositions are static and dynamic in the sense that: “dispositions
9
See [27] for the bundle theory of objects; and see [28] for dispositionalism, viz. the view that all
properties are dispositional.
10
Another difficult example would be the image schema CYCLE, which seems to be about processes
rather than about dispositions – such as heartbeat, breathing, seasons, etc. However, one might interpret it as
being about the dispositions that are realized by such heartbeat, breathing, seasons, etc. (the disposition of the
heart to beat regularly, the disposition of a human to breath regularly, the disposition of the seasons to come
back regularly, etc.) It is more difficult, however, to interpret such dispositions as affordances or effectivities.
11
In a similar vein, Kuhn [2] says: “they [image schemas] are internally structured (e.g., the
CONTAINMENT schema involves behavior associated with an inside, an outside, a contained entity, and
possibly a boundary)”.
connect the static structure of the world, i.e. the natural kinds of continuants, with the
dynamical structure, i.e. the types of possible and actual causal processes” [8, p. 3, our
italicization added].12 In the aforementioned example, PATH can be about the class of
disposition inhering in material pathways (which are static entities) that can be realized
by an object moving along such pathways (which are dynamic entities).
3.4. Combining Image Schemas
Characteristically, image schemas can be combined in many different ways [2,12,13].
To take Kuhn’s [2] example, CONVEYANCE (a vehicle for transporting something) is
plausibly taken to be a combination of PATH and SUPPORT (or PATH and
CONTAINMENT). By our lights, a combination of two image schemas is1 (which is
about a class of disposition D1) and is2 (which is about a class of disposition D2) might
be modeled as being about a collective complex composed by D1 and D2. A collective
disposition is defined by the upper ontology Basic Formal Ontology (BFO) [35] as: “A
disposition inhering in an object aggregate OA in virtue of the individual dispositions of
the constituents of OA and that does not itself inhere in any part of OA or in any larger
aggregate in which OA is a part” [36, p. 410].13 For instance, a crowd has the collective
disposition to do the wave in virtue of each individual crowd member’s disposition to
stand at the appropriate time [36, p. 409]. Understood by analogy with the wave of a
group of people, for example, CONVEYANCE could be formalized as being about a
class of dispositions composed by the class of dispositions that PATH and SUPPORT
are about (or PATH and CONTAINMENT). Mereological relations between dispositions
could help to analyze more finely such dependences [21].
4. Conclusion
To recapitulate briefly, we took a first step towards an extension of our ontological
analysis of affordances and effectivities to image schemas: several important image
schemas (not only CONTAINMENT, but also PATH, SUPPORT, CONVEYANCE,
etc.) are about classes of family-directed effectivities and affordances. It might be
possible to think that image schemas are the result of “dispositional evolution” of an
individual’s effectivities. At first, an infant might conceptualize only individual-directed
affordances and effectivities: e.g., one effectivity of John to be inside this house and
another effectivity of his to be inside that baby park; and the affordances offered by this
house and that baby park to contain him. Through repeated interactions with individual-
directed affordances, the infant later learns to conceptualize classes of family-directed
affordances and effectivities, such as the classes of affordances of sites to contain objects
of appropriate sizes. Such conceptualization leads to his image schema
CONTAINMENT. We also discussed briefly some consequences of our dispositional
account of image schemas.
Future work includes:
12
More specifically, in [8] and [9], those static and dynamic features of dispositions are accounted for
respectively by the categorical bases of dispositions, and their triggers and realizations.
13
An object aggregate is a BFO category: “A material entity that has as parts (exactly) two or more
objects that are separate from each other in the sense that they share no parts in common. Examples include a
heap of stones, a population of bacteria, a flock of geese” [35, p. 181].
i. the application of our dispositional interpretation of image schemas to e.g.,
analysis of metaphors [37] (e.g., the metaphor “marriage is a prison” stems from
the CONTAINMENT-based conceptualization of marriage); and
ii. comparison and/or integration between our dispositional formalization of image
schemas and e.g., the logic [38] for image schemas and directed movement.
A long-term project would be to provide a full formalization of affordances and image
schemas that would contribute to the building of a core ontology [39] for cognitive and
behavioral modeling: an ontology that covers the most basic categories and relations
among them regarding agency, cognition, perception, and actions. As was implied in [4],
it will also have crucial implications for the ontology of the environment [40-42].
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