12

A framework for commensurability

Liam Magee

S: But you always need to put things into a context, don’t you?

P: I have never understood what context meant, no. A frame makes a picture look nicer, it may direct the gaze better, increase the value, but it doesn’t add anything to the picture. The frame, or the context, is precisely the sum of factors that make no difference to the data, what is common knowledge about it. If I were you, I would abstain from frameworks altogether. Just describe the state of affairs at hand (Latour 2004, p. 64).

The preceding chapter developed an implied theoretical approach to the question of the commensurability of knowledge systems, one based around the direct commitments expressed in the systems themselves, and of the indirect and inferred commitments of the cultures responsible for them. This chapter formalises and makes explicit that approach, by developing a model for assessing the commensurability of knowledge systems. In constructing a framework for assessing commensurability of ontologies, this chapter cements several levels of argument expressed in this book together. It presents, first, a speculative theoretical model of what it is that is being investigated in a commensurability assessment—what sort of entity underpins a formal knowledge system. Then the framework itself, designed to profile and explore differences in these systems, is described. The framework comprises a) a model of an idealised commensurability situation, where two systems are to be aligned; b) a series of dimensions for evaluating the cultures responsible for those systems; c) a quantification of the assessment; and d) a procedure for applying the dimensions and interpreting the results. Collectively these tools form part of what could be considered an analyst’s toolkit for evaluating the degree of fit between two knowledge systems. This chapter, then, offers one possible practical approach for working within the social web of knowledge.

What to measure—describing ‘ontological cultures’

Having worked through a range of theoretical positions in the preceding chapter, it is now possible to put forward our own model of the kinds of conceptual entities which are both explicit in knowledge systems themselves, and implicit in the practices and beliefs of the people who design and use them. These ‘entities’ have so far been described through a series of near-cognate, proximally synonymous terms, ushered in throughout this study to denote both a given system or arrangement of concepts, and, on occasion, also the social environment, and the people who produce and consume them. Yet none of these terms—perspectives, world views, paradigms, epistemes, conceptual schemes or spaces, historical ontologies, lifeworld, habitus—seems quite adequate for the kinds of entities wanted here. The following account aims to characterise these entities in descriptive terms, before then offering a formalised account as a part of the framework further on below. The account may seem more dogmatic that is intended; just as Minsky notes in a similar framework endeavour, this account proceeds while ‘pretending to have a unified, coherent theory’ (Minsky 1974).

What is envisioned here, then, is an elastic, dynamic, fluid yet interconnected ‘structure’ shared across members of a group or organisation; neither a subjective, individual cognitive ‘lifeworld’, nor a stable, socialised epistemic ‘system’, but something at an intermediate and intersubjective level of granularity. ‘Conceptual scheme’ seems adequate though insufficient, as the sought-after concept must also embrace the structural conditions and social practices that give rise to such schemes. Stopping at the conceptual misses out on these elements. A more embracing term is needed, which directs attention out from subjective cognitive abstractions towards the objective and intersubjective spheres in which those abstractions are generated, and to which they correspond.

‘Culture’ is one possible term; it both signifies a collective group and, more remotely, connotes a homogenous, self-replicating organism. The term has the advantage of being at the right granular level, since it is elastic, and can be stretched and scaled along several dimensions; it can describe a large or small, short or long-lived, casually or formally, historically or spatially organised collective of individuals. One of the functions of the cultures considered here, though, is that they produce very particular kinds of artefacts—formal knowledge systems. To describe just those cultures engaged in the production of knowledge systems particularly, I have added the epithet ‘ontological’. Taken literally, an ‘ontological culture’, then, is something which produces formal knowledge systems like semantic web ontologies—organisations, communities and other social groups who, as one of their practices, organise slices of the world into classificatory schemes. More tenuously, ‘ontological culture’ can also be taken in several other senses too: a culture which, to coin a neologism, ontologises; actively constituting its world and the beings in it (meaning something similar to Hacking’s use of the phrase ‘historical ontology’); or even as a biological ‘culture’, which is differentiated from more mundane microbial kinds of culture by being ‘ontological’ in the philosophical sense. The conjoined term, as a result, operates as a weak double pun, implying each of these meanings. Though concisely descriptive, this term does however strain at convention use; occasionally through the study the more conventional term ‘knowledge cultures’ has been preferred—though lacking in specificity the latter term also has an existing resonance in the sociology of knowledge and science, for instance, Knorr-Cetina (1999) and Peters and Besley (2006).

An ‘ontological culture’ inherits many of the characteristics ordinarily assigned to cultures generally. The remainder of this section presents a basic narrative, unfolding a series of terms as it develops a description of ‘ontological culture’. These terms, in turn, are formalised into a more coherent model, which is employed in the more technical discussion of the framework further on.

The organic connotation of ‘culture’ implies a certain autonomy—that cultures are, like Luhmannian systems, first-order sociological, rather than psychological or biological entities. They are in some sense irreducible to the agents or actors who comprise them. Actors instead perform semi-deterministic roles in accordance with the functional goals of a culture, of which there can be many: for example, generating profits, delivering services, providing welfare and conducting research. A typical overriding goal is one of self-maintenance—one of the ways it achieves this goal is by replicating its beliefs and practices. This may happen in a more or less predatory fashion, and in part takes place through communicative practices which have the intended effect of norming participating agents—of fostering adherence to beliefs and practices. In a general sense, having goals gives a culture a quality of intentionality—its practices are directed and goal-oriented, much as those of a biological agent might be. Retaining the organistic analogy, cultures reproduce, evolve, inhabit spaces, communicate with other cultures, and ultimately expire. While analysable and modelable, this cultural activity is partly stochastic, predictable only within broader, non-deterministic and probabilistic parameters.

A culture also operates within a general environment—what it sees as its ‘world’; or, in Habermasian terms, its ‘lifeworld’ (Lebenswelt). This environment supports other cultures; cultures can stand in structural relations to one another. Cultures can even be nested; for instance, when a greater culture harbours an embedded revolutionary cell. The relationships within and between cultures constitute semi-porous, permeable networks—sub-cultures, cross-cultures or ‘hybrid cultures’ are all examples. These structural delineations and permeations can be traced through the practices enacted within those cultures—canonically, within discursive practices. Discursive practices produce epistemic artefacts—representations of knowledge—which reflect the perspectival orientation of the culture towards the objects it encounters—or engenders—in its world. However, a perspective is not fixed—it reflects a point-in-time reification of a floating, variable conceptual scheme, which coordinates the production of beliefs within a culture. Other forms of practice, discursive or otherwise, are always ‘kicking back’ against a given perspectival view, which survives just so long as it can withstand or absorb these challenges. This is particularly the case in ‘experimental’ cultures such as scientific and, in the narrow sense exploited here, ‘ontological’ ones—cultures whose a priori rather than by-product function is the very production of knowledge. A characteristic of such cultures is their own self-explication of the beliefs and practices they engage in—formalised in rule-governing theory and rule-governed methodology respectively. This characteristic ensures repeatable observations—a kind of perspectival continuity across time, space and other cultural boundaries. Perspectives also, critically, remain one-sided; from any point of view there is always another, perhaps infinitely many other points of view available, through other accultured lens. Aspects of objects are both seen and occluded under a given perspectival lens; belonging to a culture, no matter how highly self-reflexively critical, means sharing both its insights and its blindnesses (de Man 1983).

Cultures, then, have conceptual schemes or, in Quine’s other metaphor, a ‘web of beliefs’ (Quine 1964). These beliefs can be described as structured like a network, spanning from the concrete, synthetic and empirical through to the abstract, analytic and conceptual—some beliefs are closer to the world than others. Again following Quine’s breakdown of the synthetic-analytic divide, a belief can be plotted along a scale of ontological-epistemological: ontological—here in the philosophical sense—to the extent that it refers to objects in the world; or epistemological—to the extent that it refers to other beliefs (or their expression in language). A belief is canonically expressed in a proposition, an assertion of a relationship between concepts, objects and properties. Together beliefs are mutually supporting, forming in the ideal system a coherent, consistent and non-contradictory whole. Within the semi-bounded environment of a culture, contradictions may nevertheless emerge in discursive practice between agents. One of the roles of discourse is to establish the grounds on which such intersubjective inconsistencies arise, to make assonance out of shared cognitive dissonance. Collectively, a network or web of beliefs constitutes a perspective—or, to use other common optical metaphors, an outlook, a point of view, a vantage point or an orientation. A perspective, however, is not here a passive lens through which the world is viewed; rather it actively constitutes, constructs and intends—in the active, phenomenological sense of ‘intending’—how things are viewed and arranged. Actors partake or subscribe to belief networks to the extent they are imbricated in a culture, acquire its ‘habitus’, although this is never (quite) a total imbrication. Through the roles they play and practices they enact, actors rather develop more or less intensive, comprehensive and enduring commitments to a set of beliefs. Understanding epistemic extent—the degree to which a belief is taken to be knowledge—is an important part of developing a profile of a culture.

Beliefs are transmitted in language, via what Habermas terms communicative practices. Communicative practice generally serves to break down what are otherwise incommensurable divides between cultures, and permit actors to participate in the ‘game of giving and asking for reasons’, in Brandom’s phrase. Hence assertoric utterances are paradigmatic instances of communicative practices—used to proclaim, query, test, revise, transmit, reconcile, and, in part, maintain cultural boundaries and integrity. Conveying of beliefs in language, while bearing the risk of a dissenting response, is above all an economic decision—it results in less work for belief transmission than other kinds of practices, of a presumably more coercive kind.

Beliefs form ‘webs’ in a less benign Quinean and more insidiously Foucauldian sense—as socially norming practices, discursive and otherwise (Foucault 1970). It might be possible in some cases to identify beliefs which are intrinsic and ‘core’ to a culture—those which motivate practices and subsidise ancillary beliefs, and which constitute the non-negotiable intransigent elements of a cultural ‘perspective’. These are likely to be those which are practically intractable to empirical or communicative challenge, since their invalidation threatens maintenance of the identity and boundaries of the prevailing culture. Belief revision is consequently largely a piecemeal affair, at least within the confines of a given culture, as the ‘carrying-out’ of practices and even the revision of certain beliefs can only take place while the remainder of the belief system remains relatively stable. In this model, epistemic revolutions, as opposed to revisions, are rare.

Yet beliefs, as purely ideational and immaterial constructs, are essentially unknowable directly, and only can be inferred via the evidence of a culture’s practices. For ‘ontological’ cultures—those that produce explicit representations of some slice of the world they are concerned with—a conceptual scheme can be directly interpreted in highly regulated ways, via the semantic specifications embedded in those representations. Such explicit representations cannot, however, be interpreted, purely and unreservedly, as the accomplished perspective of the culture which produces them. Rather they are narrow, restricted and temporarily discrete frames on an ever-changing flux of objects—or, in another formulation, sense-data ‘perceivings’ which only a posteriori congeal into the sorts of things conceptualisable as objects—subject to a continually changing dynamic process of theorisation and practice. Moreover they are also products with intended communicative effects. What is made explicit, then—the arrangement of concepts—needs interpreting not only in terms of its mode of explication, but against what remains tacit—a broader background of cultural beliefs and practices. Unlike the first kind of interpretation, operating directly on the axioms of a system itself and proceeding along set or model-theoretic—in other words, strictly analytical—lines, the second kind is necessarily dependent on exploratory, heuristic interpretive devices, using suggestive rather than direct forms of evidence. It is possible, then, to present knowledge systems generated by a culture as, instead of a stark unmediated delineation, a sort of highly detailed foreground, cast against a vague, impressionistic yet significant cultural backdrop. The resulting ‘portrait’ of a culture is then comparable with other depictions—partly in the precise quantitative sense of two geometric conceptual graphs being compared isomorphically, but also in the deliberately imprecise sense of two holistic images being comparing impressionistically.

