Assessing Sowa's Conceptual Graphs for Effective Strategic Management Decisions, Based on a Comparative Study with Eden's Cognitive Mapping

Simon Polovina
School of Computing, Information Systems and Mathematics
South Bank University, London, UK


This paper examines the potential for Sowa's conceptual graphs to improve practical strategic management decision making in business activity, by a detailed comparison between conceptual graphs and Eden's already established strategic business-level cognitive mapping technique. An appropriate, contemporary and realistic example of an office relocation problem is used to explore the comparison, which reveals that conceptual graphs do indeed significantly enhance Eden's technique. The paper therefore calls for this avenue to be exploited further for the benefit of strategic decision making, given its highly qualitative nature resulting in it being most difficult-to-model aspect of business activity.

  1. Introduction
  2. The Example Problem
  3. The Cognitive Map for the Example Problem
  4. Modelling the Poles in Conceptual Graphs
  5. Refining the Graphs
  6. Generalising the Model
  7. Modelling the Undefined Poles in Conceptual Graphs
  8. Modelling the Links in Conceptual Graphs
  9. Modelling the Other Knowledge in the Example Problem
  10. Allowing Inferencing
  11. Comments On Cognitive Mapping in Conceptual Graphs
  12. Concluding Remarks
  13. References

1 Introduction

This paper examines the capability of conceptual graphs, as devised by Sowa and applied by Polovina, in practical business strategic management [1,2]. The paper attempts this by comparing conceptual graphs with the cognitive maps of Eden [3]. Eden's mapping technique, which is an established knowledge-based structured diagram technique for strategic planning, is based on the advanced personal constructs methodology begun by Kelly [4]. The cognitive mapping technique both a) employs a highly structured approach, and b) is designed as a practical human expert end-user support tool. Eden's cognitive maps thereby offer a valuable comparison with conceptual graphs. Should conceptual graphs sufficiently enrich cognitive maps then conceptual graphs can be implemented meaningfully to enhance business strategic decision making, especially given its highly qualitative nature resulting in it being most difficult-to-model aspect of business activity.

As its basis, the examination employs the realistic office location problem that Ackerman, Cropper, and Eden choose in highlighting the benefits of cognitive mapping [5]. An up to date discussion by Ackerman et al., employing the same example, can be found on the Web at An analysis of the same problem is performed using conceptual graphs.

2 The Example Problem

The example given by Ackerman et al. is as follows:

"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 in the South West may have something to teach us. Moreover current management initiatives point us in the direction of greater delegation of authority."

3 The Cognitive Map for the Example Problem

Ackerman et al. cognitively map the above problem resulting in Figure 1. This figure illustrates two essential elements underlying the 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 meant to focus the concept by a meaningful contrast to the first pole. Poles may lead to other poles by means of directed links.

Figure 1: Ackerman et. al.'s cognitive map for the offices location problem

This can be clarified further by examining the text of the map for the computer software package Decision Explorer which, as shown by the diagram of Figure 1 above, depicts these cognitive maps graphically (Decision Explorer runs on Windows 3.1, 95 or NT. More details about Decision Explorer can be found from the Web at, email or phone [+44] 0 141 552 3082). To begin with, the map's concepts can be represented by the following table:

1  open local offices...centralise services at Leeds
2  local representation...[not] local representation
3  increased running costs...[not] increased running costs
4  higher administration costs...[not] higher administration costs
5  improve level of service...[not] improve level of service
6  too much decentralisation...[not] too much decentralisation
7  risk of impaired treatment of clients...ensure uniformity of treatment
8  lack of understanding about risk...[not] lack of understanding about risk
9  use experience of s w local offices...[not] use experience of s w local offices
10 lower purchase costs of local offices...higher cost in Leeds
11 greater delegation of authority...[not] greater delegation of authority
12 follow current management initiatives...[not] follow current management initiatives
Note that a sequential number is usually added to signify each concept entered by the user. For any concept where a contrasting pole was not entered the term `[not]' is added to create a `default' contrasting pole. 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 confusion when it comes to making links as this consideration means an emergent pole may be required to lead to a contrasting pole and vice versa. The `-' symbol is thus added to the directional link to combat this problem.

