The Capability-affordance Model

A Method for Analysis and Modelling of Capabilities and Affordances

Vaughan Michell

Informatics Research Centre, Henley Business School, University of Reading, U.K.

v.a.michell@reading.ac.uk

Keywords: Capability, Affordance, Active Resources, Driving Resources, Passive Resources, Affordance Mechanism,

Affordance Path, Affordance Chain, Critical Affordance Factor, Affordance Efficiency, Affordance

Effectiveness, Affordance Quality.

Abstract: This paper builds on an earlier paper modelling business capabilities as a function of resources and process

to support enterprise architecture decision making. This paper develops the earlier capability model by using

a realist perspective to apply the theory of affordances and the Z specification language to show how

capabilities and their actualisation can be modelled as a tuple or set of resource affordance mechanisms

(AM) and affordance paths AP subject to critical affordance factors. The paper identifies and develops the

concept of objective and subjective affordances and shows how these relate to the capability resource

model. We identify an affordance chain by which affordances work together to create a capability. We

define the affordance modelling notation AMN as a method of representing the affordances in a system of

interacting resources. A medical case study (based on interviews at a local hospital) is used to show how

capabilities can be identified and modelled using the theory of affordances. We also propose a model of

affordance efficiency, effectiveness and quality that enables the performance of a capability and its

constituent affordances to be measured and modelled.

1 INTRODUCTION

The performance of a business enterprise has

become increasingly important, especially in

recessionary times. The term capability has been

widely used in enterprise architecture and other

business as a concept describing the ability of a set

of business resources to perform, but it is difficult to

pin down and measure (Michell, 2011; Curtis et al,

1995). Analysis of capability has been mainly at

high level (Grant, 1991; Hafeez et al, 2002; Josey et

al, 2009; Merrifield et al, 2008; Beimborn et al,

2005). Without a more reproducible model of

capability it is difficult to consistently understand

existing business capabilities, or to use the concept

to measure the relative performance of the various

resources and business structures. This makes it

difficult for an enterprise to make critical resource

investment and divestment decisions and to

understand and develop core competences that are

vital to maintain and grow competitive advantage

(Liu et al, 2011).

1.1 Capability

An earlier paper (Michell, 2011) sought to reduce

this gap by building on resource theory to identify a

definition of the capability of business resources of

an enterprise for use in enterprise architecture. The

following section re-iterates and develops the

definitions using and adapting Luck and d’Inverno’s

work on agent frameworks and Z Notation (Luck

and d’Inverno, 2001). We defined the business

environment E to comprise a set of objects we called

business resources R

, where i= 1-n:

Environment E = {resources R

Env = =

Resource

Each resource is what Luck et al call an object.

Hence we use the term object resource. The set of

object resources {R

} have what Ortman and Kuhn

(Ortmann and Kuhn, 2010) call qualities q that can

be divided into perceivable features and facts about

the object e.g. size, weight, chemical composition

etc., what Luck calls ‘a collection of attributes‘.

Another class of quality is what Luck calls

capability and Ortman calls affordance. We will

Michell V.

The Capability-affordance ModelA Method for Analysis and Modelling of Capabilities and Affordances.

DOI: 10.5220/0004461200600071

In Proceedings of the Second International Symposium on Business Modeling and Software Design (BMSD 2012), pages 60-71

ISBN: 978-989-8565-26-6

discuss the difference and their relationship later in

the paper.

We identified agents as either human intelligent

or artificially intelligent. We now extend this by

defining a human agent by combining the artificial

intelligence definition (Stoytchev, 2005) with Luck

and d’Inverno’s definition to give: A human or

artificially intelligent agent is a resource object that

can perceive its own environment through sensors

and acts on the environment according to their self-

motivations through effectors.

We identified passive resources as resources

requiring other agents to realise their capability ie

they are inert and not capable of their own motion or

change of state which relates to Luck’s lower level

definition of an object (Luck and d’Inverno, 2001).

We identified the concept of a driving resource in a

process to refer to object resources actively enabling

and driving a business transformation compared

with those (objects) passively used in the

transformation involved in a business process

(Michell, 2011). Driving resources in a business

process are autonomous agents (human/artificial)

controlling a range of transformations. Our scope

focuses on business activities where all the entities

in a business environment are object resources to be

used by a business enterprise. We defined capability

as: a property of a resource (tangible or intangible)

that has a potential for action or interaction that

produces value v for a customer via a

transformation process that involves the interaction

of the resource with other resources (Michell, 2011).

We use Luck’s definition of action as ‘a discrete

event that can change the state of an environment’

(Luck and d’Inverno, 2001). The tangible and

intangible resources in a business environment

undergo transformations and a change of state as a

result of an action of one resource interacting with

another. Each of these resources has a capability of

adding benefit of a specific value dependent on what

resource and process is used to execute the

capability i.e. Cv (capability of value V) = f

(resource, process P). We adapt Ortman and Kuhn’s

definition of value, to business value is the result of

any action that is of benefit to the business/client

(Ortmann and Kuhn, 2002). The Capability Cv

results from transformation interactions between two

or more resources that increases the business value

of the transformed resource (with respect to a

business client), i.e. the capability process contains

value transformations as defined by Weigand et al

(Weigand et al, 2006).

Cv = f (resource interaction, process of

interaction).

At the detail level each driving agent resource in

the sequence of transformations will be driven by

what Luck et al call motivations to achieve an

outcome or goal state G (Luck and d’Inverno, 2001),

which the transformation aims to achieve. We can

say that this goal state has attributes and a value to

the driving resource that is greater than the value

before the transformation. Using Z notation we can

say a resource R is transformed between a state a

and a’ such that actions are an effect on the

environment that result in a partial change in the

environment. We identified the process as a

sequence of actions. A process is what Luck refers

to as a total plan where Totalplan ==seq Action. To

develop the resource capability model we need to

use a structured method that enables an action level

perspective of capability as the interaction between

object resources.

1.2 Affordances

Gibson (Gibson, 1979) defined the term affordance

based on the root ‘phenomenon in gestalt

psychology (cited in (You and Chen, 2003)).

Gibson’s ecological approach saw ‘affordance as an

invariant combination of properties of substance and

surface taken with reference to an animal’ and ‘what

the environment offers and animal or intelligent

agent’. The theory of affordance provides a

perspective on the interaction of objects in an

environment that supports the capability approach.

Stamper (Stamper & Liu, 1994) expanded the

concept of affordances using behavioural norm

concepts into organisational semiotics and the idea

of affordance relating to the invariant behaviour of

both physical objects and intangible entities such as

social behaviours and concept models such as

ontology. Norman (Norman, 2004) refers to the term

‘perceived affordance’ for the concepts to describe

the interaction of objects with people and design

implications of man-made objects such as handles

optimised for pulling via a gripping section or plates

for pushing (Gaver, 1991). Norman sees affordances

as ‘referring to both potential and actual properties

of a designed device’. You and Chen identified the

difference between the semantics of design resource

objects and affordance theory (You and Chen,

2003). Ortman and Kuhn (Ortmann and Kuhn, 2010)

see affordances as one part of a set of qualities of an

object which separately include physical qualities or

facts about the objects such as size, temperature etc.

Turvey (Turvey, 1992) developed a mathematical

model of affordances as a property of a pair of

things e.g. object and agent where the affordance is

The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances

wholly dependent on the nature of the system of

interaction. Unlike physical qualities of an object

resource, an affordance is a property of the

interacting object resource systems manifested only

when they are interacting. Turvey’s model highlights

the criticality of the interaction between the two

object resources. This suggests we should really

refer to the term ‘affordance pair’ as the affordance

interaction property of two systems. Using Turvey’s

notation and the capability notation from the

previous paper an affordance between two resources

and R

, where R

is the passive resource with

property p and R

is an active agent resource with

property a can be represents as Af

. Af

is a tuple

of a passive resource and a driving agent and

represents the interface interaction or affordance of

the pair of object resources. This interaction

property is different from the properties of the

separate object resource systems. The affordance Af

is represented as an ordered pair. However, in this

paper we use the rule that the active or driving

resource should precede the passive resource

undergoing transformation (in cases where this is

perceptible), in this case a human agent based on

Turvey’s order in the stair example. We use the

notation: Af

= f(R

). However, there is a

dichotomy in views of affordance as Gibson

(Gibson, 1979) reminds us that an affordances is at

once both an objective property of an object

independent of perception and a subjective property

depending on the perception of the viewer. Our

capability definition is a function of the resource

objects and of the actions (process) by which the

resources interact and affordance theory relates to

the mechanism of the resource interaction. This

echoes Montesano et al’s view of affordances

‘capture the essential world and object properties, in

terms of the actions the agent is able to perform’

(Montesano et al, 2007). We adopt a realist

perspective with physical, cognitive and in particular

geographical reality relating to Gibson’s ecological

affordance view (Smith and Mark, 1998). We use

the theory of affordances and Z notation as a formal

language and frame of reference to represent the

capability-affordance model, focusing mainly on

physical affordances. In the following we attempt to

discuss and relate these two views and show the

relationship between capability and affordance.

2 OBJECTIVE AND SUBJECTIVE

AFFORDANCES

This section focuses on objective and subjective

affordances, as already mentioned.

2.1 Objective Affordances (OA)

Affordances that exist independent of perception are

inherent objective or ‘passive ‘structural properties

of the environment or object resource. For example a

solid floor objectively and passively affords support

of objects placed on it vs. the perceptive view of

affordance which relies on an agent identifying how

an object resource could be used. We suggest these

passive objective affordances (OA) are what keep

object resources in an unchanging, ie motionless

state of equilibrium. Also these affordances are not

perceptions or possibilities of what might happen –

the possibility has already happened and we are

observing executed affordances. The interface

relationship has been ‘actualised’ and the affordance

is acting in a state of equilibrium. Using Luck’s state

approach and Ortman and Kuhn’s quality approach

we can say that objective affordances relate to the

qualities of a passive resource in stable equilibrium

at a externally perceived level, i.e. we exclude

semiotics at a microscopic level as Noth’s view

(Noth, 1998) to avoid problems with motions of

microscopic organisms etc. We therefore suggest a

resource has a set of state determining qualities that

are required to be balanced in order to execute a

passive objective affordance. This would comprise

for example the force experienced by an object, its

spatial position and other quality attributes.

Objective affordance then relates to actual physical

qualities or properties that relate to the natural

behaviour of the object resource such for example

the laws of natural science such as physics

(Newton’s laws) chemical and biological laws etc.

The passive objective affordance is a stable state

where:

 Transformation forces on the object are

balanced

 The object’s special position is unchanging

 The object’s attributes are not changing

(chemical composition, dimensions etc.)

In summary the affordance transformation

mechanism in objective affordances is in a state of

stable passive equilibrium. An example is the weight

of a cup due to gravity is balanced by the structural

strength and reactive force (due to Newton’s Third

Law) of the surface on which the cup sits. The

Second International Symposium on Business Modeling and Software Design

equilibrium is stable as the potential transformation

mechanism e.g. the forces are in balance and the cup

resource object is a passive resource and therefore

possesses no means of motive force or

transformation mechanism capability of its own. We

can say that the interface mechanism between the

two resources; cup and table is stable and has no

active transformation mechanism. This suggests that

affordance depends on the mechanism of

transformation at the interface of the affordance pair.

In this case the affordance interface mechanism is

the force of gravity modelled by Newtonian

mechanics i.e. F=ma to stably maintain the cup in

contact with the table. Objective passive affordance

relates to what Norman (Norman, 2004) calls the

intrinsic properties of things (Norman’s ‘actual

properties) and innate affordances. This passive

objective affordance exists without the need for

perception. This relates to Turvey’s (Turvey, 1992)

focus on an environments capability to support an

activity. Then Affordance = the disposition (of the

object) i.e. force balance on table. Effectivity = the

complement of the disposition i.e. cup supported as

a result of the transformation mechanism being

achieved ie force balance. This equilibrium state of

object resources continues unless acted upon by an

external force (e.g. Newton’s First Law) which

brings us to subjective affordances.

2.2 Subjective Affordances (SA) and

Perceived Actions

Ortmann and Kuhn suggest ‘Perceiving affordances

generates possibilities for action.’ (Ortmann and

Kuhn, 2010). We suggest that subjective affordances

(SA) depend on perceived actions. This uses the

‘perceived design affordance’ (Norman, DA14) that

relates to users understanding of the possible ways

(affordances) of using designed features in designed

objects. Our term refers to active resources such as a

driving resource i.e. an agent intelligently perceives

the affordance or possibility for using a resource

object to make a substantive transformation and has

an intention to use it. We include the term action

here as the intention is to do physical substantive

work, and we us this term to differentiate from non-

substantive actions relating to knowledge and

semiosis. We also include the term subjective as it

depends on the driving resource’s goals and

motivations in the intended action and also critically

on the selection of the path of action or process from

our earlier definition. This relates to Gibson and

Uexkull seeing affordances as perciptibles (Ortmann

and Kuhn, 2010). It is these perceived ‘action

affordances’ that relate to planned actions in

business processes, activities or human visions and

conceptual models of possibilities for action.

Subjective affordance depends on an agent’s

perception as to how the properties or qualities of

the object can be envisaged to be used to achieve a

goal. The intention or goal of the outcome must

complement the affordance (Ortmann and Kuhn,

2010). The goal; also helps a) to define a set of best

action paths or processes that could be used and b)

to define the value or client benefit of the result

expected to be achieved on completion of the action.

However, the affordance depends on the interface

between an affording object and the driving agent

that is attempting to use it. In its simplest form

active affordance is the property of interaction of

two entities or systems that enable an action to

achieve a goal or transformation. The affordance

relates to a mechanism for a potential action

achieved by a transformation mechanism that

changes an object resource state from state a to a’

in Z notation.

 This may be physical e.g. a force form an agent

(active resource) sliding a cup between two

positions on a table i.e. cup-table affordance

pair affords sliding

 This may be chemical e.g. sugar dissolves in

water i.e. sugar-water affordance pair affords

dissolving due to chemical forces.

