Distributed knowledge, implicit knowledge and cognitive holes

Distributed and implicit knowledge

The term distributed knowledge is normally applied to multi-agent systems.  It was originally introduced by Halpern and Moses (Knowledge and Common Knowledge in a Distributed Environment) and a good description is given by Fagin, Halpern et al. in Reasoning About Knowledge:

A group has distributed knowledge of a fact F if the knowledge of F is distributed among its members, so that by pooling their knowledge together the members of the group can deduce F, even though it may be the case that no member of the group individually

knows F. For example, if Alice knows that Bob is in love with either Carol or Susan, and Charlie knows that Bob is not in love with Carol, then together Alice and Charlie have distributed knowledge of the fact that Bob is in love with Susan, although neither Alice nor

Charlie individually has this knowledge. While common knowledge can be viewed as what “any fool” knows, distributed knowledge can be viewed as what a “wise man”—one who has complete knowledge of what each member of the group knows—would know.

It is interesting to note that Halpern and Moses had originally used the term implicit knowledge to describe the distributed knowledge defined above but decided to change it to avoid clashes with different usage in the literature. This is a pity because implicit knowledge seems to be the more apposite term. Through the phrase even though it may be the case that no member of the group individually knows, the definition given above admits two subtypes of distributed knowledge: that which is not possessed by any member of the group of agents; and that which is possessed by a least one member of the group. 

In the approach to teaching and learning being developed in kungkhies, the difference between these two types of distributed knowledge is so important that the term implicit knowledge has been reclaimed. 

Distributed knowledge is defined as the pooled knowledge of all the group. 

Implicit knowledge is defined as new knowledge that follows from or can be deduced from the distributed knowledge. 

This distinction becomes important when considering the distributed and implicit knowledge associated with the mind of a single student. In this case, the agents involved are different knowledge units in the one mind. Whilst the precise meaning of this statement will be discussed elsewhere, all teachers will recognise the situation in which a student knows A and B yet is unaware of the implicit knowledge C where (A + B → C).

The conversion of implicit knowledge into real knowledge is one of the fundamental processes of teaching and learning. 

Its formalisation creates interesting possibilities in the analysis of the development of pedagogical theories.

Why a cognitive hole?

The term cognitive hole in kungkhie theory was chosen in part for reasons of imagery and will no doubt elicit some antipathy in some who might find the concept (or its name) a bit unrealistic in the prevailing climate of connectionism.

However, it was also chosen partly due to the influence of something that Ernst von Glasersfeld was fond of pointing out. He said that you can’t use words to teach. How terribly odd—what else have we got? What he meant was that you can’t teach a concept simply by telling a student its name. What a teacher has to do is to provide signposts to the new concept. Knowledge lies this a-way. It is the job of a good teaching activity to both form a signpost and to encourage creation of the new knowledge.

This is what a good activity level in a kungkhie should do: form multiple sign-posts, ‘cognitive directors’, to where the new knowledge lies, to the construction zone—the cognitive hole.

Cognitive holes and implicit knowledge

The final justification for the cognitive hole is that it is very close, at least in certain circumstances, to the concept of implicit knowledge defined above. Due to its role (under whatever name) in the fields of computer science and epistemic logic (see, for example, Roelofsen, F. (2007), Distributed Knowledge), the concept becomes a useful crossover that will facilitate the illumination of human teaching and learning by the results of its bloodless counterparts.

A cognitive hole might be said to be an aliquot of implicit knowledge.

The kungkhie induces knowledge that surrounds the implicit knowledge and uses the activities to shunt a student’s cognitive processes to the path of converting implicit knowledge into real knowledge.

Implicit knowledge and learning design

Implicit knowledge now provides a useful design principle for learning design.

Learning design will be addressed here in the form of the kungkhie, but the propositions should apply to any form.

For this purpose it is useful to introduce the idea of proximal implicit knowledge. No precise definition is possible here, but by proximal implicit knowledge it is meant that the implicit knowledge should not be too far removed from the existing knowledge. There should not be too many conceptual steps required to reach it. (The point at which proximal implicit knowledge becomes distal implicit knowledge is always going to be a matter of judgement.)

And so, the design principle that emerges is as follows.

Knowledge associated with a given cognitive hole level of a kungkhie should contain proximal implicit knowledge derived from the knowledge associated with the cognitive hole level immediately below.

This principle, and others, for designing good kungkhies will be discussed elsewhere. However, it might be remarked here that this sort of approach will be what many teachers adopt naturally. Nevertheless, the result of this formalisation, at the very least, provides a formal way of analysing not only course creation and learning design but also wider concerns such as curriculum content and design.

A frame-based pedagogy

Semantic frames provide a useful means for representing knowledge. In the Mean Mythic Ferrets project knowledge is regarded as the capacity for action.

The central thesis of a frame-based pedagogy is that associated with each frame - a clearly individuated information structure - will be a corresponding cognitive functional unit whose purpose is to carry out the actions corresponding to the knowledge required to understand the frame.

In general these cognitive functional units will be composed of simpler functional units. One way of looking at this is that, corresponding to the semantic frame (information) network there is a corresponding action network.

This is not a particularly new idea, more a different perspective on existing theses in the literature of epistemology and cognitive science.

Daniel C. Dennett talks about thinking tools and virtual machines for carrying out particular kinds of thinking tasks: see his book Intuition Pumps and Other Tools for Thinking, for example.

Similar ideas can be found in the work of Douglas Hofstadter: see for example, his book, I Am a Strange Loop.

Jerry Fodor in his book, The Modularity of Mind, describes faculty psychology, in which the mind is considered to be comprised of a number of (innate) modules, or faculties, each responsible for a particular cognitive task.

The term cognitive tool is in widespread use (see, for example, information engineering blog) and is often taken to mean some mental device that aids cognition.

And so, define for each frame, a frame module or frame virtual machine or frame cognitive tool that is responsible for processing the information provided by a frame to produce actions that indicate that a sentient agent possesses the knowledge represented by the frame.

This frame virtual machine represents the class (b) of structural ingredients of the processes of an embodied cognitive agent in the following quote from Brian Cantwell Smith (Reflection and Semantics in a Procedural Language) :

Any mechanically embodied intelligent process will be comprised of structural ingredients that a) we as external observers naturally take to represent a propositional account of the knowledge that the overall process exhibits, and b) independent of such external semantic attribution, play a formal but causal and essential role in engendering the behaviour that manifests that knowledge.

A frame virtual machine represents the procedural aspects of knowledge. This will incorporate both cognitive processes and their external physical consequences. For example, the "add two integers" frame virtual machine would include functionality for carrying out an addition together with the ability to convey the result to another cognitive agent. At the very least the frame virtual machine will be able to express what the agent should be able to do, even if it does not yet have the organs to achieve this.

Three benefits

At least three major benefits can be accrued from a frame-based pedagogy.

Firstly, the functionality of each frame virtual machine is a set of actions which are the intended learning outcomes (ILOs) associated with each frame. Hence this approach requires that there is a coherent relationship structure between ILOs, a network of ILOs, in fact.

Secondly, since all frames sit in a semantic frame network, this allows a formal method of examining the relationships between ILOs, semantic frames and learning activities.

Thirdly, the coherent grouping of ILOs should provide guidance to the creation of learning activities in the process of learning design. For example, there is a natural convergence of ideas between, on the one side, frame virtual machines and, on the other, proximal implicit knowledge and cognitive holes in the kungkhies learning design method.