Accordingly each directed link shows a pole to pole, and contrasting pole to contrasting pole, link. The added `-', or `negative' link, shows a pole to contrasting pole, and contrasting pole to pole, link. The negative link occurs where `use experience of s w local offices' leads to `[not] lack of understanding about risk', and `[not] use experience of s w local offices' to `lack of understanding about risk'. Another type of link, the `connotative' link, is employed when the user knows there is an insufficiently definable yet somehow valid connection between concepts. Such links would be shown as undirected links. The connotative link can be applied to the relationship between concepts `1' and `8' as overcoming `lack of understanding about risk' may lead to either operating centralised services or opening local offices. Both the negative link and the connotative link are also reflected in Figure 1.

The above problem is now explored using conceptual graphs. The conceptual graphs representation of the above problem is based on the same cognitive map as identified above. This approach should ensure a common comparative basis, yet highlight vividly any distinguishing features between the two representations.

4 Modelling the Poles in Conceptual Graphs

Starting with the poles themselves, they appear to fall into two categories. The first category has user-defined contrasting poles whilst the second's contrasting poles remain undefined.

Figure 2: The initial conceptual graphs for the defined contrasting poles

Concentrating on the defined concepts to begin with, these may be modelled initially by the conceptual graphs in Figure 2. In this figure the pair of poles become a conceptual graph by placing each pole into a separate conceptual graph concept and together surrounding them within a negative context. These negative contexts signify that whatever is contained within them, taken as a whole, is false. Therefore each graph provides contrast by stating that it is false that both poles can exist simultaneously. As elaborated below, if one of the concepts is true then the other becomes false.

Take the middle graph in Figure 2, which refers to the poles `centralise services at local offices', as a representative instance. Lets say we decide to see what happened if `centralise services at Leeds' was chosen. As a conceptual graph this could be shown initially as in Figure 3. This true graph dominates its matching concept inside the middle graph in Figure 2, hence this inside concept can be removed, or deiterated, to yield Figure 4.

Figure 3

Figure 4 shows that `open local offices' is false. This occurred because `centralise services at Leeds' is true. Should the decision be `open local offices' instead then `centralise services at Leeds' would be false accordingly.

Figure 4

The whole picture for this scenario is shown in Figure 5. Unlike the earlier cognitive map that only passively records the poles, a computer-based conceptual graph processor could make these new assertions automatically as the appropriate new graphs are added to its base of knowledge. The important repercussions of these inferences will become evident later.

Figure 5: `centralise services at Leeds' false when 'open local offices' is true

Note that the above `true-asserts-false' form does not assert one pole as true should the other be false. For example the poles `centralise services at Leeds' or `open local offices' cannot be asserted as true from their contrasting pole being false. To do this would require the additional `false-asserts-true' graph shown in Figure 6. In this figure there are nested negative contexts. Remember that in conceptual graphs, a whole negative context and its contents can also be deiterated provided it matches an appropriately dominating negative context and its contents.

This removal can be illustrated from the graph in Figure 4 (`open local offices' is false). This graph dominates the matching part in the false-asserts-true graph of Figure 6 because it is surrounded by a lesser number of negative contexts. Hence its matching graph can be removed from the latter figure to yield the result shown in Figure 7.

Figure 6

Figure 7

This result has left two negative contexts around `centralise services at Leeds'. These double negate to give the same graph as in Figure 3 (`centralise services at Leeds' is true).

In the present cognitive mapping technique the `false-asserts-true' aspect is insufficiently clear. The present approach may prefer the user to assume if one pole is false then the other is true, yet it is quite possible that the decision maker may for instance do nothing or decide to open mobile offices instead. In this case the above `false-asserts-true' graph would be incorrect. The bipolar nature of the present method cannot cope with this scenario. Even worse, it could provide a too narrow framework which stifles originality of thought: The model does not lend itself to decision makers realising other alternatives, such as mobile offices. In view of this deficiency, the `false-asserts-true' aspects cannot be transposed to the conceptual graph representation in a manner which guarantees validity.

5 Refining the Graphs

Moving on, it is possible to leave the conceptual graphs in this `true-asserts-false' two concept form and manipulate them as elementary propositional logic statements (The details of propositional logic and predicate logic can be found through any seminal text on logic such as Kowalski [6]. Sowa, in Appendix A.5: "Symbolic Logic", pages 384-391 also discusses these matters [1]). Indeed Ackerman et al. stress that the sentences should remain as they are because the decision maker can identify with what he or she has stated directly. With conceptual graphs the above concepts could be refined nonetheless to the more powerful predicate logic level thereby capturing more about the problem, yet arguably remain human expert readable. The refinement is demonstrated by the graphs shown in Figures 8(a) to 8(d), which refine the graphs in Figure 2.

Figure 8(a)

Figure 8(b)

Figure 8(c)

Figure 8(d)

Figures 8(a, b, c, d)
: Refined conceptual graphs

The graphs in Figure 8 now include relations, referents and coreferent links as well as essentially more proper hierarchical type labels. The left-hand graph inside the nested negative context of Figure 8(d) (or " `8(d) " for short) may be read as "The characteristic of an office is a higher purchase cost" for example. The referent `Leeds' 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.

6 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 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 9.

Figure 9: An inference involving hierarchical relationships and referents

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, in which case `central office' and `local offices' in the appropriate dominated graphs would instead read `Yorkshire central office' and `Yorkshire local offices' respectively.

7 Modelling the Undefined Poles in Conceptual Graphs

Continuing further, recall that where the contrasting pole is not defined on input, Decision Explorer creates it by prefixing the term `not' to the input emergent pole as stated earlier. The concepts with undefined contrasting poles could thus be modelled initially in conceptual graphs as given by Figure 10 (The concepts `greater delegation of authority' and `follow current management initiatives' however would not be modelled this way as explained later).

Figure 10: Conceptual graphs for concepts with undefined contrasting poles

On examining these graphs however, it rapidly emerges that there is no real need to include such poles as conceptual graphs at all. To illustrate, given `lack of understanding about risk' was true or false, this would merely assert `lack of understanding about risk' 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.

8 Modelling the Links in Conceptual Graphs

The cognitive map links may be modelled initially as implications in conceptual graphs as shown in Figure 11. The nature of these graphs is explained by Figure 12. 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.

Figure 11: Conceptual graphs denoting the links in the cognitive map

Figure 12: Modified implication in conceptual graphs

Note that the negative link found in Decision Explorer 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.

All the above of course highlights another question as to whether the present cognitive mapping technique should indicate that all default contrasting poles are accurate enough to attach other poles logically to it. There is the distinct possibility that such links could be erroneous, with the result of the user being mislead by the model.

For instance, picking up on the mobile office dimension discussed earlier, it seems that `local representation.[not] local representation' leads to `improve level of service.[not] improve level of service' respectively. However it may be possible to have `[not] local representation' and `improve level of service' through `use mobile offices'. It would then be false that `[not] local representation' implies `[not] improve level of service'.

9 Modelling the Other Knowledge in the Example Problem

The concept `use local office experience' has some background information relating to it about the source of that information from some actual offices in the South West. This may best be described by the graph in Figure 13, which can be added to the knowledge base and then called upon as necessary.

Figure 13

This leaves us with `greater delegation of authority', `follow current management initiatives' and the relationship between `lack of understanding about risk' and the choice of office.

The first two of these concepts are modelled by Figure 14 whilst the latter relationship is modelled by Figure 15, which describes the `lack of understanding about risk' relationship. Recall that, for Decision Explorer, the tacit `lack of understanding about risk' relationship in the cognitive map was refined into a connotative link, which the graph is intended to reflect. Once again these graphs can be called upon as knowledge about the problem is elicited.

Figure 14

Figure 15

10 Allowing Inferencing

Now the conceptual graphs knowledge-base can sensibly start to infer new knowledge. An example, revealing the direct links arising from the choice of office, is shown by Figure 16. In this figure there are coreferent links to concepts labelled as `t', which may best be thought of as `it' instead of the full concept's name, to aid readability by avoiding repetition. The `t' essentially equates to the conceptual graphs' universal supertype, but with an attached coreferent link that immediately specialises it.

Figure 16: Directly linked interrelationships surrounding choice of office

To illustrate, let us state that `central office: Leeds' is true. From Figure 16 we can see that this statement implies that `too much decentralisation' is false, thereby its contrasting pole, `ensure uniformity of treatment' becomes true (See Figure 11). This in turn causes `impaired client treatment risk' to be asserted as false (See Figure 8(a) ).

11 Comments On Cognitive Mapping in Conceptual Graphs

The following general points have emerged from remodelling the offices problem as conceptual graphs:
  1. Like the present cognitive mapping methodology, the concepts and relations in conceptual graphs can be based on a language that the decision maker identifies with. Conceptual graphs can also be arranged to retain the visual cues the end-user may require.
  2. Unlike present cognitive maps, conceptual graphs allow the further refinement of the problem through, say, the interrelation of generalised and specialised knowledge. Initial conceptual graph models may start by being a literal paradigm of cognitive maps at the existing level. Subsequently they may be refined by graphs which, as illustrated by the office purchase costs, break down these phrases along increasingly greater expressive dimensions.
  3. Through its bipolar limit, which conceptual graphs overcome, the current cognitive maps could stifle creative thought by the decision maker.
  4. The '[not] emergent pole', which is the default contrasting pole in the present maps, turn out to be meaningless when modelled as a conceptual graph.
  5. Conceptual graphs do not need any additional devices to show the `negative' links unlike the present cognitive mapping technique. Any user visuality element therein need not be compromised by this link's absence.
  6. By always implicitly linking concepts with default contrasting poles current cognitive maps obfuscate the distinction between legitimate and potentially damaging relationships. Conceptual graphs, on the other hand, remove this arbitrary situation by focusing the user's mind on what in fact are valid and invalid contrasting poles, including default ones.

12 Concluding Remarks

Clearly conceptual graphs can enrich cognitive mapping. Though it may successfully elicit knowledge through its contrasting poles and links, cognitive mapping cannot extract properly the genuine impact of these relationships nor put the user on enquiry to seek for further dimensions that may affect the problem. Moreover it can be wrong, as the references to mobile offices have revealed for example. A conceptual graphs processor could automatically recognise and deal with the contrasting aspects of the cognitive mapping technique. This would occur as a direct part of the negative contexts upon which conceptual graphs inference is based. As well as inference, the processor would also be able to check for any inconsistencies as they are entered into the knowledge-base. All this should free the user to declare merely what he or she believes and then review that mental model, or its computer paradigm, in the light of the processor's output.

Although critical of the current approach, this paper does not seek to dismiss it. As Eden states, the present cognitive maps can be drawn quickly and thereby get an immediate handle on the problem situation at hand, thus it remains a valuable initial modelling tool. However as a more permanent building block of knowledge, its limitations are simply too significant to ignore. Conceptual graphs supply a similarly visual but much more highly principled basis from which more meaningful knowledge can be eventually built. The conceptual graphs approach is therefore worthy of further exploitation for the benefit of strategic decision making, especially given its highly qualitative nature making it the most difficult-to-model aspect of business activity.


  1. J. F. Sowa; Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, 1984.
  2. S. Polovina; The Suitability of Conceptual Graphs in Strategic Management Accountancy, PhD Thesis, Loughborough University of Technology, UK, 1993.
  3. C. Eden; "Working on Problems Using Cognitive Mapping", Operations Research in Management, Littlechild, Stephen; Shutler, Maurice (eds.), Prentice-Hall, 1991.
  4. G. Kelly; The Psychology of Personal Constructs, Norton, New York, 1955.
  5. F.R. Ackerman, S.A. Cropper, C.L. Eden; "Cognitive Mapping for Community Operational Research-A User's Guide", Operational Research Tutorial Papers, A.G. Mumford, T.C. Bailey (eds.), Operational Research Society, 1991.
  6. R. Kowalski; Logic for Program Solving, Amsterdam, North-Holland, 1979.