Picking up methodological cues from Gardenfors (2000), to generate a portrait involves analysing cultures across any number of possible dimensions, some of which might be especially salient within a particular translation situational context. Generically, cultures can be described in a number of commonly occurring dimensions: size, rate of growth, ‘core’ or foundational beliefs, practices, perspectives, material and environmental conditions, influence, aggressiveness, health, longevity, maturity, internal organisational structure, relation to other cultures, organisational type and purpose (economic, political, legal), and so on. Other, specific variables relating to the situation in which translation takes place can be used as well. One possible formalisation of generic variables is described in the set of dimensions outlined below. Regardless of exactly which set of variables are selected, and how they are respectively weighted for saliency, what matters at this stage is that it is possible to describe, qualitatively and quantitatively, the explicit conceptualisations and tacit structures, beliefs and practices which underpin them, as a kind of portrait or profile. Commensurability of cultures involves, then, a comparison of the quantitative and qualitative profiles developed in this way. The ‘tacit’ part of a profile is not, of course, truly silent—it represents aspects of a culture which need hermeneutic or heuristic interpretation, typically kinds of discursive, textual practices in which conceptual commitments need to be ‘drawn out’ and inferred. Hence the methodological strictures about what counts as evidence, and what limits apply to the inferences drawn from it—this form of interpretation is necessarily suggestive and exploratory, rather than definitive and explanatory.

Presenting a framework for commensurability

The above characterisation is sufficiently abstract to describe the vague kinds of entities which reside behind knowledge systems. The remainder of the chapter now makes a sharp transition from theory to practice, from a theoretical model to a framework that might help an analyst work through practical problems of system translation. As indicated earlier, treatment of differences in knowledge systems takes place at least implicitly in several common information technology tasks—system integration, database design, information retrieval, decision support, resource planning, project management, and so on. A starting point for the framework is to describe what might be an idealised translation scenario, to serve as an approximation of the various real-world situations in which translation takes place. This provides a way of orienting the question of commensurability from the point of view of an analyst engaged in a translation process. The formalisation of the model also provides a way of moving from a qualitative to a quantitative characterisation of commensurability. From here, several generic dimensions for describing knowledge systems and their underlying cultures are proposed. A schematic procedure for applying the dimensions is then discussed, followed by some concluding notes on the interpretation of the commensurability assessment.

It is worth briefly reviewing the motivations for the framework. Referring back to Chapter 3, ‘The meanng of meaning’, there are broadly two ways of handling differences in knowledge systems. Computer science approaches focus on how to achieve individual concept alignment. They typically employ algorithms and external data definitions to match concepts from different systems. Matches can then be used to develop transformation rules to convert data from one system to another. These approaches can be broadly described as forms of semantic atomism—concepts are primary to the schemes containing them. Here by contrast system commensurability is considered in terms of plausible schematic alignment. This approach is fundamentally reliant on an interrogation of the cultural character of these systems. Following one of Brandom’s key distinctions it can be considered a form of semantic holism, where the overall underlying cultural conceptual scheme is primary with respect to the individual concepts stipulated within it (Brandom 2000). Furthermore it can be described as predominantly interested in the pragmatic character of knowledge systems—what kinds of use they are put to. The difference in approach, then, is largely one of orientation and method; semantic holism as advocated here is consistent with algorithmic matching techniques described above, and it can be used as a supplementary heuristic to these techniques.

Modelling a commensurability scenario

Leading on from the preceding description, here a formal model of an idealised commensurability scenario or situation is presented. The scenario is idealised in that it may not correspond directly with the many actual contexts in which system translation, integration or alignment takes place, but it ought at any rate to capture key or exemplary features, which enable the model to be generalisable to those contexts. The model distinguishes between knowledge systems and the ‘ontological cultures’ responsible for authoring and using them. The model includes concepts explicitly defined by the system, as well those tacitly implied by it—background assumptions not evident in the system itself, but which can be inferred by the translating analyst. The model describes the differences between ‘cultures’, in the sense defined above, against several dimensions. It assumes that assessment of commensurability is for the purpose of aligning or harmonising two systems—or scoping out at any rate the work involved in such a task.

The model supports the idea of partial or gradual commensurability between systems. In the preceding chapter, the idea of ‘commensurability’ was picked up from Kuhn’s account of scientific paradigms—there, commensurability is represented in all or nothing terms. I suggested that at face value this goes too far, leading to forms of linguistic or cognitive relativism, and begging the question of how communication across cultural or paradigmatic divides could happen at all. Commensurability then becomes a reified, ontological property of the systems; not, instead—and more helpfully—an analytic tool for describing their translatability relative to a context. If commensurability is considered in comparative rather than mutually exclusive terms, however, the ontological character and associated critique drops away. By extension, discussion of fine-grained, more or less commensurable cultural conceptual schemes can dispense with the charge of relativism. ‘Local’ schematic incommensurability, for example, can have reference to ‘global’ commensurability, and a mutually untranslatable pair of systems might well be translatable when transplanted to another situational context, with new goals, additional information, different translators and so on. This also accords with everyday intuition— language users frequently agree to disagree about their use of individual concepts, for instance, while still sharing sufficient common ground for these localised disagreements to be understood.

The model assumes the following scenario:

1. There are two formal systems which need to be aligned or harmonised, Sys1 and Sys2, which ought to meet the following conditions (additional systems need to be considered as multiple pairwise comparisons):

a. They are based on some more or less explicit formal language, with appropriate syntax and semantics (candidates are the relational model, XML schema, RDF and OWL).

b. In the term-assertion distinction, the systems in question must include a non-empty set of terms (or concepts), but not necessarily assertions (or objects or individuals).

c. The actual process of alignment or harmonisation is performed algorithmically, based on a series of transformational rules converting instances of concepts in Sys1 to instances of concepts in Sys2. However, the details of this process are not relevant to the assessment of commensurability which precedes it.

2. There are two conceptual schemes, Sch1 and Sch2, corresponding to the two formal systems. The schemes contain both explicit and tacit beliefs held by two ‘cultures’, Cult1 and Cult2, in the broad sense described above.

3. There is at least one designated purpose for the alignment or harmonisation. Collectively the set of purposes is defined as P (individual purposes could be designated using lower-case and prime notation, for example, p’, p”, etc.).

4. The purpose(s) are established within a situational context, Cxt. Assessment of commensurability can be viewed as a judgement on the relative fit of cultures for a given purpose. The degree of applicability of the judgement is thus relative to the dynamics of the situational context. Making explicit the context in the determination of commensurability promotes reusability—subject to contextual qualifications—of the assessment. This may for instance be a simple statement of the environmental or situational conditions in which the alignment or harmonisation process takes place, or a more formal analysis (SWOT and PESTLE analysis are examples of such formal contextual analyses).

5. There is some agent conducting the alignment or harmonisation, Agt. The agent is assumed to be a human individual or group, with appropriate techniques for characterising the formal systems.

6. Overall the alignment or harmonisation scenario consists of two systems (Sys1 and Sys2), developed and used by two cultures (Cult1 and Cult1), a set of purposes (P), a context (Cxt) and an agent (Agt).

7. Commensurability, Cms, can be defined as the degree of conceptual fit between two cultures, Cult1 and Cult2, responsible for the knowledge systems Sys1 and Sys2 respectively, given P, within Cxt, by Agt.

The purpose of the model can be restated in plain language, assessing the commensurability for the ‘ontological cultures’ responsible for formal knowledge systems, suitable to particular purpose(s) within a context, and to be conducted by an agent(s). The problem is further refined after the model of commensurability (Cms) is further elaborated below.

The model contains a series of semantic dimensions, following Gardenfors (2000), which are applied to knowledge systems on the basis of interpretation of the cultures responsible for them. The model is therefore multi-faceted or multi-dimensional. Dimensions can be further characterised as follows:

image Dimensions (Dims) are salient properties of a ‘ontological culture’ (the word ‘property’ itself is deliberately not used, to avoid ambiguity with properties defined within the systems themselves).

image Collectively the defined dimensions of the model form a set of dimensions (DimSets).

image Dimensions can be grouped at multiple levels, thus forming a tiered hierarchy.

image Dimension values are interpretations of aspects of a system and the culture responsible for it, relative to the purposes and other systems specified in the situational context.

image Interpretations are in the first instance qualitative; they can also be converted to quantitative measures to support statistical analysis. This entails assumptions about the dimensions and their application—a point further expanded below.

Figure 12.1 shows the relationship between the major components of the model.

image

Figure 12.1 Commensurability model

Quantifying commensurability

The qualitative measures can be interpreted quantitatively, as ordinal measures. Here dimensions are represented as integer values between 0 and 10—any scale can be applied, so long as it is consistent across all dimensions in the dimension set. Analysing commensurability then proceeds by assigning a value of 0 to 10 to each of the dimensions in the set for each of the systems being compared. This produces a set of values for Sys1 and Sys2, respectively V1 and V2, corresponding to each dimension belonging to the dimension set DimSet. Commensurability between Cult1 and Cult2 is then derived from the collection of values V1 and V2 taken for Sys1 and Sys2, as follows:

1. The difference between two dimension values for Sys1 and Sys2 is defined as the semantic distance (d) for the dimension in question.

2. Based on the collective purposes, P, and situational context, Cxt, the agent can assign a weight, w, against each of the dimensions. The weight is considered to be some value between 0 and 1. By default the weight is assumed to be 0.5 (permitting a relative strengthening or weakening of the weight). Weighting permits differential emphasis on dimensions of relevance or saliency to a given context.

In a further refinement to the analysis, weights could also be applied against dimension groups. This could have the effect of either applying the weight to each of the dimensions within the group, or supplying a separate level of weighting. The first case is simply an overriding of the individual dimension weighting case; the implications of the second are not considered in detail here, but would have the effect of establishing multiple commensurability measures for different layers of the model.

3. Given n dimensions, three forms of commensurability measures can then be derived:

a. The average of the semantic distances. This is the sum of the differences between the dimension valuations, divided by the number of dimensions. It ignores the weightings. Its formulaic expression is:

image

b. The weighted average of the semantic distances. This is the sum of the weighted differences, divided by the sum of the weights. Its formulaic expression is:

image

c. The square root of weighted average of squared semantic distances. This is the sum of the weighted squared differences, divided by the sum of the weights, from which the root is calculated. This measure accentuates the weighting effect. Its formulaic expression is:

image

The second of these calculations, the weighted average, is the preferred formula for most purposes, since it is readily interpreted in relation to the unweighted average, but provides the benefit of differential assessment of dimension saliency. The derived value provides a quantifiable measure for the commensurability of the two cultural conceptual schemes, given the defined purpose(s) within a context, and as applied by the agent. The previous definition can now be restated more precisely:

1. Let Sys1 and Sys2 be two knowledge systems, and Cult1 and Cult2 be the cultures engaged with the respective systems.

2. An agent Agt is tasked with aligning or harmonising Sys1 and Sys2 in a given situational context (Cxt), for a set of stated purposes (P).

3. Let Cms be the unknown variable, the degree of conceptual fit or commensurability between Cult1 and Cult2.

4. Then the calculation of commensurability, Cms, proceeds as follows:

a. Define some set of dimensions, DimSet, for describing conceptual schemes.

b. Interpret Sys1 and Sys2 against each of the dimensions, Dim, in the set DimSet.

c. Take the semantic distance, d, as the absolute difference between each of interpreted valuations.

d. Assign weights, w, against each of the dimensions, Dim, in the set DimSet, based on assessments of saliency of the dimension for the given purpose(s), P, within a context, Cxt.

e. Sum the weighted distances (Σwd), and divide by the sum of the weights (Σw).

f. The resulting weighted average provides a measure of commensurability, Cms, for the cultures Cult1 and Cult2, underlying Sys1 and Sys2.

This measurement can be used in turn as an estimate for assessing the complexity of aligning or harmonising the two knowledge systems. Some further remarks about how the measurement is interpreted and used are warranted at this stage:

image Dimensions tend to be descriptive, rather than judgemental. However, judgement is usually involved in the assignment of values to dimensions, hence the overall assessment should not be presumed to be value-free—rather, the point is that such value judgements are made explicit.

image In certain cases, applying a quantitative scale may imply a false degree of precision, and require greater rigour than the context warrants. In these cases, it might be sufficient to rate the systems as either ‘low’ or ‘high’, or perhaps ‘low’, ‘medium’ or ‘high’. In such cases, quantitative analysis can still be carried out by choosing appropriate values within the ranges set by dimensions with the greatest number of values. For example, if at least one dimension is scaled [0, 10], then other dimensions must have appropriate values within the lower and upper bounds (between 0 and 10), and an equivalent mid-way value. Value ranges such as [3, 7] and [2, 5, 8], for example, could be valid interpretations of the respective qualitative evaluations above.

image Dimension valuations can in some circumstances be added directly to the systems themselves. Most formal systems provide various metadata or annotation mechanisms. For instance, OWL provides annotation or metadata facilities which can be applied to the system as a whole, or to specific entities (classes or properties, for example) within it. Although the dimension valuations are related to a specific context, they may also be useful for future assessments of commensurability, or simply as annotated comments on the system itself.

image The set of dimensions constitute themselves a series of ontological claims about cultures and conceptual schemes. These claims are part, then, of a second-order conceptual scheme; the degree to which they require further explication and rationalisation will depend on context.

Contrasting ontology matching approaches

As discussed earlier, recent work in schema and ontology alignment views that task as a ‘bottom-up’ problem, that is, to be solved at the level of individual concepts (Shvaiko and Euzenat 2008). Designers of matching algorithms employ various strategies for determining matches. They generally take the form of generating a set of matches based on:

image A concept, C1, taken from Sys1

image A concept, C2, taken from Sys2

image A relation between concepts C1 and C2: one of equivalence, generalisation, specialisation or disjointness

image A degree of confidence in the match.

It is clear why such approaches are semantically atomic, according to the terms outlined in this study. The degree of fit of the systems as a whole is derived from the completeness and precision of the set of matches obtained between individual concepts. Different strategies and algorithms can be compared with human interpretations in this regard. Nevertheless these approaches do not capture important contextual information about the knowledge systems, nor can they infer implicit information about the underlying cultural conceptual schemes. Rather this can only be inferred by a human agent who is capable of interpreting knowledge systems against a broader epistemological backdrop of purposes, contexts and other social agents. Such interpretation is argued here as a form of semantic holism—in which specific conceptual representations can only be understood within a general social whole of meaning production and consumption.

Interpretation, of the kind required to describe dimensions of a conceptual scheme, is, however, a notoriously arbitrary process. Obvious criticisms are that interpretation is at best partial, subjective, and in some cases irrelevant or not feasible given a cost-benefit analysis or other justificatory measures. There are several possible responses to these criticisms of the framework:

image It supplements rather than competes with alignment algorithms, so it can be regarded as a form of human rather than computer-aided design tool.

image It is intended as a heuristic aid to alignment activities, not as a definitive prescription, for tasks not amenable to algorithmic analysis.

image It merely formalises intuitions at work in everyday practice, albeit with a series of epistemological and methodological assumptions in tow.

image Its inclusion of an appropriate set of dimensions and application of method serves to corral the worst excesses of interpretive work.

The dimensions presented in the next section endeavour to perform some of this corralling work.

Describing commensurability—a generic dimension set

The framework also includes a default generic set of dimensions for describing knowledge systems and the cultures behind them. In practice, as the case studies bear out, the default set often needs revision, extension and weighting to fit the requirements of a given translation situation. By abstracting out the formal model and process for quantifying commensurability, it is possible to use any suitable dimension set, without loss of general applicability.

Inevitably the choice of dimensions appears arbitrary, and need justification on grounds of saliency and relevance to the systems under consideration. The dimensions have been selected on the basis of utility for determining commensurability. Some of the intrinsic dimensions seem logical for any kind of system analysis; others—particularly those relating to context—are governed specifically by the account of commensurability presented here. The dimensions are intended to draw out salient differences in systems and their underlying cultures and conceptual schemes.

The set presented here itself is intentionally abstract, and aims to capture the general tendencies of the culture responsible for a knowledge system. The set distinguished between intrinsic and extrinsic dimensions of systems. The intrinsic dimensions reflect the concepts, properties and individuals stipulated in the system itself, and its overall structural and stylistic features. Several of these have been extracted and simplified from schema and ontology metrics discussions mentioned in the literature review, notably in Tartir et al. (2005) and Yao, Orme and Etzkorn (2005). Unlike metrics, which can be computed just with reference to a single ontology, these dimensions are comparative—for example, the scope of a system can be judged to be general or specific only with reference to other systems under consideration.

The extrinsic dimensions aim to understand the implicit concepts that stand behind the system, which operate within the broader social environment in which the system is constructed. The distinction thus serves to differentiate a characterisation of the system itself from the characterisation of the environment in which it is constructed and used. A number of the extrinsic dimensions have been extracted or correlated to those developed in the standardisation and knowledge management literature discussed in Chapter 3, ‘The meaning of meaning’. Others appear to be generic distinguishing traits differentiating knowledge systems, part of which has been borne out in the case studies which follow.

Intrinsic dimensions of a knowledge system

Intrinsic dimensions describe the knowledge system itself. There are four types of intrinsic dimensions:

image structure—describes structural characteristics of the system; for example, whether the system is relatively large or small, or detailed or sparse

image style—describes stylistic aspects of the system; for example, whether the system predominantly declares concepts or properties

image scope—describes the scope of the system; for example, whether the concepts concentrated on a particular area, or dispersed over several

image subject—describes the subject(s) dealt with by the system, and how these are characterised; for example, whether the concepts are relatively abstract or concrete.

Table 12.1 presents each of the dimensions with a brief explanation.

Table 12.1

Intrinsic dimensions of a knowledge system

Dimension group Dimension Description
Structure Dimensions that describe the structural characteristics of the system
Small-large Whether there are a small or large number of concepts in the system.
Light-dense Whether the system contains a small or large number of properties and sub-classes for each class; this dimension corresponds to that of ‘inheritance richness’ mentioned by Tartir et al. (2005), and of ‘Average Depth of Inheritance Tree of Leaf Nodes (ADIT-LN)’ introduced by Yao, Orme and Etzkorn (2005).
Self-contained-derivative Whether the system uses only constructs defined internally, or makes use of imported constructs (can be determined by the presence of owl:imports declarations, and the extent to which imported constructs are used within the ontology).
Free-restricted Whether the classes defined within the system have a small or large number of constraints applied to them; this dimension corresponds to that of ‘relationship richness’ mentioned by Tartir et al. (2005).
Sparsely-heavily populated Whether the system contains a small or large number of individuals.
Style Dimensions that describe the stylistic aspects of the system
Classificatory-attributive Whether the system uses predominantly sub-classes or properties/attributes to describe relations between classes; this dimension corresponds to that of ‘attribute richness’ mentioned by Tartir et al. (2005).
Literal-object composition Whether the system uses predominantly data type literal or object type properties.
Quantitative-qualitative Whether the system uses predominantly numeric or textual values for its data type properties.
Poorly-highly annotated Whether the system is well described (uses a high number of metadata annotations).
Scope Dimensions that describe the scope of the system
Coherence-dispersion Whether the concepts listed in the system belong to an existing coherent system, or are seemingly ‘random’ in their selection.
Concentrated-diffused Whether the concepts are tightly clustered around a particular area or field, or are diffused over a range of fields.
General-specific Whether the concepts are general in relation to a given field or fields, or are instead highly specific.
Subject Dimensions that describe features of the subject(s) dealt with by the system
Concrete-abstract The degree the system relates to concrete objects (books, proteins, people) or tends towards abstract objects (space, time, substance). Ontologies are sometimes described as being ‘upper-level’, ‘mid-level’ or ‘low-level’ according to their level of abstraction—this dimension describes the same feature.
Natural-social Whether the system describes objects from a naturalistic or socialistic perspective (in philosophical terms, adoption of realist or constructivist perspective).
Spatial-temporal Whether the system describes predominantly spatial objects (books, people, organisations) or temporal objects (events, periods, durations).
Phenomenalist-scientific Whether the system describes objects from an everyday ‘phenomenalist’ perspective, or from the standpoint of science.

Extrinsic dimensions of a knowledge system

Extrinsic dimensions describe the social context in which the system is developed. As with the intrinsic dimensions, there are four types of extrinsic dimensions:

image perspective—describes the stated intention or purpose of the system; for example, whether the system represents an ideal or a pragmatic conceptualisation of a field or domain

image purpose—describes the underlying motivation (as best inferred) of the system; for example, whether strong financial or political motives underly the system’s construction

image process—describes the process of the system’s design and construction; for example, whether the system design was relatively centralised or distributed

image practice—describes how the system has been received; for example, whether the system is better characterised as a de facto or de jure standard.

Table 12.2 presents each of these dimensions.

Table 12.2

Extrinsic dimensions of a knowledge system

Dimension Group Dimension Description
Perspective Dimensions that describe the general perspective or orientation of the system
Pragmatic—idealistic Whether the system is pragmatic—representing how concepts are presently represented in information systems—or idealist—suggesting how concepts ought to be represented.
Academic—applied Whether the system is intended for academic research or for ‘real-world’ applications.
Serious—spurious Whether the system is intended for serious use.
Speculative—grounded Whether the system is a speculative or hypothetical point of view about the objects it describes.
Committed—uncommitted Whether the system is committed to the conceptual scheme it operationalises.
Compatible—independent Whether the system is intended by design to be compatible with other systems.
Purpose Dimensions that describe the underlying motivations and purposes of the system
Financially motivated: weak-strong Whether the system is motivated by financial considerations (for example, to promote related products and services, to cut costs of data management).
Legally motivated: weak-strong Whether the system is motivated by legal considerations (for example, to support particular licensing arrangements, or to work around legal obstacles).
Politically motivated: weak-strong Whether the system is motivated by political considerations (for example, to influence policy makers, or to form strategic alliances with organisations).
Ethically motivated: weak-strong Whether the system is motivated by ethical considerations (for example, to promote interoperability among non-profit organisations).
Personally motivated: weak-strong Whether the system is motivated by personal considerations (for example, to enhance individual career prospects).
Theoretically motivated: weak-strong Whether the system is motivated by theoretical considerations (for example, to promote a given ontological orientation).
Process Dimensions that describe the process of the system’s design and construction
Representative-unrepresentative of community Whether the system is representative of the community that makes use of it.
Central-distributed design Whether the system is designed by a central body or via a distributed community.
Closed-transparent process Whether the system is designed in a way that elicits and incorporates critical review and feedback.
Formal-informal construction Whether the system uses a formal process, such as those used by international standards bodies.
Explicit-implicit assumptions Whether the system makes explicit background assumptions, as understood by those involved in its design.
Rigorous-random method Whether the system makes use of a rigorous method in its design.
Practice Dimensions that describe how the system is used
Active-inactive community Whether the system is designed and/or used by an active community.
Low-high adoption rate Whether the system has a high adoption rate among its candidate users or market.
Low-high maturity Whether the system is mature—has gone through multiple iterative cycles or versions.
Backward compatible-incompatible Whether the system is compatible with earlier versions of the system.
De facto standard: low-high Whether the system is a de facto standard among its users.
De jure standard: low-high Whether the system is a de jure standard—has received ratification from appropriate standards bodies.
Industry support: low-high Whether the system is widely supported within the industry (as evidenced by supporting documentation, tools, services, etc.).
Documentation availability: low-high Whether the system is supported by available documentation.

Pre-empting the methods discussion below, the extrinsic dimensions clearly require considerable interpretation. In contrast, some of the intrinsic dimension values may be derived algorithmically, especially in the case of the structural and stylistic dimensions. It is also clear that accurate evaluation of extrinsic dimensions may require considerable discovery effort. The extent of effort needs to be justified against the benefit of the assessment, on the basis of some kind of cost-benefit analysis. Nevertheless evaluation itself can be more or less formal or extensive—for certain purposes and contexts, existing knowledge or opinion may be sufficient, or the dimensions introduced here can be applied in an ad hoc fashion.

In conjunction the intrinsic and extrinsic dimensions provide a characterisation of the knowledge systems in their underlying conceptual scheme and the background cultures responsible for them. The intrinsic subject and extrinsic intention dimension groups do most to capture the implicit elements of the conceptual scheme; while the other intrinsic groups summarise what is already explicit but not immediately conveyed in the system; and the other extrinsic groups contextualise the system in ways that make more evident the causes behind the construction of the system itself. The next section outlines how the model can be applied in a given commensurability assessment scenario.

Assessing commensurability—applying the dimensions

As a final part of the overall framework, a basic procedure is proposed for the application of the dimensions to the systems. The method of construction can be minimal or highly sophisticated, depending on the context of the assessment. Nevertheless, some explicit treatment of method, in terms of how the model might be applied, is useful. The method assumes the idealised scenario presented in the discussion of the analytic procedure above—namely, Sys1, Sys2 represent the two systems, Cult2, Cult2 represent the underlying cultural schemes, P represents the purpose(s), Cxt represents the context, and Agt represents the agent.

First, the intrinsic character of Sys1 and Sys2 are described. This involves:

1. Surveying of parts or all of the definition of Sys1 and Sys2; the ‘definition’ may be precisely specified in a formal language, or need to be inferred from secondary documentation. The following is a list of potential sources for analysing the definition:

a. the source definition of the system: the concepts and properties declared in XML Schema files, RDF/OWL ontologies or relational models

b. system documentation, which may be in the form of annotations to the source definition, external documentation or academic publications

c. diagrammatic representations of the system, such as entity relational (E/R) or Unified Modeling Language (UML) diagrams

d. available metrics summarising structural or stylistic aspects of the system

e. secondary sources analysing or discussing the systems.

2. Analysing and rating the systems according to the intrinsic dimension groups structure, style, subject and scope. In the case of structural and stylistic dimensions, it may be useful to employ algorithms for counting numbers of concepts, properties, annotations, restrictions and individuals. The following list gives examples of how the given intrinsic dimension groups and dimensions might be analysed:

a. structural dimensions—may involve counting the number of concepts and properties, finding ‘import’ declarations, and checking the extent of constraints applied to concepts and properties

b. stylistic dimensions—may involve counting the relative number of concept and property declarations, examining property types (whether they are literal or relations), examining literal property types (whether they are numerical, textual or other), checking the internal documentation (whether the system entities are annotated), and examining whether there are multiple methods to describe an objectb. process dimensions—may involve looking at how the system is developed: what explicit or implied policies determine how the system is designed, versioned, ratified and publicised

c. scope dimensions—may involve interpreting whether the concepts are coherently grouped or seemingly random, concentrated around their subject matter or diffused, and general or specific

d. subject dimensions—may involve interpreting whether concepts are concrete or abstract, temporal or spatially oriented, and refer to natural occurring or socially constructed objects.

3. Analysing the valuations and differences between the intrinsic properties of the system by grouping averages by dimension group.

Second, the extrinsic dimensions of the systems are analysed. This in turn involves:

1. Surveying the social environment in which Sys1 and Sys2 are developed. Depending on the scale of the method, availability of sources and nature of the systems, this could incorporate several different methods:

a. interviews with the system designers and with other users of the system

b. affiliation or participation in working groups, standards committees and design teams

c. analysis of online social groups—blogs, wikis, forums, mailing lists—in which aspects of the system design are discussed or negotiated

d. review of secondary materials: press, academic publications, conferences, journals and books that discuss aspects of the systems

e. review of peripheral materials: government policies, company financial reports, industry group minutes, standard body procedures related to organisations sponsoring, advocating or using the systems.

2. Analysing and rating the systems according to the extrinsic dimensions. This requires interpreting the materials in dimension groups of perspective, purpose, process and practice. The following list gives examples of how the given extrinsic dimension groups and dimensions might be analysed:

a. purpose dimensions—may involve examining the stated and implied intentions behind a system, including any economic, political, philosophical or technical rationales evident in the context of the presentation of the systems themselves (websites, accompanying documentation) and other sources (forums, commentaries, and so on)

b. process dimensions—may involve looking at how the system is developed: what explicit or implied policies determine how the system is designed, versioned, ratified and publicised

c. practice dimensions—may involve examining how the system is used within different environments; whether it is widely endorsed, supported and integrated within an ecosystem of other systems, standards and products

d. perspective dimensions—may involve direct interpretation or indirect sourcing of commentary about the general ‘orientation’ of the system: whether it is oriented towards everyday ‘lay’ or scientific vocabularies; whether it adopts a realist or constructivist position towards the objects it describes; or whether it uses existing vocabularies or enforces a new normative vocabulary of its own.

3. Separately analysing quantitatively the valuations and differences between the extrinsic properties of the system, to generate averages by dimension group.

Finally, the weighted average of all of the dimensional differences is obtained to provide a quantitative measure of commensurability, using the procedure outlined above. Any qualitative remarks, against dimensions or dimension groups, can also be summarised into an overall qualitative assessment.

Interpreting commensurability assessments

Qualitative and quantitative assessments need to be interpreted relative to the specific context in which the assessments have taken place. This is particularly the case for the quantitative measurement. Low values of in commensurability should correlate to quicker and less problematic alignments between the systems concerns; conversely, low values should indicate slower and more difficult alignments. High values might also suggest the need for various further activities: more consultation with those knowledgeable about the respective systems; iterative cycles of translation; more rigorous testing procedures; or, finally, that the task of translation is not viable within available constraints. In some situations, these determinations might have other, flow-on effects and impacts: the desirability for one system over another, for example, or even of the ‘strategic fit’ between two organisational cultures. Just as the background cultures responsible for two systems impacts on their relative commensurability, the ‘embeddedness’ of systems means their compatibility can be an indicator and even determinant for general questions of cultural alignment and affiliation. These, naturally, need to be asked with reference to specific operating conditions; so here no more than a vague indication can be provided for what commensurability assessments might mean, and how they ought to be interpreted, within those conditions. Some of these considerations are presented below in itemised form, however, to prompt this interpretative process:

image What does a high value, signalling a high degree of in commensurability, indicate? What if any consequences does this have?

    Does it mean that the systems are radically incommensurable, and any effort to align them will be in vain? Or does it entail practical consequences: a greater amount of work is required, additional resources or time need to be allocated, or further analysis or different approaches need to be explored? Or does it indicate a preferential choice of one system over another, where the dimensions have been interpreted as selection criteria?

    Conversely, what does a low value signify? That the systems are commensurable for the stated purposes, or that alignment or harmonisation of the systems is comparatively trivial?

image How do the quantitative and qualitative assessments compare? Are they consistent, and if not why not? Do some of the dimensions perhaps need to be re-weighted?

image How do the assessments fit with intuitive understandings of the general ‘fit’, or commensurability, of the systems concerned?

image What other steps or stages—consultation, testing, the alignment itself—need to be modified as a result of the assessments? Qualitative as well as quantitative findings could prompt particular decisions here.

image What follow-up actions or decisions might eventuate from these assessments? Do they indicate preference for one system over another? Are there alternate ways of achieving the ends to which the system alignment or translation is directed?

image Are there broader implications of these assessments? Do they reflect important ‘extra-systemic’ features, such as the ‘strategic fit’ between organisations or organisational units?

Applying the framework

Against the background of a broad charaterisation of the social web of knowledge earlier in this book, here we have proceeded to develop a general theoretical rubric and detailed framework for assessing the commensurability of both formal systems and the cultures responsible for them. The framework has four components: a model of an idealised commensurability scenario, a series of dimensions conforming to the demands of the procedure, a means for quantifying commensurability and a method for applying the framework and interpreting the results. The framework mobiles a series of analytic tools for understanding both the explicit and implicit commitments entailed by formal knowledge systems—those directly stipulated in the systems themselves, and those inferred through an examination of the background cultures in which they are produced and used. The series of dimensions uses the distinction between intrinsic and extrinsic dimensions to capture each of these types of commitments. The separation of the model and methodology permits the adoption of entirely different dimensions, allowing for considerable flexibility in how other criteria and even different ontological and epistemological assumptions come into play in the analysis.

Assessing the commensurability of systems is a necessary but ultimately insufficient step for building webs of meaning and knowledge around contemporary representations of knowledge. Assessment needs to be corroborated with specific pathways of concept transformation and translation; these, in turn, of course need to be guided by the kinds of methodological, heuristic and analytic rigour an assessment framework provides. However, inter-system translation threatens to become a task of exponential complexity as the number, size and underlying assumptions of these systems themselves proliferate. One way to corral such complexity—within arithmetically rather than geometrically growing bounds, at least—is to develop interlanguages—kinds of reference languages designed to guide translation between the micro-languages articulated (again, both explicitly and implicitly) within knowledge systems. The next chapter looks at the development of one such interlanguage, and how it helps with building the social web.

References

Brandom, R. Articulating Reasons: An Introduction to Inferentialism. Cambridge, MA: Harvard University Press; 2000.

de Man, P. Blindness and Insight: Essays in the Rhetoric of Contemporary Criticism. Abingdon: Routledge; 1983.

Foucault, M. The Order of Things: An Archaeology of the Human Sciences. New York: Vintage Books; 1970.

Gardenfors, P. Conceptual Spaces. Cambridge, MA: MIT Press; 2000.

Knorr-Cetina, K. Epistemic Cultures: How the Sciences Make Knowledge. Cambridge, MA: Harvard University Press; 1999.

Latour, B. ‘On Using ANT for Studying Information Systems: A (Somewhat) Socratic Dialogue’. In C. Avgerou, C. Ciborra and F. Land (eds), The Social Study of Information and Communication Technology: Innovation, Actors and Contexts. Oxford: Oxford University Press, pp. 62–76.

Minsky, M. A Framework for Representing Knowledge. http://dspace.mit.edu/handle/1721.1/6089. 1974. [(accessed 19 January 2010).].

Peters, M.A., Besley, T. Building Knowledge Cultures: Education and Development in the Age of Knowledge Capitalism. Lanham: Rowman & Littlefield; 2006.

Quine, W.V.O. Word and Object. Cambridge, MA: MIT Press; 1964.

Shvaiko, P., Euzenat, J., Ten Challenges for Ontology Matching. In OTM 2008: Proceedings of the 7th International Conference on Ontologies, Databases, and Applications of Semantics (ODBASE). Berlin and Heidelberg: Springer. 2008:1164–1182.

Tartir, S., Arpinar, I.B., Moore, M., Sheth, A.P., Aleman-Mez, B., OntoQA: Metric-Based Ontology Quality Analysis. Proceedings of IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources. IEEE Computer Society, 2005:45–53.

Yao, H., Orme, A.M., Etzkorn, L. Cohesion Metrics for Ontology Design and Application. Journal of Computer Science. 2005; 1:107–113.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset