Chapter 3 3 Conceptual Graphs and Cognitive Mapping 3.01 Introduction Chapter 2 provided initial evidence that conceptual graphs are a suitable knowledge-based decision support tool for strategic management accountants. This chapter starts to pursue a more substantial confirmation of conceptual graphs’ technical capability in the strategic analysis problem domain, by comparing them with the cognitive maps of Eden (1991). Eden’s mapping technique, which is a leading knowledge-based structured diagram technique for strategic planning, is based on the advanced ‘personal constructs’ methodology begun by Kelly (1955). The cognitive mapping technique both a) employs a highly structured approach, and b) is designed as a practical human expert end-user support tool. Given all the discussions so far, it thereby offers a valuable comparison with conceptual graphs. Should conceptual graphs sufficiently enrich Eden’s cognitive maps then the choice of conceptual graphs will be further strengthened accordingly. As its basis, the examination employs the realistic office location problem that Ackerman, Cropper, and Eden (1991) choose in highlighting the benefits of cognitive mapping. An analysis of the same problem is performed using conceptual graphs. 3.02 The Example Problem The example itself is as follows (Ackerman et al. 1991, page 41): “We need to decide on our accommodation arrangements for the York and Humberside region. We could centralise our service at Leeds or open local offices in various parts of the region. The level of service we might be able to provide could well be improved by local representation but we guess that administration costs would be higher and, in this case, it seems likely that running costs will be the most important factor in our decision. The office purchase costs in Hull and Sheffield might however be lower than in Leeds. Additionally we need to ensure uniformity in the treatment of clients in the region and this might be impaired by too much decentralization. However we are not sure how great this risk is in this case; experience of local offices in Plymouth, Taunton and Bath 64
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Chapter 3
3 Conceptual Graphs and Cognitive Mapping
3.01 Introduction
Chapter 2 provided initial evidence that conceptual graphs are a suitable
knowledge-based decision support tool for strategic management accountants.
This chapter starts to pursue a more substantial confirmation of conceptual
graphs’ technical capability in the strategic analysis problem domain, by
comparing them with the cognitive maps of Eden (1991). Eden’s mapping
technique, which is a leading knowledge-based structured diagram technique
for strategic planning, is based on the advanced ‘personal constructs’
methodology begun by Kelly (1955). The cognitive mapping technique both a)
employs a highly structured approach, and b) is designed as a practical human
expert end-user support tool. Given all the discussions so far, it thereby offers
a valuable comparison with conceptual graphs. Should conceptual graphs
sufficiently enrich Eden’s cognitive maps then the choice of conceptual
graphs will be further strengthened accordingly. As its basis, the examination
employs the realistic office location problem that Ackerman, Cropper, and
Eden (1991) choose in highlighting the benefits of cognitive mapping. An
analysis of the same problem is performed using conceptual graphs.
3.02 The Example Problem
The example itself is as follows (Ackerman et al. 1991, page 41):
“We need to decide on our accommodation arrangements for the York and Humberside
region. We could centralise our service at Leeds or open local offices in various parts of
the region. The level of service we might be able to provide could well be improved by
local representation but we guess that administration costs would be higher and, in this
case, it seems likely that running costs will be the most important factor in our decision.
The office purchase costs in Hull and Sheffield might however be lower than in Leeds.
Additionally we need to ensure uniformity in the treatment of clients in the region and
this might be impaired by too much decentralization. However we are not sure how
great this risk is in this case; experience of local offices in Plymouth, Taunton and Bath
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Chapter 3
in the South West1 may have something to teach us. Moreover current management
initiatives point us in the direction of greater delegation of authority.”
3.03 The Cognitive Map for the Example Problem
Ackerman et al. cognitively map the above problem and produce the diagram
in Figure 3.01 as a result. This figure illustrates two essential elements
underlying this cognitive mapping interpretation. Namely these elements are
‘concepts’ and ‘links’. Each concept is represented as one emergent ‘pole’,
which describes one side of the problem, and a ‘contrasting pole’ which is
Figure 3.01: Cognitive map for offices location problem(Source: Ackerman et al. 1991, page 47)
meant to focus the concept by a meaningful contrast to the first pole. Poles
may lead to other poles by means of directed links. All this is clarified further
by examining the map as it appears in COPE, which depicts these cognitive
1 The passage actually states ‘South East’ but this is a typographical error as confirmed by the
references to 'South West' later in the article.