2.3 Objective Affordance – A

Multiplicity of Options

Any resource in a business environment is a

collection of capability options or opportunities or

affordances which depend on how the resource is

related to another resource and what affordance

mechanism is to be employed to achieve the state

transformation and meet the goal. For example a

simple passive resource such as a brick can be used

as a doorstop (weight affordance mechanism Af

), as

a missile (kinematic mechanism of a thrown brick

affordance Af

), as a structural support component

in a wall (rigidity and bonding affordance

mechanism Af

i.e. R -= f {Af

}

This type of affordance depends on identifying

an object’s potential for action when an active agent

or driving resource can visualise the way in which

the object can be used in conjunction with their end

effectors and senses. Turvey (Turvey, 1992) in his

nest building argument provides support for the

driving and passive resource view (Michell, 2011) in

The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances

his view of disposition and complement by

differentiating between the properties of an animal

(or agent) affordance which seeks to identify the

affordance properties of the environment i.e. how

the resources can be used by the person, (i.e. via

manipulation, construction, imagination etc.). This

relates to Turvey’s focus on the animal’s capability

to perform an action. So, effectivity equals the

disposition i.e. the effectiveness of the

transformation mechanism in meeting the

transformation goal (to be discussed later). And

affordance equals the capability of the

transformation mechanism necessary to achieve the

goal. In our capability terms the agent driving

resource in a process seeks to identify the

disposition of the resources (objective affordance) to

achieve the transformation action required by the

process.

2.4 The Relationship between

Objective and Subjective

Affordances

In summary, objective affordances refer to executed

and operational affordances ie an on-going system

interface relationship where the mechanism of

transformation becomes an equilibrium mechanism

and the path is completed and meets the goal eg

affording structural support. In contrast the

subjective affordance has to be perceived or planned

and therefore the mechanism and path may change

and so may the outcome or actualisation and the goal

which is dependent on both of these as below.

Objective

affordances

Subjective

affordances

• Affordance is actualised

• Transformation mechanism is active

• Action path is actualised

Substantive

Affordance

• Affordance is perceived

• Transformation mechanism is

potential

• Action path is potential

Figure 1: Objective/Subjective Affordance Types.

2.5 Subjective Affordances and Action

Paths

However, a subjective affordance does not just

depend on the transformation mechanism, it also

depends on the way or path taken to actualise or

execute the affordance. Consider the often quoted

example of ‘the cup affords drinking’. It does only

if a) the cup is grasped firmly without obscuring the

opening, b) if the cup is brought to an animal’s

mouth by an action that changes the position of the

cup to the proximity of the mouth, c) it is tilted to

enable gravity to act on the fluid and or the animal

sucks to aid the fluid transfer. We will explore this

issue of path in terms of our capability model.

3 MODELLING AFFORDANCES

3.1 Affordance Modelling Notation

(AMN)

In reality, as we have seen, capability rarely

comprises one affordance, but depends on multiple

affordances. We will use a medical example of a

capability ‘to anaesthetise a patient’ to explore the

relationship between capability and affordance. The

goal is to ensure the patient has a controlled

unconscious state, the value being that a medical

intervention can be performed without adverse

reactions (e.g. pain, movement) from a normally

conscious patient. For succinctness we will consider

a sub-capability a single action of administering a

medical injection. We will explore the interaction

between the anaesthetist, the syringe and the patient.

Using our capability terminology (Michell, 2011)

the anaesthetist is the active agent driving a passive

resource (the syringe) to execute the capability C

injecting an anaesthetic drug into a patient via a

process/action P

that results in the value of ‘patient

anaesthetised and can be safely operated on’. In the

diagram we denote the affordance by the term A

where A is the affordance and x and y refer to the

notation for the two elements in the affordance pair.

We use an underline notation to refer to the fact that

an affordance relates to a vector dynamic

transforming action or a static force balance and

hence has magnitude and direction. We use a line

terminated by balls in the shape of a dumb bell with

each ball resting of the relevant element or

component to show the relationship between the two

components of the affordance system. The syringe is

an example of a designed device (Brown and

Blessing, 2005) and can be considered as a system

comprising 3 components (excluding cap) a plunger,

body and needle which fit together as a passive

system of affordances as in the figure below:

Second International Symposium on Business Modeling and Software Design

syringe

Body b

syringe plunger p

Anaestheti

Fluid f

syringe needle n

Apb

Ahp

Ans

Afb

Afn

Anaesthetists hand h

Figure 2: Syringe Affordance Pairs.

3.2 The Affordance Chain (AC) and

Objective Affordances

Maier and Fadel identified that multiple affordances

can be associated with a particular subsystem (Maier

and Fadel, 2006). Thus the affordance of the syringe

is a combination of the affordance of the component

subsystems comprising the syringe i.e. Af (passive)

= f{Af

} i.e. the passive affordances of the syringe

relate to the mechanical structure and engineering

mechanics of the syringe in terms of physical

science e.g. Newton’s three laws. Reviewing the

capability model we can see that there are a number

of passive objective affordances. The Plunger-Body

Affordance – A

ensures the plunger is retained in

the barrel and slides easily up and down it by the

affordance pair predicated on the fact that the

plunger is designed to interface with the barrel and

has only one degree of freedom in an axial direction.

The affordance mechanism AM depends on friction

and the affordance path is the axial plunger motion.

In the Hand-Plunger affordance A

, the plunger has

a tube (with a seal) and top to it which supports the

affordance of ‘holding’ the top of plunger in order to

exert downward force (A

). This downward force

acts on any fluid contained by the syringe body

). This affordance (affords force transmission to

fluid) is dependent on the properties of interaction of

the plunger and body. The plunger must slide and

be a secure fit vs. body, must be made out of

materials not affected by the fluid to be injected etc.

The act of compressing an incompressible fluid

forces the fluid out through needle via an affordance

i.e. the needle – fluid affordance. An affordance

property of the needle (affords fluid transportation)

is that its hollow tubular nature directs the

anaesthetic and is chemically inert vs the fluid (a

potential negative affordance). A further affordance

exists between the needle tip and the patient’s skin

. The small surface area at the point enabling a

small force on the plunger to be safely and

effectively transmitted (due to mechanism of

mechanics i.e. pressure = force/area) as a large

pressure on the patient skin surface affords

penetration of the skin. However this of course is not

possible without the subjective affordances of the

active driving resource, the anaesthetist who is

responsible for identifying the target vein and

ensuring the tip of the needle enters a vein etc.

We define an affordance chain (AC) as a

connected and related set of affordances (and hence

affordance mechanisms) acting together as a system

at a point in time to achieve a specific goal of

enabling a new macro affordance mechanism, i.e.

the capability; Ca = AC = f (A

1,2

, A

2,3

, A

3,4

…A

i,j

)

where j= i+1 in a sequence from driver to final

resource. The idea of affordance chain allows us to

link the micro level affordances to the actions that

we define as part of the process referred to in our

definition of capability.

3.3 Subjective Systems of Affordances

There are three affordance pairs within the capability

that depend on the interaction of a passive with a

driving active resource. Aph

refers to affordance

between the plunger and the anaesthetist’s hand. By

definition of the syringe structure the plunger must

be depressed to work according to its design

parameters. The needle in contact with the patient’s

skin provides another affordance pair Ans

. One half

of the affordance pair comprising the anaesthetist

and patient can both act dynamically, deontically

and independently, unlike the passive syringe which

requires interaction with both these active resources,

one of which – the anaesthetist, is driving the

overall capability transformation. Another

affordance may be the anaesthetists second hand

resting on the patient to steady the needle – this is a

subjective agent affordance, but is not illustrated for

clarity. The third affordance pair Afp

is the

interaction between the anaesthetic fluid f and the

The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances

patient’s body physiology p. Here the driving

resource is the anaesthetic which has a sleep

inducing transformation mechanism, if of the right

fluid composition and if the delivery or action path –

i.e. into a vein is efficacious.

4 LINKING CAPABILITIES AND

AFFORDANCES

Based on the above discussion we can rewrite our

original capability model:

Capability = f (resource interaction, process of

interaction) i.e. any capability depends on a

transformation based on the affordance mechanism

and an affordance path, both of which are functions

of the set of resources {R

} needed to deliver the

capability: Capability = f (Affordance mechanism

AM(R

), Affordance path AP(R

)).

4.1 Affordance Mechanisms

The affordance mechanism should describe the

potential transformation mechanism at the interface

between the two object resource systems R

and R

and its properties that enable the transformation.

Mathematically the affordance mechanism is a

transfer function that describes the transformation in

terms of input resource properties and output

resource properties that defines the transfer between

input and output qualities. Affordances are

actualised by an affordance mechanism AM that

represents the transformation. Our affordance

mechanism transfer function relates to what Turvey

calls Function j in his crystal refraction (Turvey,

1992). He shows a light ray Z capable of refraction

(q) interacts with a crystal X capable of refracting

the ray (p) to give transformation of light ray to a

refracted or bent ray and a new position as a result of

a Function j – which we call the affordance

mechanism which can be represented as a

mathematical function or refraction equation.

However, this transformation is subject to critical

affordance factors f

being within the correct

window to enable the affordance to actualise or

manifest itself. Refraction is dependent on the

affordance path i.e. if light ray strikes crystal to

obliquely it will be reflected – dependent on the

critical affordance factor – the angle of the light with

respect to the normal to the crystal surface.

Kornhauser’s example (Turvey, 1992) of the

affordance actualisation of bird flying into a branch

depends on the affordance mechanism for

‘fracturing’. This is the law of conservation of

momentum that transfers the bird’s momentum to

the branch and results in an impact reaction -

impacts its organs. However the actualisation also

depends on the affordance path where exactly the

bird hits the branch, how far it travels and what

absorbs the momentum.

4.1.1 The Critical Affordance Factor

The bird’s velocity (assuming a straight unimpeded

flight) has a safety envelope that determines unsafe

momentum transfer. This should include a lower

level of speed to ensure the bird does not miss the

branch. The speed is the critical affordance factor in

the affordance mechanism that will determine the

safe actualisation of the affordance. In Warren’s

stair climbing the riser height is a critical affordance

factor (Warren, 1984).

4.2 Affordance Paths (AP)

The affordance path should describe how the

resource systems must be acted upon to be brought

together to enable the interface transformation

mechanism specified by the affordance to occur. It is

the path followed by actions to enable affordances.

An affordance path AP is the set of possible

actions that could be taken to enable the

affordance mechanisms to act and execute the

capability.

A capability affordance path is a process or

sequence of actions necessary to realise the

capability. It refers not just to a set of closed actions

(like the affordance chain), but a process of

connected sequential actions that typically occur in a

business i.e. linked ordered but discrete actions as

part of a business activity. This will comprise

physical or substantive actions e.g. the act of

injecting an anaesthetic as well as non substantive

i.e. semiological actions (Stamper et al, 2000) e.g.

verbal communication or inspection actions by the

anaesthetist as a control on the action of injecting

and assurance of the resulting value/goal

achievement. We can say:

 AP is set of actions within an ordered sequence;

 AP contains actions represented affordance

chains;

 AP contains semiological actions.

Affordance path = ∑ substantive affordance

chains + semiological affordance actions

The Affordance path also results in a change of

the variables AP = f U a ´a’

Second International Symposium on Business Modeling and Software Design

This relates to Luck and d’Inverno’s total plan.

I.e. Affordance Path AP =Total plan = seq Action

Note affordance paths P relate to Brown et al’s

(Brown and Blessing, 2005) ‘operations’ to preserve

the link to capability. The anaesthetist has an almost

infinite range of possible affordance paths. Consider

the ways in which the substantive action of injection

can be accomplished ie he can hold the syringe with

one hand on the barrel and simultaneously resting on

the patient to steady it and the other on the plunger.

We can simply prod the patient with the syringe etc.

The syringe has 1 degree of mechanical freedom –

the plunger slides along the axis to afford the

delivery of the fluid/anaesthetic. The passive

structural affordances (A

, A

) at once constrain

the motion and also effect the delivery of the

capability value i.e. injecting the anaesthetic into the

patient. The quality of the action path chosen will

impact the efficacy of the affordance mechanism and

determine how well the capability transformation is

achieved. That is C = f (AM,AP) where AP is the

set of substantive and semiological actions as shown

in Figure 3.

CAPABILITY

AFFORDANCE

MECHANISM (AM)

Critical affordance factor

AFFORDANCE

PATH (AP)

AFFORDANCE

many

1:1

many

1:1

Figure 3: Affordance Mechanism and Path.

5 CAPABILITY-AFFORDANCES:

A MEDICAL CASE STUDY

5.1 Drug Injection Capability

Based on structured interviews conducted at a health

trust hospital (see acknowledgements) the following

analysis was developed. The Capability C

injecting an anaesthetic drug into a patient via a

process/action P

results in the value v of ‘patient

anaesthetised and can be safely operated on’.

Capability = f (resource affordance, process/actions

of executing the affordance) = f (adding business

value). But this capability results from four

interacting systems, the anaesthetist, the anaesthetic

fluid, the syringe and the patient. The syringe as a

designed object resource can be further decomposed

into its active components. The syringe is a set of

interacting passive objective affordances where the

laws of physics hold the assembled component

affordances together in a state of equilibrium (ie

objective affordance as we have seen). At a more

macro or capability model level of what we can

perceive, we can say; Capability of anaesthetising a

patient = f {resource} = f (A-anaesthetist, S-syringe,

F-anaesthetic, P-patient). The capability is

dependent on a tuple or affordance chain by which

the anaesthetist acts on the syringe which in turn acts

on the fluid which in turn acts on the patient through

a number of transformation mechanisms. It also

relates to further affordance paths related to the

semiological affordances involved in inspecting the

patient and controlling the syringe action. The

syringe affordance chain can be decomposed into its

mechanisms and actions as seen in Figure 4.

5.2 Affordance Path & Mode of Action

The syringe tool has a designed way of being used –

ie a set of preferred potential affordance paths. The

syringe is a passive, but designed resource or a

device Ds and must be guided by the surgeon in a

specific designed way, at a certain angle to achieve

results to meet the desired goal. This relates to

refers to Chandrasekaran and Josephson’s the mode

M(Ds,E) (Chandrasekaran and Josephson, 2000) of

deployment of the syringe device. The mode may

come from tacit best practice knowledge or

following procedures or documents defining usage

procedures. For example, the mode of holding the

syringe and injecting, the mode of the anaesthetic

etc. Hence the mode refers to an optimum

affordance path for the affordance chain ACs of the

syringe: Mode M (Ds, E)= optimum f(affordance

paths P

-P

OR actions mentioned earlier). But the

optimum mode is achieved by the Anaesthetist’s

sensor affordances (sight/touch etc) and his tacit

knowledge/conceptual model of the environment.

The mode defines certain action behaviours to

ensure the affordance mechanism is optimised eg:

ensure syringe is in the correct location to meet a

vein, it doesn’t slip (negative affordance) and it

reaches the correct depth to interact with the vein.

5.3 The Affordance Diagram - AMN

As affordances are pervasive we propose a simple

affordance modelling notation AMN to provide

The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances

Affordance

type

Affordance 

Ref.

AffordanceDescription AffordanceMechanism(AM) AffordancePath(AP) Variableschanged Criticalaffordance

factorfa

dynamic Ahp

plunger affords pushing and grasping apply force Fhp on plunger acting along axis

of plunger

move plunger to end of

travel (eg1 cm)

plunger location relative

to body

Fhp, f1 <Fhp<f2

sufficient to

smoothly move

plunger& overcome

friction

dynamic Apb

Affords sliding and force transmission frictional sliding force of plunger seal on

syringe body

slider slides 1cm bottom of body axially to

end of travel

plunger travel to

limit of body l

dynamic Afb

Affords containment and force

transmission

fluid force containment and expansion

towards needle tube

fluid moves down body fluid moves from body to

needle

bursting pressure of

plunger and tube

static Afn

Affords fluid path transmission fluid force expansion towards needle

tip/skin

fluid moves down

needle tube

pressure on fluid bursting pressure of

needle tube

static Ans

affords skin penetration pressure = force/area at the tip, where

force Fns achieves steady penetration

needle penetrates skin

to a depth d

skin penetrated force magnitude Fns,

f1 <Fns<f2

dynamic Afp

Affords anaesthesia (anaesthetic body

interface)

induced sleep via chemical interaction

between anaesthetic and nerve/brain

centres

anaesthetic induced

sleep

conscious => unconsci ous anaesthetic reaction

kinetic factor tba

Figure 4: Anaesthetic Affordance Table.

Affordance Diagram for drug injection

Capability:

syringe

Ana esthetist

patient

Ana esthetist

patient

Anaes thetist

patient

Semiosis Action: identify

Vein and target site

Substantive Action:

inject anaesthetic

Semiosis Action:

Control inspection

Mode – specifies the metrics and states

of the action

Acti ve

resource

Passive

resource

Driving

Resource

Substantive Affordance system

Ie subs tantive force/a ction

transformation

Passive

resource

system

Semiological Affordance system

Solid resource

(no subsystems)

Eg a rock

Componentised

resource

(with subsystems)

Eg s yri nge

Key

Ana esthetist

patient

Substantive Action:

Swab site

Affordanc e path

Goal G : vein identified

Goal G : anaesthetic injected

Goal G : check anaesthetic

Inje cted c orrectl y

Goal G : patient wound

cleaned

Figure 5: Anaesthetic Affordance Diagram.

succinct visibility of the affordance and system

interactions. We use ellipses for active resources

and differentiate between driving agent resources as

a solid colour. Passive resources are represented as

boxes with designed passive resources made from

components identified by a shaded box. We also

distinguish between action affordances modelled

using the solid dumb-bell notation and intangible

semiosis driven affordances involving perception

e.g. anaesthetist identification of vein and control

actions via a dotted line as on Figure 5.

5.4 Mode Representation

The mode specifies the ideal and optimised metrics

and states of the action involving a designed object

resource, e.g. the syringe as represented by

procedures for using the syringe. Similar procedures

are expected to exist for the identification of the vein

and control inspection of the injection process,

although these may be in the form of tacit

knowledge and experience. The sequence of actions

and the mode actually used vs the optimised mode in

the procedures may vary greatly (and does in

practice between anaesthetists). This corresponds to

the anaesthetist using the syringe in a different way

and perhaps using different resource affordances,

which may not deliver the desired transformation

goal of anaesthetised patient and the value they

require to perform the medical intervention.

6 AFFORDANCE QUALITY,

EFFICIENCY AND

EFFECTIVENESS

This section explores how we can measure the

performance of the transformation and the execution

of the capability. The perceived benefit from the

Second International Symposium on Business Modeling and Software Design

executed affordance and the value added by the

executed capability, depend on the way the

affordance is executed by the driving agent, i.e. in

the process or action of the agent in following the

prescribed mode. In each case different parts of the

syringe and potentially different designed and non-

designed syringe properties may take part in the

action, even though the overall capability (to inject

an anaesthetic) remains the same. In the interests of

medical safety there are appropriate mode guidelines

to follow that describe the optimum mode. However

the decision on how the substantive action of

injection is executed and the affordance path that

makes up the capability is deontic – an obligation.

The set of actions are subject to variation depending

on the behaviour of the anaesthetist. This leads to

variation in the efficiency and effectiveness of the

capability of the anaesthetist which we will review

later.

6.1 Efficiency: Ey

An efficient action is an action (transformation) that

uses minimum energy compared with other actions

(Natarajan et al, 1996). E.g., if the drug is over

diluted it will be inefficient i.e. drug property has

insufficient strength to cause anaesthesia. We define

efficiency as the ratio of energy usefully employed

vs the total energy employed in an action (or

sequence of actions). Affordances which utilise the

designed mode M of the device, or that of a

specified action or behaviour would be expected to

be optimally efficient. In terms of affordances:

Negative affordances (e.g. errors) are ineffective i.e.

unplanned/unwanted . We can attribute a number (0-

1) as a measure of affordance efficiency to represent

how close to the design mode of the device or

procedure the affordance is. Then the efficiency of

an affordance chain is simply the scalar product of

the affordance efficiencies of the affordance pairs of

the parts of the chain. For the syringe example the

overall efficiency for any affordance chain 1-n is Ey

of Af (1-n) = E Af12* EAf23*EAf3n.

For the syringe example the efficiency of the

injection process depends on the efficiency of the

affordance chain between the anaesthetist and the

patient receiving the anaesthetic fluid. This involves

the respective affordance efficiency of the hand-

plunger, the plunger-body, the fluid-body, the fluid

needle, the needle-skin and the fluid- patient

affordance pairs. The overall efficiency of the chain

is the capability efficiency= ∑efficiency of

affordance chain actions + semiological action

Eci = EAhp*EApb*EAfb*EAfn*EAns*EAfp.

6.2 Effectiveness: Es

We can say that actions that meet requirements e.g.

process goals are effective (Muchiri et al, 2010).

Actions that don’t meet process goals are ineffective.

For example, if the wrong drug is used the injection

is ineffective. As we have seen, actions depend on

the affordance mechanism and the quality of the

affordance interface that enables the mechanism to

be executed. We can say: a)

negative affordances are

ineffective (unplanned/unwanted); b) positive

affordances not required for the goal are ineffective.

Effectiveness therefore refers to the proportion of

positive affordances vs total number of affordances

experienced. We define Effectiveness Esb as:

Effectiveness = ratio of effective actions/ (effective

+ ineffective actions)

To calculate the effectiveness of an affordance

chain we need to: a)

identify effective affordances

Afe and b) identify ineffective affordances Afi.

The Effectiveness of an affordance chain is:

Capability effectiveness = sum(Afe)/(sum Afe =

Afi).

6.3 Quality: Qas

The overall performance of any system s can be

defined as its qualify Qs. Quality relates to

performance to specifications. Optimal action

specifications relate to the mode of operation as we

have seen earlier. Quality also relates to performing

actions that meet the overall action or affordance

chain goals i.e. effectiveness

We therefore define quality of the affordance

system as as the scalar product of the efficiency and

effectiveness ratios ie Qas= Ey *Es. Hence the

quality of an affordance chain of i elements is the Qc

= ∑ Eyi*Esi.

6.4 Capability Quality, Efficiency,

Effectiveness

We note that the above discussion shows the quality,

efficiency, effectiveness of an affordance chain.

Affordance chains relate to composite actions where

all the resource objects are interacting. However,

our original process level definition of capability

refers to a sequence of actions. For example the

capability of the process anaesthetise patient will

include the inject patient action (the composite

affordance chain), but also other actions eg

communication and message passing between agents

and waiting periods where affordances are not

active. In this case The capability refers to the

The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances

affordance path and hence the overall capability

quality, efficiency and effectiveness will relate to the

affordance chain efficiencies.

7 SUMMARY AND

CONCLUSIONS

In this paper we have analysed the original resource

capability model in terms of affordance theory of

Gibson et al based on a realist approach and the use

of Z notation. We have shown that capability can be

modelled as a tuple of a set of resource affordance

mechanism and actions that are dependent on one or

more critical affordance factors and how these relate

to the work of Turvey and others. The paper has

identified and developed the concept of objective

and subjective affordances and showed how these

relate to the capability resource model and existing

theories. We identified an affordance chain of

subjective affordances by which affordances work

together to enable an action and an affordance path

that links action affordances to create a capability.

We introduced the affordance modelling notation as

a visual method of representing the affordances in a

system of interacting resources. A medical case

study was used to show how capabilities can be

identified and modelled using the theory of

affordances. We also proposed a model of

affordance efficiency, effectiveness and quality that

enables the performance of a capability and its

constituent affordances to be measured and

modelled.

7.1 Further Work

Further work is now needed to identify the

practicality of the approach and to test the method in

detail with larger capability sets and including more

semiological affordances. Also to provide a

complete worked example of affordance mechanism

and path and a measure of capability from the

system of affordances that constitute it.

ACKNOWLEDGEMENTS

The author would like to acknowledge the support of

the Royal Berkshire Foundation Trust Simulation

Centre for his Honorary Senior Lectureship in

Health Informatics. Also to acknowledge his

colleague Dr Debbie Rosenorn-Lanng Director of

the Simulation Centre for the opportunity to witness

and analyse medical procedures.

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The Capability-affordance Model - A Method for Analysis and Modelling of Capabilities and Affordances