Notwithstanding its centrality to agency and cognition, the concept of affordance is notoriously difficult to model computationally, partly owing to its conceptually multifaceted character. This paper elaborates on previous formalontological studies of disposition by proposing a theory of reciprocal dispositions, and formalizes affordances and effectivities as reciprocal dispositions, contributing to the development of an ontological module for generic affordance representation.
Since its invention by Gibson [
This paper furthers the project (originally sketched out by Toyoshima [
The paper is organized as follows. Section 2 explains our basic methodology and our theory of dispositions in detail. Section 3 presents a general overview of our dispositional approach to affordance and provides a formal characterization of some core notions therein. Section 4 is devoted to the discussion. Section 5 concludes the paper with some brief remarks on future work.
A cloud of suspicion hangs over dispositions in formal ontology (see e.g., [
To dispel this worry, we need to remind first the general theoretical setting into which the notion of disposition is inserted. In philosophy, dispositions are usually taken to be one of the topics that are loosely grouped under the heading of “natural necessity”. When one says that it is necessary for a glass to be broken when pressed with a certain force, for instance, one is speaking of the kind of necessity supplied by “nature” rather than by e.g., logic or mathematics (compare: “Necessarily, two plus two equal four”). Major issues of natural necessity are listed below with their elucidation by the example of (Newtonian) force and pressing: • • • •
Laws of nature: any object has an acceleration given by the ratio of the resultant force applied on it divided by its mass (Newton’s Second Law of Motion). Causation: pressing with a certain force caused a glass to be broken.
Dispositions: a fragile glass is disposed to break if pressed with a certain force. Counterfactuals: if a glass were pressed with a certain force, the glass would break.
It has been of primary philosophical interest to determine which is most fundamental among those concepts of natural necessity. Some may wish to take laws of nature to be most basic and have an eliminativist or reductionist approach towards dispositions. Others would counter that dispositions grounds all other notions of natural necessity and claim that both the truth of counterfactuals and causal relations between processes are determined by dispositions.
Most importantly, the notion of disposition is indispensable for a comprehensive
description of reality, in order to account for notions such as fragility, inflammability,
solubility, or arguably even physical entities such as Newtonian forces [
For the sake of further elucidation, it would be useful to draw a sharp distinction
[
Because dispositions constitute a central notion in the context of natural necessity, any formal ontology should clarify their status. BFO seems to adopt an ontology of causal powers, whereas DOLCE does not. DOLCE must nonetheless provide its own treatment of dispositions, which would in turn necessitate the DOLCE conception of lawhood.
All these discussions would offer a fresh perspective on prior formal-ontological
works [
We will attempt a formal specification of affordance on the basis on the abovementioned formerly developed theories of dispositions. As we argued, this formalization could be articulated with a large range of upper ontologies, whatever their stance is concerning the fundamental nature of dispositions.
Our formalization will be written using first-order logic, with occasional use of the
Manchester Syntax [
A disposition is a property that is linked to a realization, namely to a specific behavior of an independent continuant that is the bearer of the disposition. To be realized in a process, a disposition needs to be triggered by some other process: for example, to account for the fragility of a particular glass0, it will be stated that a particular strong_shock0 can trigger the disposition fragility0 of glass0 (fragility0 has_trigger strong_shock0) which is then realized by a process glass0_breaking (fragility0 has_realization glass0_breaking) – where “has_trigger” and “has_realization” are primitive relational predicates.
The fragility of a glass exists because of a certain molecular structure of this glass.
The electrical resistivity of a material exists because of its physical constitution. We
endorse here the notion of categorical basis [
Following Röhl and Jansen [
We will use a recent theory of mereology among dispositions [
Several axioms are satisfied by those kinds of disposition-parthood [
The bearer of a disposition-part (whether mod-part or add-part) is a part of the bearer of the disposition-whole.
A mod-complex (that is, a disposition that has a proper mod-part) is triggered by a process if and only if at least one of its proper mod-parts is triggered by this process; and it is realized in a process if and only if at least one of its proper mod-parts is realized in this process.
If an add-complex (that is, a disposition that has a proper add-part) is triggered by a process, then all its add-parts are triggered by a part of this process; and if it is realized in a process, then all its add-parts are realized in a part of this process.
To formalize affordances, we need now to expand our theory of dispositions by introducing the notion of reciprocal disposition.
Reciprocal dispositions have been discussed in philosophy [
We will say that d1 and d2 are reciprocal dispositions and write: “d1 has_reciprocal_disposition d2”, where has_reciprocal_disposition is a symmetrical relation. This relation is anti-reflexive: a disposition is not reciprocal of itself. Similarly, d2 is not a reciprocal disposition from the disposition of door0, which is closed by lock2, to be opened by key1 (both dispositions are closely related, but their relation is not what we mean by “reciprocal”). Therefore, we endorse the axiom stating that the bearers of two reciprocal dispositions do not have any common part: (BEARER) b bearer_of d ∧ b’ bearer_of d’ ∧ d reciprocal_disposition_of d’ Þ ¬∃b’’ [(b’’ part_of b) ∧ (b’’ part_of b’)]
We can introduce the mereological sum of key1 and lock2 noted key1+lock2, assuming
throughout this paper the standard, classical extensional mereology [
Barton et al.’s [
The bearers of d1 and d2 are parts of the bearer of d3.
If d3 is realized in a process, then both d1 and d2 are realized in a part of this process (namely, this very process).
If d3 is triggered, then both d1 and d2 are triggered by a part of this process (namely, this very process).
More specifically, we could call this relation between d1 and d3 or d2 and d3 a
“causally equivalent add-part”: those add-parts d1 and d2 and their add-sum d3 have the
same triggers and realizations, and therefore, we can informally say that they play the
same causal role; but they have different bearers (the bearers of the add-parts being a
part of the bearer of the add-sum). They also have different categorical bases: the
categorical basis of d1 (named “q1”) is formed by key1’s qualities that make it fit with
lock2; the categorical basis of d2 (named “q2”) is formed by lock2’s qualities that make
it fit with the structure of key1; and the categorical basis of d3 (named “q3”) is the
mereological sum of q1 and q2. Barton et al. [
What matters for the existence of d1 (respectively d2) is not only the existence of its
categorical basis q1 (respectively q2) that inheres in their bearer key1 (respectively lock2),
but also some external qualities. As a matter of fact, d1 also depends existentially on the
qualities q2, and d2 also depends existentially on the qualities q1. Such qualities are called
the “external basis” [
This implies that d1 and d2 can be subject to so-called “Cambridge change” [
The term “affordance” was coined by Gibson [
A dispositional view of affordance was initially proposed by Turvey [
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” [p.179]. He also calls the complement of an affordance “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. In what follows we elaborate a substantially refined version of this idea of affordance and its formalization, based on the theory of dispositions that was delineated in the last section. In particular, we aim to deploy, for space reasons, a core formal framework for representing affordances (and effectivities), rather than a full axiomatization of them.
The first thing to point out is that Turvey’s usage of the terms “disposition” and
“dispositional property” is obscure in light of our distinction between dispositions and
causal powers. He assumes “property realism” [Section 3] which would mesh better with
the grounding of the disposition concept in an ontology of causal powers; but, he also
4 For simplicity we will henceforth refer only to page or section numbers in citing Turvey [
Given Turvey’s key idea that “An affordance is a particular kind of disposition, one whose complement is a dispositional property of an organism” [p.179], we introduce Affordance as a subclass of Disposition. Most importantly, Turvey’s notion of “complement” remains unspecified. He says: “Given that a dispositional property is not defined (i.e., it is a nonexistent property) when there is no complement, then an affordance is not defined (i.e., is nonexistent) without a complementing animal property and, in like fashion, an effectivity is not defined (i.e., is nonexistent) without a complementing environment property” [pp.179-180]. It requires further elucidation for our goal to characterize precisely in which sense those two dispositions depend existentially on each other.
We formalize it by introducing another subclass of Disposition named Effectivity, and stating that any effectivity has an affordance as reciprocal disposition:
A reciprocal axiom, not mentioned by Turvey, must be added, namely that the existence of an affordance implies the existence of an effectivity that is its reciprocal disposition:
For example, afford might be the affordance of stairs0 enabling Mary to climb it, and effect might be the effectivity of Mary enabling her to climb stairs0.
Turvey [Section 7] proposes the following formal account of affordances and effectivities (the name of instances are ours). Let agent be a particular agent, env a particular environmental entity, effect a property of agent and afford a property of env. He considers the junction junction of agent with disposition effect and env with disposition afford. Then, he argues that afford is an affordance of env, and effect is an effectivity of env that is the complement of afford, if and only if there is a third property afford/effect that is possessed by junction, and such that junction possesses neither afford nor effect, and such that neither env nor agent possesses afford/effect.
Taking a simpler view on this, our account introduces the mereological sum agent+env to play the same role as junction in Turvey’s theory. It then states that if afford is an affordance and effect is the corresponding effectivity, then afford and effect are reciprocal dispositions; therefore, there exists a causally equivalent sum afford/effect. This leads to a proposal slightly simpler than Turvey’s, as it interprets the junction simply as a mereological sum, but retains its important features: following our theory of reciprocal dispositions, afford/effect inheres in agent+env, neither afford nor effect does inhere in agent+env, and neither agent nor env is the bearer of afford/effect. We introduce a class Affordance/effectivity complex such that afford/effect is an instance of this class.
Turvey also states that “an effectivity, as the term suggests, is the causal propensity for an animal to effect or bring about a particular action, to manifest what is needed for [the junction of its effectivity and the environment’s affordance] to be realized” [p.179]. This is accounted for in our theory by the axiom (REAL), which implies that an affordance is realized by a process iff the corresponding effectivity is realized by the same process (and iff the corresponding affordance/effectivity complex is realized by the same process). For example, the class of Mary climbing up stairs0 (let us call it Mary climbing stairs0) is a realization of the corresponding affordance, effectivity and affordance/effectivity complex.
Similarly, by application of (TRIG), any trigger of an affordance, its associated effectivity or its associated affordance/effectivity complex is a trigger of the two others. For example, the class of Mary positioning her feet on stairs0’s surface and contracting her muscles in the adequate way (let us call it a climbing effort by Mary on stairs0, or Mary's stairs-climbing situation on stairs0) is a trigger of the corresponding affordance, effectivity and affordance/effectivity complex (see Figure 1 below).
To illustrate further, consider another example, namely the affordance of gap0 enabling John to hide (that is, not to be seen from some positions). This affordance is a disposition of gap0 that can be triggered by John being into gap0, and realized by John not being seen from those positions; and its reciprocal effectivity is a disposition borne by John that can be triggered and realized by the same respective processes.
Our proposal is deeply rooted in Turvey’s dispositional account of affordance, which has
been nonetheless subject to criticism. According to Şahin et al. [
The agent perspective takes affordances to residing within the agent interacting in the
environment through his own behaviors. For instance, Stoffregen [
We contend that the agent perspective on affordance would be interpretable in terms of the affordance/effectivity complex inhering in the agent-object(s) mereological sum, which grounds the affordance disposition(s) of the object(s) and the effectivity disposition of the agent. Although we formalize affordance as inhering in the environment, and effectivity as inhering in the agent, those dispositions have an external basis – and this form of existential dependence is in line with Stoffregen’s and Chemero’s above-mentioned positions.
The observer perspective on affordance is “used when the interaction of an agent with
the environment is observed by a third party” and “one must also have the capability of
taking the observer perspective when perceiving affordances, at least for the agents of
the same species as the observer” [25, p.14]. We would prefer to hold that this view
pertains to epistemology of affordance rather than ontology of affordance. It is
nonetheless a noteworthy inquiry to take a dispositional look at the observer aspect partly
because of its relevance to the application of the affordance concept, e.g., to robotics [
One of the most natural extensions of our dispositional approach to the observer perspective would be arguably to think of the observer conception of affordance (which consists in “the capability of taking the observer perspective”) as the disposition of the agent-object(s)-observer system (i.e. the system whose components are an agent, some object(s), and an observer) composed by the affordance disposition(s) of the object(s), the effectivity disposition of the agent, and the observation capability disposition of an observer. A formal representation of this disposition could be built out within our ontological framework previously given.
Quite importantly, this model assumes that a capability is a subtype of a disposition.
We find this premise plausible, although it is difficult to define explicitly a capability
(see e.g., [
Our formalization raises a few issues that could be discussed in future works. First, our
ontology introduces the mereological sum agent+env as the bearer of the
affordance/effectivity complex, but refrains from speaking of the ‘system’ composed by
agent and env. As a matter of fact, it is not straightforward to ontologize the notion of
system (see e.g., [
Second, the notion of causally equivalent sum of two reciprocal dispositions can be compared to the notion of collective disposition, which is defined within the BFO framework as follows: “A disposition inhering in an object aggregate OA [the BFO category] 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” [8, p.410]. 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, for example [8, p.409]. However, the relation between an affordance and an effectivity on one side, and an affordance/effectivity complex on the other side, is importantly different from the relation between the individual dispositions to stand up and the disposition of the crowd to do the wave. In the latter case, the dispositions of each individual crowd’s member to stand exists independently of each other. On the opposite, if afford and effect are two reciprocal dispositions, afford exists only as long as effect exists, and vice-versa. Moreover, the afford/effect complex seems to be ontologically prior to the dispositions afford and effect; whereas the individual dispositions to stand up at the right time seem to be ontologically prior to the disposition of the crowd to do the wave.
Third, note that two reciprocal dispositions d1 and d2, as well as their causally
equivalent sum d3, have the same mereological sum of categorical basis and external
basis, namely q1+q2. One could wonder whether this (in conjunction with them having
the same class of triggers and the same class of realizations) would imply that d1, d2 and
d3 are, after all, identical – updating the identity criteria among dispositions suggested
by Barton et al. [
Fourth, we have seen that two reciprocal dispositions d1 and d2 are externalparticular-dependent. However, we can introduce related dispositions that are not so. For this, let us consider Q1 the universal of qualities that characterize a key that can open a lock similar to lock2, and Q2 the universal of qualities 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. Let us consider Key1 the class of keys which have a quality instance of Q1 (thus, key1 instance_of Key1) and Lock2 the class of locks that have a quality instance of Q2 (thus, lock2 instance_of Lock2). Then, we can introduce additional related 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. Similarly, d2 and d2’ are not identical: contrarily to d2, d2’ does not depend existentially on key1. That is, neither d1’ nor d2’ has any external basis: they are not external-particular-dependent.
This strategy can be adapted to affordances and effectivities, since we have defined
them as reciprocal dispositions. On top of defining the affordance provided by stairs0 to
Mary to climb it, we could define the affordance provided by stairs0 to the general class
Personc1 to climb it. Similarly, on top of defining the effectivity of Mary to climb stairs0,
we could define the effectivity of Mary to climb Stairsc2 in general (see Figure 2 below).
The former, more specific affordances and effectivities (let us call them
“individualdirected affordances and effectivities”) are in line with Turvey’s analysis of affordances
(as they depend existentially from each other), and seem to be useful when studying a
limited system (such as the Mary/stairs0 system); the latter (let us call them
“familydirected affordances and effectivities”) are useful when studying a wider system - such
as the system composed by many agents and many stairs. We leave open here the
question of whether ecological psychology should accept entities such as
individualdirected affordances. On one hand, such entities might appear to have undesirable
characteristics, namely being subject to Cambridge change. On the other hand,
experiments such as Warren’s stair-climbing experiments [
In summary, we have developed a formal characterization of affordance as a disposition by leveraging recent formal-ontological findings on dispositions. We have also discussed the way other perspectives on affordance could be ontologized along dispositional lines, and how individual-directed affordances could be complemented by family-directed affordances. This work constitutes the initial step towards the formalization of an ontological module for generic affordance representation.
In the future we will be able to proceed along at least three major lines of research.
First, our logical specification of affordance will be richer as our formal understanding
of disposition becomes deeper. In particular, a rigorous formalization of the relationship
between dispositions and modality [
Second, the interrelationship between agents and the environment would be
incompletely accounted for unless we take into consideration not only the capability of
the environment to act on agents but also agents’ abilities to interact with the
environment, the former and the latter being respectively captured foundationally by the
theories of affordance and image schema [37, Section 2]. Image schemas are, roughly,
schematic prelinguistic patterns of cognition that are learnt during infancy: for example,
repetitive visual experiences of plates placed on tables form the image schema of
“support”. Our approach should be thus supplemented by a dispositional interpretation
of image schema for a long-term goal to furnish a full-fledged dispositional ontology of
agency, cognition, perception, and action. For instance, Galton’s [
Third and relatedly, a strong correlation between affordance and learning/creativity
is well worth pursuing. It has been traditionally worried (as in [
AB acknowledges financial support by the CIHR-funded Quebec SPOR Support Unit. The authors thank Barry Smith and Olivier Grenier for helpful feedback on this paper.