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maps in computer software2. To begin with, the map’s concepts are
represented by the following table in COPE:
1 open local offices...centralise services at Leeds2 local representation...[not] local representation3 increased running costs...[not] increased running costs4 higher administration costs...[not] higher administration costs5 improve level of service...[not] improve level of service6 too much decentralisation...[not] too much decentralisation7 risk of impaired treatment of clients...ensure uniformity of treatment8 lack of understanding about risk...[not] lack of understanding about risk9 use experience of s w local offices...[not] use experience of s w local offices10 lower purchase costs of local offices...higher cost in Leeds11 greater delegation of authority...[not] greater delegation of authority12 follow current management initiatives...[not] follow current management initiatives
Note COPE adds a sequential number to signify each concept entered by the
user, and automatically adds the prefix ‘[not]’ to create a ‘default’ contrasting
pole for any concept where a contrasting pole was not entered. The links are
entered by taking the two appropriate concept numbers and placing a ‘+’
symbol between them. The concept before the symbol leads to the concept
placed after it. For example, ‘10+1’ shows that ‘lower purchase costs of
local offices’ leads to ‘open local offices’. This also stipulates the
contrasting pole ‘higher cost in Leeds’ leads to the contrasting pole
‘centralise services at Leeds’. The cognitive mapping methodology
also happens to stress that it is important the emergent pole should always
represent what the user can best identify with. However, this is likely to create
problems when it comes to making links as this constraint means poles may
lead to poles of the other kind. The ‘-’ symbol thus replaces the ‘+’ symbol to
combat this problem. This is illustrated by the following links table in COPE:
conforms to the type label ‘central office’ and ‘Hull, Sheffield and Harrogate’
conforms to ‘local offices’. Part ‘8(a) is merely a shortening of one of the
concept’s phrases. This graph could easily be refined further, as indeed may all
the graphs throughout the entire offices example, hence ‘8(a) may be viewed
as an example of an intermediate step in model development. The greater
degrees of refinement are demonstrated by ‘8(b), ‘8(c) and ‘8(d). In ‘8(b), ‘Leeds’
is an instance of a central office in that Leeds will have its own peculiarities
but shares the same characteristics as any central office in general. This would
permit inferences to be made about Leeds from both what is known about
central offices in general and Leeds in particular.
3.06 Generalising the Model
The above shows that a knowledge-base can be built up based on the
appropriate degree of generally applicable knowledge. This also prevents
4 See footnote 3.
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unnecessary duplication when the same knowledge applies to more than one
particular concept. The degree can be appreciated by developing the Leeds
example in a little more detail. It may be that certain things are applicable to
Leeds in its own right, Leeds as a Yorkshire central office, as a northern
central office, or an English central office as well as a central office. The same
principles apply to the local offices. Taking the central office case as
representative, the type hierarchy would then include (where subtype <
supertype):
central office < office.English central office < central office.Northern central office < English central office.Yorkshire central office < Northern central office.
The most specialised conformity for ‘Leeds’ is ‘Yorkshire central office’. This
means Leeds conforms to all of the above central offices, but not to say
‘Southern central office’ (Southern central office < English central
office). Thereby any inference in respect of Southern central offices would
not apply to Leeds but any for Yorkshire, Northern, central office and office
would.
The graphs in ‘8(c) and ‘8(d) concern the purchase costs of the offices.
Examining ‘8(c), the left graph shows that if a purchase cost is higher then it
cannot be lower and vice versa. The right graph shows that if one is false the
other is true. The coreferent link in both cases establishes that they refer to the
same cost. These graphs are therefore so general in nature that they can be
used beyond the offices example.
Turning to ‘8(d), these graphs imply that a central office is an office which has
a higher purchase cost whilst local offices are offices with a lower purchase
cost. Should ‘central office’ or ‘local offices’ dominate these graphs
respectively, the appropriate inference would be made accordingly. This is
demonstrated in Figure 3.09.
Conceptual graphs thereby also raise the user’s awareness through their
inherent structure: As the user refined the graphs so they become more and
more based on hierarchical type labels and specific instances within those
labels, the user would have to think about the appropriate degree of
relevance. The graphs as they currently stand apply to any local or general
office. Alternatively they may be written to infer about Yorkshire offices only,
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Chapter 3
in which case ‘central office’ and
‘local offices’ in the appropriate
dominated graphs would instead
read ‘Yorkshire central office’ and
‘Yorkshire local offices’
respectively.central office
office
characteristic
higher purchase cost
central office: Leeds
office: Leeds
characteristic
higher purchase cost
office: Leeds
characteristic
higher purchase cost
matches concepts in:
Yorkshire central office: Leeds
The graph:
giving:
resulting in:
Figure 3.09: An inference involvinghierarchical relationships and referents
From the limited information in
the Ackerman example it would
not be safe at this point, however,
to include the graphs ‘8(d) within
the knowledge-base. Therefore the
restricted forms shown in
Figure 8.10 are included in their
place. This figure prevents
deiteration and its consequent
assertion occurring unless the
referent is specifically ‘Leeds’ or
‘Hull Sheffield and Harrogate’
respectively.
3.07 Modelling the UndefinedPoles in ConceptualGraphs
Continuing further, the concepts
with undefined contrasting poles
can be modelled initially in
conceptual graphs as shown in
Figure 3.11. The concepts ‘greater
delegation of authority’ and ‘follow
current management initiatives’
are not included in this figure and
will be dealt with after the discussion on links below. Where the contrasting
pole is not defined on input, COPE creates it by prefixing the term ‘not’ to the
input emergent pole as stated earlier. As COPE embodies the present
cognitive mapping methodology, this step poses a question. That question
asks if this is most accurately replicated in conceptual graphs by taking the
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Chapter 3
input pole and encircle it with a negative context, as denoted in Figure 3.11.
An alternative might be to write, without using a negative context,
‘not emergent pole’ instead. The graphs would then be based on the form
given by Figure 3.12.
central office: Leeds
office: Leeds
characteristic
higher purchase cost
local offices: Hull, Sheffield and Harrogate
offices: Hull, Sheffield and Harrogate
characteristic
lower purchase cost
Figure 3.10: Restricted graph to account for lack of knowledge in existingproblem
Unlike their defined counterparts, the ‘false-asserts-true’ scenario can be seen
to be valid for undefined contrasting poles, hence the graph form in
Figure 3.13 would also need to be
added into the knowledge base for
each alternative. This reveals the
alternative is superfluous because
the term ‘emergent pole is false’
clearly equates to
‘not emergent pole is true’.
Another question is thus raised
asking if there is any need to
include such poles in conceptual
graphs anyway. For instance given
‘local representation’ was true
or false, this would merely assert
‘local representation’ is true
or false respectively. This tautology
shows such concepts in fact turn
out to be meaningless. Therefore
they can be excluded from the
conceptual graphs representation.
lack of understanding about risk
use local office experience
lack of understanding about risk
use local office experience
local representation local representation
improved service levelimproved service level
increased running costs
higher admin costs
increased running costs
higher admin costs
emergent pole emergent pole
General form:
Figure 3.11: Conceptual graphs forconcepts with undefined contrasting
poles
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Chapter 3
Figure 3.12:
not emergent poleemergent pole
Figure 3.13:
emergent pole not emergent pole
3.08 Modelling the Links in Conceptual Graphs
The cognitive map links may be modelled initially as implications in
conceptual graphs as shown in Figure 3.14. The nature of these graphs are
explained by Figure 3.15. As can be seen from these figures, without worrying
about the graphs affected by double negation for the moment, the ‘leads from’
pole becomes a concept which is enclosed in a negative context. This context
also encloses another negative context that encloses the concept of the ‘leads
to’ pole. The ‘negative’ link found in COPE becomes redundant because the
order in which the poles are drawn are irrelevant in conceptual graphs. The
user could still retain the visual order through arranging the shape of the
graphs according as to what, say, that user would like to see at the top or
bottom part of his or her graph drawings. The concept ‘use local office
experience’ has been refined to ‘use local office experience:#256’ as
it describes a particular office experience identified by the serial number
‘#256’. This number may be a reference to the relevant documentation on
this issue for example.
As for the double negated graphs, the effect in the case of the graphs
describing the false ‘local representation’, ‘increased running costs’,
and ‘too much decentralisation’ implications of ‘central office:
Leeds’ is they now appear to be like existing cognitive mapping concepts
instead of its links. Hence these graphs show there are links that emerge to be
additional contrasting poles. Conceptual graphs have yielded this fact
explicitly and drawn it to the user’s attention, whilst it remains unnecessarily
implicit and thereby easily undetected in the existing cognitive map.
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Chapter 3
local representation improved service level
increased running costs higher admin costs
lack of understanding about risk use local office experience: #256
improved service levellocal representation
local representationcentral office: Leeds
increased running costscentral office: Leeds
higher admin costsincreased running costs
central office: Leeds too much decentralisation
too much decentralisation
use local office experience: #256lack of understanding about risk
ensure uniformity of treatment
Figure 3.14: Conceptual graphs denotingthe links in the cognitive map
Y
YZ
X
General form of implication(illustrated by X asserts Y, not Y asserts not X):
Say X in fact is equal to not Z. This would result in:
Similarly, say Y was equal to not W. This would give: