The purpose of this paper is to introduce an approach to conceptual modeling and acquisition that combines useful features from two well-known knowledge representations: repertory grids and conceptual graphs. Conceptual graphs have the expressive power and reasoning support needed for an effective knowledge-based system, while repertory grids have the cognitive/psychological basis and generality needed to provide excellent elicitation and acquisition facilities. This hybrid approach lends itself to several knowledge acquisition methods, such as using conceptual graphs to build repertory grids, using repertory grids to build conceptual graphs, and using them together to perform heuristic classification. The paper shows how each representation, with only minor adaptation, can accommodate "hooks" into the other so that each may exploit the power of the other in providing efficient knowledge elicitation and acquisition support.

1. INTRODUCTION

2. BACKGROUND

3. MERGING REPERTORY GRIDS AND CONCEPTUAL GRAPHS

3.1. Repertory Grid as a Concept

3.2. Knowledge Acquisition Using Repertory Grid Graphs

3.3. Track Repertory Grids

4. SOME EXPERIENCE

5. DISCUSSION

6. CONCLUSION

7. REFERENCES

1. INTRODUCTION

The purpose of this paper is to present and describe the features of a hybrid knowledge representation, then suggest some approaches whereby the hybrid can be used for knowledge acquisition, and finally present some preliminary work in identifying issues and validating parts of that approach. Our approach to conceptual modeling and acquisition combines useful features from two well-known knowledge representations: repertory grids and conceptual graphs. Conceptual graphs have the expressive power and reasoning support needed for an effective knowledge-based system, while repertory grids have the cognitive/psychological basis and acquisition strength needed to provide excellent elicitation and acquisition facilities. This paper suggests a strategy, provides some examples, and identifies further avenues of inquiry.

The outline of the paper is as follows. First we briefly describe repertory grids, then describe conceptual graphs as a knowledge representation. The main part of the paper is a description of how the two can be merged into a flexible and powerful knowledge representation. A recent extension to repertory grids known as "track" repertory grids is shown to provide additional power to the approach. Some illustrations will be presented. The last section of the paper summarizes our experience so far and suggests further avenues of research.

2. BACKGROUND

Repertory grids are a well-known knowledge acquisition and representation technique based on the work of Kelly on personal construct theory (Kelly, 1955; Bradshaw, Boose et al., 1987; Gaines and Shaw, 1993). A repertory grid consists of a matrix whose rows contain construct labels (e.g., attributes) and whose columns represent individuals (or groups of individuals) using element labels to which those constructs or attributes may be applied. For example, in acquiring information about students for the purposes of an academic advising system, the grid in Figure 1 was obtained. This is not meant as a general description of a student; in fact, the grid was obtained during an actual exercise in analyzing the domain of student registration and advisement.

In this grid, the elements are kinds of students: entering freshman, transfer student, etc. The constructs are attributes that may be applicable to each kind of student. The ratings are on a scale of 1 to 6, where 1 indicates the construct does not apply, and a 6 means the construct strongly applies. These ratings were suggested by Wolff, who used them in some of his work, e.g., (Spangenberg and Wolff, 1988a).

Boose and Bradshaw introduced the notion of "laddering" into repertory grids; namely, the identification of subtypes and supertypes based on partially shared constructs (Bradshaw, Boose et al., 1987). For instance, in the example, transfer student and A.P. student both share the same rating for the constructs entering school, some courses completed, and need ESL course which indicates that some subtypes of student could be identified. This allows a repertory grid system to maintain associations between grids representing sub- and super-types.

Repertory grids have been applied to a wide variety of domains, usually aimed at various kinds of heuristic classification or expert system formation. Their general applicability makes them very attractive in knowledge acquisition (KA). It is therefore a natural step to seek ways to increase their power in general knowledge-based reasoning. Our approach in this paper is to use an already-existing representation whose power in reasoning and logic is already well-established.

We are proposing a useful combination of repertory grids and the conceptual graphs, a knowledge representation developed originally by John Sowa (Sowa, 1984; Sowa, 1992) based on C.S. Peirce's existential graphs (Roberts, 1973) and on semantic networks (Sowa, 1991). The chief benefit from this hybrid is to combine repertory grids' psychological basis and usefulness in supporting knowledge acquisition with conceptual graphs' usefulness in reasoning and logical inference. This idea immediately suggests two approaches to knowledge acquisition: one approach which leads from repertory grids to conceptual graphs; the other which leads from conceptual graphs to repertory grids. First we will show how repertory grids are represented in conceptual graphs, then proceed to examine knowledge acquisition with the two.

Conceptual graphs are a formalism popularized by John Sowa (Sowa, 1984) and studied extensively through a number of international workshops and conferences (Eklund, Nagle et al., 1992; Mineau, Moulin et al., 1993; Tepfenhart, Dick et al., 1994; Ellis, Levinson et al., 1995; Eklund, Ellis et al., 1996). For a tutorial on conceptual graphs, see (Polovina and Heaton, 1992); for a more detailed summary see (Sowa, 1992). A conceptual graph is a directed bipartite graph composed of concepts and relations. A concept is shown as a box with a type label and an optional individual label called a referent. A relation is shown as a circle or ellipse with a relation label. Type labels are arranged in an IS-A ordering known as a type hierarchy. A concept can have another graph as its referent; such a concept is called a context. It is assumed that the reader has some exposure to conceptual graphs.

We want to clarify the environment in which we expect this work to be valuable. Considering representation alone, using conceptual graphs with repertory grids is no more powerful than using either of the formalisms by themselves. Within an architecture for knowledge acquisition, however, the hybrid can be quite useful. We freely include the role of a human knowledge source in describing how we would use the combination, since we believe it is with human interaction that the combination bears the most fruit.

3. MERGING REPERTORY GRIDS AND CONCEPTUAL GRAPHS

Our motivation in merging repertory grids and conceptual graphs stems from an awareness of the fundamental strengths and weaknesses of each representation. Intuitively we want to use each one to complement the other by augmenting the other's strengths while overcoming the other's limitations.

Repertory grids are well-established as a general and powerful knowledge elicitation and acquisition technique to support classification. Their strengths are:

1. a solid foundation in human psychological theory,
2. demonstrated utility in eliciting and acquiring knowledge from people,
3. a general applicability in diverse domains,
4. freedom from specific paradigms or observer bias, and
5. an ability to acquire knowledge of a non-discrete nature (i.e., poles possessing a continuous set of values).

For the purposes of this work, we consider that the limitations of repertory grids are:

1. a lack of support for formal or automatic inferencing, and
2. a lack of general reasoning capabilities beyond heuristic classification.

Conceptual graphs are well-established as a formal knowledge representation, based on first-order logic and semantic networks. Their strengths are:

1. a solid foundation in logical reasoning,
2. an amenability to automated processing, and
3. a general applicability in diverse domains.

For the purposes of this work, we consider that the limitations of conceptual graphs as a knowledge acquisition framework are:

1. a lack of formal mechanisms to support elicitation,
2. a lack of a framework to link formal representations to knowledge (e.g., facts, rules, etc.) in the real world, and
3. a limited capability to reason about continuous-valued concepts.

By combining repertory grids and conceptual graphs, we hope to provide a single mechanism that has the following strengths:

• a foundation in psychological theory
• a foundation in logical reasoning
• utility in eliciting and acquiring knowledge from people
• ability to be automatically processed and manipulated
• freedom from specific paradigms or observer bias
• ability to support knowledge that is not purely discrete in nature

Our purpose in combining repertory grids and conceptual graphs is primarily to support knowledge acquisition for further processing. Before describing the acquisition processes they support, we first discuss how the combination can be represented. We present a hybrid approach such that the two representations are combined, yet each retains most of its distinctive appearance and functionality.

3.1 Repertory Grid as a Concept

In conceptual graph terms, every concept type represents an extension; namely, the set of all individuals of that type. A (standard) repertory grid represents a set of element-construct associations that together characterize a single concept (e.g., student). A repertory grid can therefore represent a concept in an enriched way: it not only includes the extension (the elements), it also includes a kind of schematic definition for each element (the constructs associated with each one). The grid thereby serves as a rich representation of a concept, with each of its attributes denoted to a greater or lesser degree for each individual. Contrast this with conceptual graphs, where definitions specify attributes in a boolean fashion - either the attribute exists or it does not.

As an illustration, consider the graph in Figure 2. It is both a conceptual graph and a repertory grid, where the repertory grid is the actual referent (individual) of type REP-GRID, and is shown within a conceptual graph a context. The intent of the graph is as follows. The elements of the grid are the extension of the Student concept, while the constructs of the grid constitute the extension of the Attribute concept shown. We can thus show not only the "meaning" of the concepts (as captured by their extensions) but also the relationship between the concepts, namely that Attribute is an attribute of Student. As the default relationship among elements and constructs, the conceptual relation attr adds little here; its usefulness will become apparent below.

The generic type Attribute is related to the repertory grids such that our paraphrase of the relationship reads as "the construct of REP-GRID is Attribute". The attributes for each row (e.g., entering school, etc.) are shown in the right-hand column of the grid. The elements for each column (e.g., transfer student) are on the top row. For convenience, we will call the related generic concepts (along with their relations) the generic part of the graph; the repertory grid concept itself we will call the grid part.

We are aware that treating either the element or construct labels as a single concept is an over-simplification of the knowledge being represented. For example, the construct have college experience is not a single attribute, but ultimately it comprises a more detailed sub-graph expressing a relationship between one set of students and their past experience, activities, etc. This representation is therefore to be considered merely an initial step in some overall knowledge acquisition process, which would have to support the refinement of these attributes. The next section introduces this process and shows how the representation supports it.

3.2 Knowledge Acquisition Using Repertory Grid Graphs

The example in Figure 2 above can be used to illustrate the basic forms of knowledge acquisition that are supported by this representation. Consider the following situations:

Only the generic part is available. Given just the generic part, we can instantiate a repertory grid and then use it to acquire instances and the attributes that are related to each one. Given the graph below: For example, given just a part of a graph as in Figure 3, we can instantiate a repertory grid concept of type REP-GRID whose element axis is to be filled in with instances of Student and whose construct axis is to be filled in with instances of Attribute.

The question of which axis goes with which concept is an important one, and it can be addressed in several ways. A simple but arbitrary one is to choose the origin of the relation arrow to be the element axis (in this case, Student, a lucky guess). A more reasonable strategy would be to have in the KA environment a small number of relations already analyzed and a choice embedded in each relation. For this example, that would mean defining the attr relation such that its incoming arc always comes from the element axis concept. Additional strategies may be based on this one: combinations of two or more relations (and their associated concepts) may have embedded pre-set choices. An example will be shown later in the paper.

In any case, assuming that some strategy exists for appropriately choosing a construct and element, we can construct an empty grid from Figure 3, as shown in Figure 4. Such a grid can be filled in using any of the well-known repertory grid acquisition methods (e.g., dyadic or triadic elicitation).

Another strategy for linking conceptual graphs with repertory grids is more general: we can consider any concept to be the basis for a repertory grid and then create a grid to be filled in. For example, Sowa's toy example of "A cat is sitting on a mat" can be treated such that the concept [CAT] is used as a starting point for creating a repertory grid with "CAT" as the element type and "Attribute" as the construct label.

Only the grid part is available. The basic features of any repertory grid are its construct label and its element label. We can therefore characterize any repertory grid by the concepts implied by those two features. We can thus represent a grid as in Figure 5 with construct and element relations.

The value of Figure 5 is to provide the Attribute and Student concepts as "hooks" to a set of conceptual graphs which can be joined to the knowledge comprising the grid.

Yet another strategy is to instantiate individual graphs for each element-construct pair where the degree rating (i.e., the matrix entry) is a 6 (or one of a range, etc.). For the graph in Figure 2, we would therefore obtain the set of graphs in Figure 6.

In order to relate the graph in Figure 6 to the generic part of Figure 2, we must obtain additional information from the knowledge source, who must choose whether the instantiated concepts are individuals (i.e., instances) of the generic part, or subtypes of the generic concept types. In this example, the knowledge source chooses to make them all subtypes, resulting in the following:

Entering Freshman < Student.	Senior < Student.		Transfer Student < Student.
A.P. Students < Student.		International Student < Student.
Entering School < Attribute.		Have College Experience < Attribute.
Some Courses Completed < Attribute.		Need ESL course < Attribute.

We have already mentioned the coarse-grained semantics of these labels. To address these issues, there are some parsing strategies, as suggested in (Wolf and Delugach, 1996a; Wolf and Delugach, 1997), that permit some refinement of the resulting graphs. These are beyond the scope of the current paper, which is primarily to suggest the potential of the hybrid.

Both the generic part and the grid part are available. In this case, there is the straightforward approach to acquire further elements and constructs from a human user to extend the repertory grid; however, since such an approach does not involve conceptual graphs at all, we do not focus on it here. A more interesting approach is to use the conceptual graph representation to form queries that the grid can answer through heuristic classification. Our working example can be used to classify an unknown student, based on answers to questions:

Is the attribute of the unknown student entering school?

Answer: no

Is the attribute of the unknown student have college experience?

Answer: yes

Is the attribute of the unknown student some courses completed?

Answer: yes

Is the attribute of the unknown student need ESL course?

Answer: no

The unknown student is of type senior.

The existing capabilities of repertory grids are thus still preserved. Although not an entirely new result, using repertory grids with conceptual graphs allows people to use an interactive process to develop refinements to the type hierarchy. The laddering notion is already known in the study of repertory grids; we merely re-cast it in the terms of conceptual graphs. Given a filled in set of repertory grids, user can be guided to answer yes or no to what is seen and identify either individuals or subtypes. The individuals' markers can then be used to fill in the generic concepts. New subtype relationships may thereby be obtained for the type hierarchy.

In the next section, we show some new capabilities that have been developed to extend repertory grids beyond the attr relation.

3.3 Track Repertory Grids

To begin the discussion of how conceptual graphs and repertory grids really interact, we introduce a simple graph obtained by a knowledge engineer dealing with a university student registration system. Consider that the graph shown in Figure 7 is part of a larger graph that may have originated during a knowledge engineering analysis.

Just as adding relations to simple concepts enhances their power to represent knowledge, so too does adding "tracks" to repertory grids present some interesting new strategies for using conceptual graphs. The full benefit can best be suggested by showing the slightly expanded graph in Figure 8, which shows a completed repertory grid graph. The base concept of the graph in Figure 7 and Figure 8 is the TAKE concept, which (as a subtype of ACT) has an agent, pt-in-time, and object relation to concepts, which are related to one another through relationships associated with repertory grids. Given the construction approach outlined above, Figure 8 results.

The idea of "tracked" repertory grids builds on the work of Wolf in extending repertory grids to handle a wider range of knowledge. In this paper, we elaborate on this general association that can be applied between repertory grids, namely the notion of a "track" between grids, as opposed to a simple "ladder". This term was introduced by Wolf (Wolf and Delugach, 1996b) in order to avoid the connotation of "up" or "down" directions when following associations between grids. A track is a general relationship between two (or more) grids, similar to a relation in conceptual graphs, so that a grid may be considered to represent knowledge from a much broader and richer perspective. If we consider the standard repertory grid to represent the answer to the question "what construct" with respect to its elements, then a tracked repertory grid may represent the answers to a general question with respect to its elements.

As one example, we may ask the question "what attributes?" with respect to elements that are university courses; then we may ask the question "when taken?" with respect to those same elements; whose resulting repertory grids look like Figure 9 and Figure 10. Note the shared element labels between Figure 9 and Figure 10. This sharing is a direct result of the two grids being "tracked" to one another. The track is also reflected in the concept Course being related as an element to both grid concepts. A larger example is given in Section 4 below. A more detailed description of can be found in (Wolf and Delugach, 1996b), and full description of defining track questions can be found in (Wolf, 1998). To summarize briefly, Figure 9 was obtained by asking the usual "what attributes?" question, which leads (by virtue of the "tracks") to a new question, "when taken?" that will be asked of the same elements.

Once the grids have been constructed, we can instantiate the elements as either individuals or sub-types, depending on the chosen strategy (see Section 3.2 above). In order to do this fully, we would need an additional grid to capture the knowledge about Student takes Course. A second level of analysis would lead to the two concepts Student and Course being considered for a repertory grid as follows. The graph in Figure 7 can be divided into sub-graphs, one of which is the graph in Figure 11, that shows the relationship between Student and Course. From the graph, a new track question can be formed, namely "student takes what course?" from which a repertory grid can be filled in, as shown in Figure 12.

We have shown that with track repertory grids, their combination with conceptual graphs offers new avenues for knowledge acquisition and provides a basis for a number of useful techniques. A number of strategies can be supported to approach acquisition either from existing conceptual graphs, existing repertory grids, or a combination.

We have indicated techniques that require either a generic graph part, a grid part, or both. Given just a generic part, we can form a blank grid, acquire new elements and constructs, expand definitions, and create tracks from which grids can be constructed. Given just a grid part, we can form "hooks" into conceptual graphs and adopt parsing strategies to refine constructs and elements to link with existing conceptual graphs. Given both parts, we can instantiate new individual concepts, specialize the graph part (either through individualization or sub-typing), form new track grids that can lead to further questions and graphs, and perform heuristic classification on observed instances. The table in Figure 15 below summarizes the strategies.

4. SOME EXPERIENCE

In validating Wolf's track grids, an exercise was undertaken to determine the effectiveness of track grids as an acquisition technique. The resulting set of track grids (a total of four grids) provided a larger example with which we were able to identify additional issues in manipulating repertory grid graphs.

The chosen domain was that of knowledge about horses. Several experts in this domain were used as subjects and the track grids in Figure 13 were acquired. The tracked grid can be explained briefly as follows. The what breeds grid has four horse breeds as its constructs (anglo-arabs, etc.); these constructs in turn comprise the elements of the what are the uses of horses grid. In a similar fashion, there are four constructs of the what are the uses of horses grid (hunter/jumper, etc.) which comprise the elements of two additional grids as shown. The multiple usage of these sets of constructs and/or elements is called "tracking" and is further explained in (Wolf and Delugach, 1996b; Wolf, 1998).

The knowledge shown in Figure 13 is represented using the hybrid repertory grid graphs in Figure 14.

From this exercise, we identified some new issues (discussed below) and clarified some others. This exercise also gave us some insight into how repertory grid graphs can be used to capture and represent operational knowledge (such as Use and Ride) that our experts considered to be part of the essential knowledge about horses.

5. DISCUSSION

The various strategies for exploiting repertory grid graphs are summarized in Figure 15 below. The strategies are based on identifying what (if any) contributions of conceptual graphs and repertory grids appear in a given knowledge acquisition situation. A graph can have one of the following contributions: (a) a generic part containing generic concepts, (b) instances, where the concepts are individuals, or (c) no graph at all. A repertory grid can have one of the following contributions: (a) filled-in with element and construct labels and values in the grid, (b) empty with just element and construct labels but no values, or (c) no grid at all.

Of course, this categorization does not address what to do when either component is a mix: e.g., if some concepts are individuals and some are generic, or if a repertory grid is partially filled. In these cases, which of the strategies are to be employed? Intuitively, we would expect to apply the given strategy to the component to which it applies, insofar as that is possible, but further experience is needed in handling these situations before we can support that claim.

One clear limitation of the overall approach is the free-form nature of both element and construct labels and the difficulty in deciding which is to be which. In the spirit of repertory grids, we want to preserve the knowledge source's freedom to express whatever elements and constructs he/she deems relevant; however, such freedom also limits our ability to make further sense out of the labels. There are some problems that arise from this limitation.

One problem is how to instantiate graphs from repertory grids. There may be several choices; for example, consider the grids in Figure 13 and the graph in Figure 14. We have the graph showing that the manner of Ride is a Manner, but should the how do you ride a horse grid's constructs be instantiated as separate instances of Ride as in Figure 16(a) or a single instance with more than one manner as in Figure 16(b)? For example, in our first illustration, we showed the element labels as instances of type Person. In fact, the "instances" shown are actually sub-types; i.e., specializations of person that comprise (albeit smaller) groups of actual instances. In this case, we could effectively incorporate laddering.

A bigger problem is how to extract more specific meaning (and hence graphs) from the element and construct labels. One approach to this problem was proposed by Wolf (Wolf and Delugach, 1996a). His approach calls for a rudimentary parsing of the label phrases of constructs to determine their meaning. Adapting and extending this approach may be quite useful.

A more speculative aspect of track grids involves their use in developing behavioral descriptions that can actually be simulated or executed on a computer. They are a natural extension of the track grids as shown here, but they require much more study before they are understood in the context of repertory grid graphs.

A very interesting avenue of inquiry would be to pursue formal concept analysis as a means of refining the sub- and super-type idea. Formal concept analysis is a conceptual clustering technique (Wolff, 1994; Wille, 1996; Wille, 1997) that maps very well onto repertory grids, both in structure and function (Spangenberg and Wolff, 1988b; Spangenberg and Wolff, 1988a). We are starting to pursue research in this area.

6. CONCLUSION

We have introduced a hybrid representation that "hooks" together repertory grids and conceptual graphs. We have offered some evidence that the hybrid can lend itself to several uses and we have suggested further avenues of inquiry.

The purpose of this paper has been to present the representation, describe its main features, suggest some approaches whereby the hybrid can be used for knowledge acquisition, and then present some preliminary work in identifying issues and validating parts of that approach.

To conclude, we have shown an interesting hybrid approach that exploits the best features of repertory grids and conceptual graphs, and shown how their combination supports several knowledge acquisition techniques. We plan to apply these techniques to a real-world environment, namely a testbed to explore concept formation in software requirements development, a domain we believe to be rich enough in depth and variety to give plenty of opportunities for testing, refining and augmenting these ideas.

Acknowledgment

I wish to thank Randy Wolf for many hours of interesting discussions and diversions involving repertory grids and conceptual graphs for some practical problems.

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