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.

Oilcan, lubricating the way to better learning outcomes

The Canonilo project uses semantic frames (FrameNet) to produce intended learning outcomes (ILOs) in standard forms. These standard forms can be visualised using the SNePS knowledge representation and reasoning software eg

In the course of Canonilo many guidelines have emerged for the production of ILOs that are clear to both human and robot.

Rather than just produce a list of these guidelines, a piece of software is called for, a tool that helps an educator to produce good ILOs.

Enter project Oilcan!

At the very least, Oilcan will be able to save thousands of hours of staff time taken up in development sessions on how to write good ILOs.

An Oilcan on every desktop!

Kungkhie Logic

A paper describing the theory underlying the kungkhies learning design platform has been made available: Kungkhie Logic.

This article provides an introduction to the theory on which the kungkhie learning design platform is based. First a simple predicate calculus of intended learning outcomes (ILOs) is presented. Superstudent is introduced, a perfect reasoner. Then the kungkhie is defined as a bipartite directed graph formed by a set of cognitive hole nodes, activity nodes and connecting arcs. The simplest kungkhie is provided as an example. Aspects of kungkhie validation related to ILOs are discussed. Definitions of distributed knowledge and implicit knowledge best suited for the development of theory related to teaching and learning in this context are given. The relationship between distributed knowledge, implicit knowledge and cognitive holes is briefly considered. 

The kungkhie aims were to produce a system of learning design that would be both simple to use from the points of view of teachers and learners, and also amenable to computer modelling and management.

Success in the former aim is helped by the simplicity of the kungkhie schema and the resultant straightforwardness of user interfaces.

Success in the latter aim will follow largely from the implementation of the theory presented in the Kungkhie Logic document.

The kungkhies platform is a meld of formal teaching and social learning. The formality arises from learning design: a set of learning activities along with guidance on the order they should be carried out.

The society arises from the ability of teachers and learners to pick, choose and publish their preferred activities for a particular kungkhie. The data on preferred activities is then used to produce popmax kungkhies, populated with the most popular activities, and recommended kungkhies, produced by The Kungkhommender, based on kungkher preferences.

To intelligently manage a learning design system one must have a handle on intended learning outcomes (ILOs). So how to formalise ILOs? At first reckoning the task might seem too complex, even with the aid of modern natural language processing software. It would take too long to try to create formal structures for each type of ILO - define, describe, explain...

But, someone else has already done the hard yakka.

It is Charles J. Fillmore and his FrameNet team at Berkeley. Their network of semantic frames provides formal structures for the ILOs. The formalisation process is then a combination of using regular expressions, natural language processing and artifical intelligence methods to produce representations of ILOs as semantic frames from an analysis of real world ILOs from specification documents.

Of course, the formalisation will not be perfect, but initial work seems promising. A description of the formalisation of ILOs will be presented in another article. The software behind the formalisation is to be found at Canonilo.

The potential rewards of intelligent ILO recognition are very great indeed.

Kungkhie Logic finishes with some remarks relating kungkhies to ideas from the computer science of knowledge representation. It is probably fair to say that there has not been a lot of linkup in evidence with the theory of human teaching and learning. Kungkhies can contribute here by providing formal representations of such things as perfect reasoners, distributed knowledge and implicit knowledge.

Go kungkhies!

Do robot snooker players dream of semantic frames?

As a result of the development of the kungkhies project [1,2] it has been discovered that intended learning outcomes (ILOs) can be formalized using the concept of semantic frames. This leads one to wonder how frames might be used to describe the academic curriculum rather than just the ILOs associated with a particular course. The advantage in doing this is that semantic frames naturally form a network that can represent relationships between curriculum content items better than the conventional method which is essentially to provide a list of statements.

A semantic frame is an information (or data) structure that describes an event, situation, concept, state of affairs, process or any other entity about which an information structure can be clearly individuated. The FrameNet project [3] has established a network of 1160 English language semantic frames. For example, the Giving frame has core frame elements of Donor, Recipient and Theme (the object given). In order to extend the semantic richness to cover usage in English language texts, additional non-core elements such as Circumstances, Manner and Means are also associated with the frame.

Putting FrameNet together has been an enormous task involving the hand-annotation of tens of thousands  of sentences from corpora. Whereas there are a handful of frames in FrameNet that are chemistry-related such as Thermodynamic_phase and Change_of_phase, a great deal of work would be required to extend the net to cover the knowledge represented by even a basic chemistry syllabus.

A good example of the difficulty involved in creating frames can be found at the first step. The most fundamental of chemistry frames must describe the meaning of the basic objects of chemistry - atoms, molecules and stuff in jars.

Let us go to the International Union of Pure and Applied Chemistry (IUPAC) for some initial guidance on meaning and look at their Gold Book [4], a compendium of chemical nomenclature compiled from various standards documents.

The terms that they define to describe the basic building blocks of chemistry are chemical substance, chemical species, chemical species of an element, molecular entity, atom and molecule.

The difficulties here are to distinguish between classes of entities and individual instances, and to distinguish between bulk quantities and individual microscopic units.

First take the classes: chemical substance, chemical species (include chemical species of an element as a subclass here)  and molecular entity.

The three Gold Book definitions are as follows.

chemical substance

Matter of constant composition best characterized by the entities (molecules, formula units, atoms) it is composed of. Physical properties such as density, refractive index, electric conductivity, melting point etc. characterize the chemical substance.

chemical species

An ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on the time scale of the experiment. The term is applied equally to a set of chemically identical atomic or molecular structural units in a solid array. For example, two conformational isomers may be interconverted sufficiently slowly to be detectable by separate NMR spectra and hence to be considered to be separate chemical species on a time scale governed by the radiofrequency of the spectrometer used. On the other hand, in a slow chemical reaction the same mixture of conformers may behave as a single chemical species, i.e. there is virtually complete equilibrium population of the total set of molecular energy levels belonging to the two conformers. Except where the context requires otherwise, the term is taken to refer to a set of molecular entities containing isotopes in their natural abundance. The wording of the definition given in the first paragraph is intended to embrace both cases such as graphite, sodium chloride or a surface oxide, where the basic structural units may not be capable of isolated existence, as well as those cases where they are. In common chemical usage generic and specific chemical names (such as radical or hydroxide ion) or chemical formulae refer either to a chemical species or to a molecular entity.

chemical species of an element

Specific form of an element defined as to isotopic composition, electronic or oxidation state, and/or complex or molecular structure. 

 molecular entity

Any constitutionally or isotopically distinct atom, molecule, ion, ion pair, radical, radical ion complex, conformer etc., identifiable as a separately distinguishable entity.Molecular entity is used in this glossary as a general term for singular entities,irrespective of their nature, while chemical species stands for sets or ensembles of molecular entities. Note that the name of a compound may refer to the respective molecular entity or to the chemical species, e.g. methane, may mean a single molecule of CH, (molecular entity) or a molar amount, specified or not (chemical species), participating in a reaction. The degree of precision necessary to describe a molecular entity depends on the context. For example "hydrogen molecule" is an adequate definition of a certain molecular entity for some purposes, whereas for others it is necessary to distinguish the electronic state and/or vibrational state and/or nuclear spin, etc. of the hydrogen molecule.

The first difficulty is that IUPAC's definition of chemical species is at odds with common usage.  In the daily life of a chemist it is used to categorize. One refers to a free radical reaction, for example, as having, say, 5 species involved, meaning 5 radicals of differing chemical constituency. [Note added April 2013: the handling of chemical species is described in https://code.google.com/p/mean-mythic-ferrets/wiki/ChemicalSpecies/ essentially the IUPAC definition together with the introduction of aomic chemical entities.]

And IUPAC defines a chemical element as

A species of atoms; all atoms with the same number of protons in the atomic nucleus.

This is not an ensemble. This reads like a species is a universal set.

The Chemical Information Ontology [5] does not use the term chemical species at all and has chemical entity as the top-level entry. Subclasses of this are molecular entity and chemical substance (the ensemble term).

The primary focus of the Chemical Information Ontology is chemical data rather than creating some sort of curricular knowledge base, and so it is not surprising that its classifications do not fit precisely the needs found here. For example, the meaning of molecular entity is retained to refer to both atomic and molecular objects. For curricular purposes, an atomic entity needs to be introduced.

And so, as a starting point, take ChemicalEntity as the base frame for chemical objects, which is inherited by AtomicChemicalEntity and MolecularChemicalEntity.

ChemicalSubstance will pertain to chemical objects to which the property amount applies, that is, bulk or ensemble quantities.

There will also be corresponding cardinality frames applying to specific atoms. For example, it is possible to use atomic force microscopes to manoeuvre individual atoms on an underlying surface. A cardinality frame would apply here to refer to atoms in a particular experiment.

The aim of the Mean Mythic Ferrets project is to create a semantic frame network for an A level chemistry curriculum.

References

1. kungkhies, http://code.google.com/p/kungkhies/
2. Canonilo, http://code.google.com/p/canonilo/
3. FrameNet, https://framenet.icsi.berkeley.edu/fndrupal/home
4. Gold Book, http://goldbook.iupac.org/index.html
5. Chemical Information Ontology, http://code.google.com/p/semanticchemistry/

After completing this blog, an assessment body will be able to...

...write effective intended learning outcomes.

As part of the Canonilo project, over 3000 chemistry-related intended learning outcomes (ILOs) were harvested from miscellaneous sources on the Web, but mainly from the specifications documents of the UK assessment boards for A-level and GCSE chemistry. Whilst the aim was to analyse these for syntactical and semantic structure, it was difficult not to notice how poorly many of the ILOs were expressed.

There are literally hundreds of guides on the Web on how to write good ILOs. Almost all of them make the recommendation that verb constructions such as understand..., understand that..., have an understanding of..., show an awareness of..., have an appreciation of... are to be avoided.

This advice is well-founded. Without going in to too much detail, the aim of using ILOs is essentially to maximise the common ground between teacher and student in the knowledge that they consider should be gained at the completion of a course of instruction.

The verb constructions mentioned above do not maximise the common ground. Student and teacher will not have a clear idea about what the other means by the expression understand that...

Hence the fact that ILOs should have at their heart dynamic verbs such as describe, define, state, list, calculate, and the rest of the usual suspects. The knowledge that a student must attain is now much clearer - it is the knowledge that enables him or her to describe, define, state, list and calculate...

Not all of the sources of the specification documents - AQA, CIE, CCEA, OCR, WJEC - were equally culpable. Some were very much better than others. However, one A-level specification document had around 30% of its ILOs starting with the verb understand: Understand the concept of..., Understand the importance of..., Understand how..., Understand that..., Understand qualitatively how...

The chemistry students involved are not being best served by this state of affairs.

Screamer them, Nifty!

It is well-known that a profitable strategy for getting funding from JISC is to think up a great title and then build a project round it. My top ten JISC project names countdown.

10.  SKOS-HASSET.  A Swedish processed meat project?

9.  SWORD-ARM. Oh, the silly billies.

8.  Bricolage.  Tres chic; trust the librarians.

7. AstroDAbis. This is a condition you get after staying up all night looking through a telescope.

6. SupOERGlue. And you need superglue to hold this contracted lexical acronym sandwich together.

5. BeRT.  Salt of the earth, they are, at Brockenhurst. (See ADAMS for middle-class version.)

4. Walking Through Time. Good wholesome stuff.

3. Blacklight in Hull.  Very sinister.

2. Bebop. Good oblique referential stuff.

1. Saving Private Data.  A while ago now - simply broke the mold.

And JISC itself gets a special award for naming a programme SWaNI. Guts.

All this tosh was inspired by the fact that I presently have a project to name. The possibilities are just too dire for some witty word play. The baseline is Chemistry Semantic Frame Network. CSFN? Do me a favour. ChemNet? Been done. SemChem? Sounds like an explosive. ChemSem? Naah. NetChem. It's just not there.

How about a bit of Latin? Reticulum for network. RetChem. ReticuChem. Chemiculum...well.. naah.

If shuffling the words around is not doing the trick then perhaps shuffling the letters will do better. So I put Chemistry FrameNet into an anagram machine to produce 3-word candidates. The results were superb.

Here's my top 5 countdown.

5. A Chemistry Ferment. Bit too sensible.

4. Ferryman Chest Mite. Nasty.

3. Amethyst Ferric Man. Very chemistique.

2. Cashmere Ferny Mitt. A bit sado-masochistic.

1. Mean Mythic Ferrets.

Has to be.