A Distributed Integration Approach to Learning
      By Joseph Goguen

1. Introduction
This note is a short informal introduction to a new approach to learning based on unifying a selection of key ideas from distributed cognition, activity theory, actor-network theory, conceptual integration (blending) theory, and semiotics; this unification is tentatively called unified concept theory, which for convenience is abbreviated UCT. In addition, a mathematical language is suggested (but not described in detail) for expressing and exploring properties of models developed in UCT. The selection of key ideas is guided by two main principles: practical applicability (e.g., in student projects for the courses I teach on user interface design), and formal consistency within the mathematical modelling language. There is also a special emphasis on the role of values in the integration of complex systems.

The view that learning is highly analoguous to the information processing concepts of storage and retrieval from memory is distressingly common; much of the literature in several different fields implicitly embraces such a model, including classical learning theory in psychology and its applications to education. A different view is suggested here, combining principles from recent research in cognitive science, especially integration and distribution, with older principles of activity, cultural historical development, material mediation, and chains of translation in networks of agents and mediators. The use of network models places UCT within the purview of the social networks branch of complex systems theory, though it differs from other work in that area in several ways.

Following this introduction, some of the contributing key ideas are sketched, and then our approach to learning is outlined, including brief discussions of values, perception, mathematical models, and case studies; some readers may wish to read the last section first, and to skip the next to last section.

1.1 What's Missing
This essay lacks citations, detailed empirical examples, and many details, e.g., of its underlying mathematical models. Moreover, its scope is very broad, so that in many ways it is more a research agenda than a finished theory. Nonetheless, I hope it may be of value in promoting discussion about the relations among various approaches to learning, collaboration, and sustainability.

2. Background
Before explaining UCT, we briefly describe some key aspects of its contributing theories, beginning with the activity theory (abbreviated AT) of Vygotsky and others. This school stresses material mediation, the important role of artifacts in mediating learning in the natural situations in which it occurs. AT also emphasizes the cultural context of learning, and its historical development, both in individuals and in groups, up the the level of whole cultures. Cole, Engstrom, and others have explored and expanded the scope and application of these and related concepts, and Hutchins has advanced the notion of material anchors as a refinement of material mediation, as part of his theory of distributed cognition, which examines the operation of networks of human agents and material artifacts. This is consistent with the actor network theory (abbreviated ANT) of Latour, Callon and others, in their work on sociology of science and technology.

What is most novel about UCT comes from recent research in cognitive linguistics on conceptual integration networks and their role in cognition, due to Fauconnier, Turner, and others, building on prior work of Lakoff on metaphor and Rosch on concepts. My own algebraic formalization of conceptual integration, using also some ideas from semiotics, plays a role here, as does my experience applying these ideas, along with ANT and ethnomethodology, to the design of computer-based systems, particularly user interfaces, and requirements analysis for systems that must function in complex social environments. The semiotic ideas include Peirce's emphasis on the triadic nature of denotation, as necessarily including an interpretant in addition to a signifier and a signified, and Saussure's ideas that signs may have complex structure, and that they should be studied as members of families of related signs, rather than individually. The interpretant provides for the interpretation of signifiers, taking account of context.

Fauconnier and Turner propose that human understanding is the integration of networks of conceptual spaces (or mental spaces), each of which contains information relevant to some aspect of the current situation, selected out of larger conceptual domains of general knowledge, and from preliminary understandings of immediate perception. These "spaces" consist of individual concepts and relations among them (not just simple concepts), and the network consists not just of the spaces, but also of conceptual mappings which establish connections among the constituents of spaces. The result of understanding is then a blend space that coherently integrates information from all components of the network. Fauconnier and Turner have proposed a number of optimality principles that constrain the choice of blend spaces and the process of integration. Their theory is often called blending theory, here abbreviated BT.

My extension of BT includes a mathematical language in which it can be more precisely expressed and studied, and two major additions. The first adds types and functions to the constants (for concepts) and relations of the (original BT) spaces; this allows consideration of complex structured signs, such as appear in user interfaces. The second addition replaces spaces by frames, which include not just signifiers in a formal language, but also perceptual representations, in the form of geometrical or topological models, in roughly the sense of Gardenfors, but extended with activity, e.g., motion, and action that can induce change, together with an interpretant between them. In this way, the image schemas of Lakoff and the prototypes of Rosch are naturally included in UCT. Integration or blending is then extended to frames, rather than just their formal linguistic components. When a single perceptual space is shared among frames of multiple individuals or groups, we have what Star calls a boundary object, and when the perceptual component is of primary interest (but not necessarily shared), we have the material anchors of Hutchins.

3. Learning
I suggest that learning has two modes that may be interleaved and even overlapping; these are acquisition and application, both of which involve the integration of networks of frames. Among points emphasized in BT are that integration is unconscious, nearly instantaneous, and often involves emergent structure in the blend space; BT speaks of "recruiting" additional material in the form of new conceptual spaces, from other domains that may at first appear to be only distantly related to the original spaces. I propose that the emergence of such novel structure characterizes acquisition, and that the use of such structure characterizes applicaiton, where "use" means real world instantiation of actions in the perceptual components of frames.

In such situations, integration need not be either unconscious or apparently instantaneous, since conscious effort over extended periods can in fact be observed. Note also that the frames involved in acquisition may be different from those involved in application, although there should be a common core frame if we are to talk about applying what has previously been learned. Moreover, the frames outside this core will in general be different in acquisitions that occurs in different times and situations. The core may evolve, adding new emergent structure, and old structures may also be modified or even deleted. Such modifications can also occur in situations of application, to such an extent that we can now regard the distinction between acquisition and application as rather artificial, being imposed by an outside observer for particular analytical purposes, rather than being intrinsic to the learning process itself. Of course, there should be mechanisms whereby frames that are used more often and/or that apply to more important situations, become easier to access. However, such mechanisms are different at the different levels of individuals, small groups, and large organizations; moreover, these mechanisms may fail, and in general, can be very complex. Hence we consider that they lie outside the cope of the formal aspects of UCT, although their study can be enriched by using ideas from UCT.

This approach applies to group learning processes, and to the sociotechnical networks of human and non-human "actants" (i.e., agents and mediators) that are studied in ANT. Moreover, it provides a natural framework for the evolution of conceptual systems, and the development of individuals, groups and organizations, as the process and result of successive integrations involving an identifiably shared (but evolving) core frame. Thus UCT calls for significantly expanding the networks envisioned by BT, to distribution over individuals and artifacts, as well as over space and time, rather than being confined to the minds of particular individuals at particular times. However, the explicit construction of integrated (blend) frames occurs (mainly) in individuals, and is (mainly) virtual for groups and organizations (an exception is if a small group writes a report, e.g. summarizing a meeting). Portions of the group blend are always instantiated by individuals, but individuals can also be entirely unaware of portions of the group blend that are distant from their concerns.

4. Values
Another novel feature of UCT is that it takes explicit account of the values (i.e., preferences, or constraints) of the components of networks. This appears in two related ways, the first of which is explicit (partial ordering) relations in the formal spaces, expressing the relative importance assigned to constituents of those spaces, and the second is the requirement that mappings and blends should preserve those value relations to the greatest extent possible. Our research has shown that many aspects of the optimality principles of BT can be subsumed under this kind of constraint, and in particular, that the styles of various literary texts (and other artifacts) can be explicated using such a theory.

Although this approach to values arose from attempts to apply BT and semiotics to problems in user interface design, they also fit very well with the "continuous chains of translation" from ANT, since what is translated along paths in an ANT network are the values of the actants involved; ANT postulates that the existence of such chains of translation is precisely what makes a network (such as that supporteing Pasteur's "germ theory" and practice of pasteurization) viable. UCT extends this insight to distributed frame networks in general, and to BT cognitive networks in paticular. In effect, this extension of ANT provides a very general theory of the sustainability of networks, such as large distributed collaborative research centers.

5. Perception and Mediation
Recent research on individual perception (e.g., vision) shows that it is far from being the passive reception of objectively existing constitutents of the real world. On the contrary, perception is a highly active and adaptive process, in which current expectations and prior knoledge are brought to bear, not only in interpreting sensory data, but also in selecting what data to interpret, and even in selecting where and how to collect data (e.g., where to focus the eyes). It seems very natural to view such activities as the ongoing construction of links between formal conceptual spaces and actual perceptual spaces, and hence as a form of low level, unconscious learning, during which newly acquired prototypes, schemas, and templates may be acquired along with their associations to formal conceptual structures, and then drawn upon for use in similar situation that may occur later. Of course, these low level processes are also highly integrated with higher level frame networks, to the extent that completely separating them is artificial. This kind of integration provides the basis for material mediation at the level of individuals.

6. Mathematical Models
This short note is not an appropriate place for technical details, but it does seem useful to sketch the kind of modelling language that has been developed for UCT, and to at least name some of the mathematical tools that it uses. BT conceptual spaces are theories in the technical sense of formal logic, consisting of declared constants and relations, plus axioms consisting of ground instances of relations. The semiotic spaces of algebraic semiotics (developed originally for user interface design applications) extend BT spaces with types, functions, arbitrary logical axioms, and some special relations to express preference (i.e., values). The frames of UCT are interpretations in the sense of model theory in formal logic, i.e., models that provide actual instances of the declared constants, relations, and functions, in a way that satisfies all the axioms; more generally, frames are indexed relations of satisfaction between theories and classes of models.

Recent work shows how to use this mathematical language to describe complex blends, such as the Buddhist monk blend of Fauconnier and Turner, and to explore their properties, especially the sometimes surprising consequences of various otherwise implicit assumptions. The language has also been used to explore properties of metaphors of time as space.

In addition to contemporary formal logic, the very abstract language and tools of category theory have been used to formalize other key concepts, including: mappings between conceptual spaces; mappings between frames; networks of spaces; networks of frames; blending of spaces; and blending of frames. Many general theorems can be stated and proved, offering further insights into BT, UCT, and their applications to learning.

7. A Speculative Example
Although full validation of the ideas proposed in this note would require extensive empirical research, it is not difficult to construct an artificial illustration of some of its main points.

Let us imagine a child learning the word "chair" and its associated concepts. The first experience might be something like its mother saying "Now we sit in our highchair", in a rich context that includes the actions of being seated in the chair by the mother, the mother's vocal tone and facial expression, visual and tactile perception of the chair, and what happens before and after the seating. Other encounters might have verbal tags such as "Now this is our potty chair", or "This is mommy's chair", again, all richly contextualized, but now also linked to the frames of prior encounters with this word, and eleciting integration with those frames, and a gradually evolving core frame.

Clearly, there is much more going on here than acquiring, storing, and retrieving a set of necessary and sufficient conditions for some real world object to count as a chair. There is the material mediation of the mother and of the various (and very different) chairs, as well as the spoken words themselves and the rich sensory-motor interactions with the environment. Moreover, the cognition involved is distributed, as is particularly clear when the child's understanding is initially only very partial, so that the mother's role in dominant. Values also play a key role in coordinating the actions in frames; these values include love for the mother, the necessities of the biological processes of eating and excreting, and the particular normative forms in which these are practiced in our culture. At some later stage, the child will be able to use the word "chair" more or less correctly, and will be able to execute the actions associated with the various kinds of chair with less and less assistance.

While this example is speculative, I think it does suggest that the various ingredients suggested in this note are indeed necessary for a comprehensive theory of what learning is and how it occurs. Moreover, our UCT approach to learning has significant implications for educational theory and practice, though this is not the place to explicate those. In addition, it suggests hypotheses and experiments to test them. But for the moment, I prefer to emphasize its potential as a stimulus to interdisciplinary discussion and building "chains of translation" among the various approaches to learning that it tries to unify.

  1. Joseph Goguen and Fox Harrell, Style as Choice of Blending Principles, in Style and Meaning in Language, Art, Music and Design, ed. by Shlomo Argamon, Shlomo Dubnov and Julie Jupp, proceedings of a symposium at 2004 AAAI Fall Symposium Series, Technical Report FS-04-07, AAAI Press, 2004, pages 49 to 56.

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