**7. The economics of knowledge**

The giving and receiving of promises quickly turns into a question of economics. There are motivations, incentives to act and costs involved in acting to keep promises. The economics of knowledge will be central to understanding both the weaknesses of current approaches to knowledge management, and the way towards a more 'natural' or less contrived approach. By taking an economic approach to the subject we join the ranks of scientific models in which rational modelling (or bounded rationality) is the explanation for motivations.

Knowledge management involves activities like the following:


The extent to which knowledge continues and grows in the minds of agents is therefore a question of the individual economic considerations of those agents. It costs little and brings rewards, knowledge will flourish. If the cost is too high, knowledge will not be maintained or spread.

The expected payoffs can be short term or long-term, and any human interpreting the value of a knowledge promise will form their own value-judgement based on how long they are willing to wait for a payoff. Through the promise model, there is a natural connection with economic game theory here, see Burgess & Fagernes (n.d.).

To model what we may expect of knowledge and its usefulness, we start by writing down the promises that are relevant, and what the benefits and costs of having these promises kept might be. Due to the subjective nature of promises, we can only suggest these things in broad terms, and it will remain for specific contexts to determine values for these things.

Agents (humans, machines or service centres, etc) can promise


#### **7.1 The value of promised knowledge**

12 Will-be-set-by-IN-TECH

the right generalization for 'bird' or 'fish', but not always. It is also true that information classified as applying in any context generalizes information true only in a special context. These are set relationships, not hierarchical ones. With a 'generalization promise', any topic can bear allegiance to a number of possible generalizations in different contexts, without

The survival of an ontology depends on its being used, which in turn depends on the agreement of all agents: i.e., keeping the promises to use the terms correctly, by all those

How does one know if a taxonomy (or technical ontology) has been a success? In our promise approach, we can simple measure this as the extent to which users keep the promises to

The giving and receiving of promises quickly turns into a question of economics. There are motivations, incentives to act and costs involved in acting to keep promises. The economics of knowledge will be central to understanding both the weaknesses of current approaches to knowledge management, and the way towards a more 'natural' or less contrived approach. By taking an economic approach to the subject we join the ranks of scientific models in which

• Disseminating knowledge, with cost of effort. This might be written off against the maintenance above, but it is normally a cost. Disseminating knowledge can also be considered a long term investment however – investing in others' educations, means that

The extent to which knowledge continues and grows in the minds of agents is therefore a question of the individual economic considerations of those agents. It costs little and brings rewards, knowledge will flourish. If the cost is too high, knowledge will not be maintained or

The expected payoffs can be short term or long-term, and any human interpreting the value of a knowledge promise will form their own value-judgement based on how long they are willing to wait for a payoff. Through the promise model, there is a natural connection with

To model what we may expect of knowledge and its usefulness, we start by writing down the promises that are relevant, and what the benefits and costs of having these promises kept might be. Due to the subjective nature of promises, we can only suggest these things in broad

terms, and it will remain for specific contexts to determine values for these things.

rational modelling (or bounded rationality) is the explanation for motivations.

Knowledge management involves activities like the following: • Acquiring knowledge, with associated gain and cost of effort.

economic game theory here, see Burgess & Fagernes (n.d.).

Agents (humans, machines or service centres, etc) can promise

• Retaining knowledge, a maintenance cost.

we might save on work down the line.

pre-designed limitations.

who participate in it.

support the ontology.

spread.

• To reveal information.

• To search for answers.

• To use information revealed to them. • To document or write down information.

• To train or teach others to interpret information.

**7. The economics of knowledge**

It is not easy to come up with a universal measure of value for knowledge, of course, but in the spirit of modelling that is what we are going to pretend. Since there is no standard for this, we are free to invent one based on the promise model.

**Definition 13** (The value of a promise)**.** *Let V*(*π*) *denote a function, which when applied to a promise π returns a real number with the interpretation of a payoff/return. A negative value represents a net cost associated with keeping the promise.*

Let us suppress, for now, the issue of when the payoff occurs, and assume that keeping the promise leads to rewards that we are accounting for far off in the future, at some final reckoning. We may add up values over the time each time the status of a promise is assessed, with values for:


However we choose to account for these values, they are perceived very clearly in our minds when we interact with knowledge.

The hypothesis I propose is then that it must be possible to increase the net value of knowledge by adopting some simple strategies.

**Hypothesis 1** (Increase value and reduce cost)**.** *Some principles:*


The cost of knowledge includes the work done acquiring, using, transmitting it, etc. If we use accounting terminology, it is a simple matter of time and materials. The cost of information retrieval or lookup by either a person or a computer is related to the algorithmic complexity of the search required to find it. This translates most likely into the time a user has to invest in accessing information.

The costs are probably quite different depending on the representation of the knowledge items one uncovers while searching. For instance a book is likely easier to interpret than a painting, As a general question we would like to know how such costs that inhibit the learning and dissemination of knowledge can be reduced.

#### **7.2 The cost of categories**

Classification into categories plays a central role in this essay because it has been such an important activity in knowledge engineering for centuries. Why is it so popular? It was introduced in order to cluster together books about similar subjects. The contention is that this reduces tangibly the cost of finding relevant information, assuming that you understand the classification in the first place4. Let us test this idea.

Suppose there are *T* topics divided into *C* categories. In a linear search (starting at the beginning and running through until we find the right one). If there is only one category, then the cost of finding a topic on average is about half the length of the search list:

$$\chi\_1 = \frac{1}{2}T \tag{2}$$

<sup>4</sup> Librarians are trained knowledge engineers who learn classifications and became smart assistants.

And the Emergence of Ontology 15

What's Wrong with Knowledge Management? And the Emergence of Ontology 163

A significant cost of working with knowledge thus comes from the need to anchor the topic in a particular place. If we could simply dump knowledge in a known location (e.g. treat every instance of the word as simply a word) then this can be done with essentially zero cost6. What this shows is that, from the perspective of someone wanting to contribute to knowledge, the presence of categorization adds a large cost deterrent to the activity. This is a plausible

This need to choose a unique category is major hindrance to creating the model, and getting data into the model. What if I make a mistake? Every programmer knows that putting data into the wrong class or structure causes huge problems down the line, so you'd better get it right! But wouldn't it be nice if you didn't have to be so careful? Isn't the computer supposed

Repetition is a key tactic in learning and training. Repetition serves two goals: to gather experience about the consistency of information, as well as confirming and reinforcing a fixed message, thus increasing its value. The scientific method, for example, is based on the idea

It will come as no surprise to anyone that merely documenting something cannot be viewed as an automatic strategy for increasing anyone's knowledge about it. Promising to write something does not imply an obligation on the part of a reader to read it. There must be a corresponding promise to read what has been written in order for it to be effective. Once read, knowledge must be remembered in order to be used. This suggests that there must be an

In economics one uses dilemma games, to estimate the trade off between short and long term strategies, see Burgess & Fagernes (n.d.). I have no comments to make on that here. What this suggests is the following: if we are to improve the actual utility of knowledge over time, then

**Hypothesis 2** (Knowledge requires practice)**.** *Any knowledge management scheme must*

Positive reinforcement is needed to turn information into knowledge, and this repetition

It is worth mentioning, as an addendum to the economic question, some limitations we should expect to bump into in knowledge engineering. Science always throws up certain scales that need to be attended to in understanding organized phenomena. The Dunbar numbers could

reason for the failure of ontology and semantic modelling so far today.

**7.4 The cost of knowledge maintenance: memory and repetition**

• An elected body must agree.

to help us, not the other way around?

approach for memory.

we have

incurs a cost.

**7.5 The Dunbar numbers**

There are three kinds of memory:

*encourage user to interact with it regularly.*

be such scales for Knowledge Management.

<sup>6</sup> This is the logic behind hash tables in computing.

that verification of knowledge increases its value.

• Rehearsed memory (e.g. muscle reflex memory).

• Short term memory (brute force, short-lived cramming). • Long term cognitive memory (associative pathways).

• Anyone can decide to change the categories.

If there are multiple categories, this generalizes to:

$$\chi\_{\mathbb{C}} = \frac{1}{2}T/\mathbb{C} + \frac{1}{2}(\mathbb{C} - 1) \tag{3}$$

So, if categories are to have any economic value,

$$\frac{1}{2}T/\mathcal{C} + \frac{1}{2}(\mathcal{C} - 1) < \frac{1}{2}T.\tag{4}$$

This gives us a quadratic constraint for *χ*, which is easily solved to give *T* > *C*. In other words, introducing categories is always likely to reduce search times a little for any number of categories, assuming that one knows which category the topic belongs to. The saving Δ*χ* = *χ<sup>C</sup>* − *χ*<sup>1</sup> actually shrinks with the number of categories however, since, if we write the total number of topics *T* = *t* + *C*, as there cannot be more categories than topics, then the saving is

$$
\Delta \chi = \frac{1}{2} (t - t/C),
\tag{5}
$$

where *t* is the number of 'pure topics', i.e. those that are not themselves subject categories. Δ*χ* gives a constant saving for large *C* at around half the number of non-categories. Thus the saving is not large if we go berserk with sub-categories. The cost does not depend on whether the topics are arranged in a flat partitioning or in a tree either5, so hierarchy does not help here either.

#### **7.3 Cost of adding a category: missing freedoms**

Categories form lists that we call directories, that we are still familiar with today (e.g. yellow pages, and Yahoo). These stem from a time when libraries were the most important search engine. Classification was conceived of as a cost saving mechanism, and for a few privileged scholars with more expert knowledge, it also worked to identify larger patterns that enhanced the meaning of the information. This worked because scholarly subjects were handled by a few well-trained people, and subjects were placed into relatively few categories or fields of study. There was little focus on overlap, more on the 'nobility' of knowledge.

For most users, however, the cost of categorization gets counted twice: both when using knowledge and contributing knowledge. The cost *χC*, above, is the cost of lookup, but also the minimum cost of adding something to the category structure, since placement requires us to parse the model to look up the right place to add something. There can be additional overheads:


The cost of agreeing on a change to the taxonomy depends on its governance, for instance:

• All agents must agree.

<sup>5</sup> The approach of introducing categories is similar to the use of hashing algorithms to locate values by replacing a linear search with a cheap constant-cost function that finds the approximate location of a value, but the difference is that there is no semantic hashing function to reduce the cost of finding subject categories in a list.

• An elected body must agree.

14 Will-be-set-by-IN-TECH

1 2

(*C* − 1) <

This gives us a quadratic constraint for *χ*, which is easily solved to give *T* > *C*. In other words, introducing categories is always likely to reduce search times a little for any number of categories, assuming that one knows which category the topic belongs to. The saving Δ*χ* = *χ<sup>C</sup>* − *χ*<sup>1</sup> actually shrinks with the number of categories however, since, if we write the total number of topics *T* = *t* + *C*, as there cannot be more categories than topics, then the saving is

where *t* is the number of 'pure topics', i.e. those that are not themselves subject categories. Δ*χ* gives a constant saving for large *C* at around half the number of non-categories. Thus the saving is not large if we go berserk with sub-categories. The cost does not depend on whether the topics are arranged in a flat partitioning or in a tree either5, so hierarchy does not help

Categories form lists that we call directories, that we are still familiar with today (e.g. yellow pages, and Yahoo). These stem from a time when libraries were the most important search engine. Classification was conceived of as a cost saving mechanism, and for a few privileged scholars with more expert knowledge, it also worked to identify larger patterns that enhanced the meaning of the information. This worked because scholarly subjects were handled by a few well-trained people, and subjects were placed into relatively few categories or fields of

For most users, however, the cost of categorization gets counted twice: both when using knowledge and contributing knowledge. The cost *χC*, above, is the cost of lookup, but also the minimum cost of adding something to the category structure, since placement requires us to parse the model to look up the right place to add something. There can be additional

• If a new category is needed, it must be localized and agreed upon by the authorized

The cost of agreeing on a change to the taxonomy depends on its governance, for instance:

<sup>5</sup> The approach of introducing categories is similar to the use of hashing algorithms to locate values by replacing a linear search with a cheap constant-cost function that finds the approximate location of a value, but the difference is that there is no semantic hashing function to reduce the cost of finding

1 2

(*C* − 1) (3)

(*t* − *t*/*C*), (5)

*T*. (4)

*<sup>χ</sup><sup>C</sup>* <sup>=</sup> <sup>1</sup> 2 *T*/*C* +

> 1 2

<sup>Δ</sup>*<sup>χ</sup>* <sup>=</sup> <sup>1</sup> 2

study. There was little focus on overlap, more on the 'nobility' of knowledge.

1 2 *T*/*C* +

If there are multiple categories, this generalizes to:

So, if categories are to have any economic value,

**7.3 Cost of adding a category: missing freedoms**

• A search for the correct category is required.

• If no category can be added, topics become orphaned.

designer of the taxonomy.

• All agents must agree.

subject categories in a list.

here either.

overheads:

• Anyone can decide to change the categories.

A significant cost of working with knowledge thus comes from the need to anchor the topic in a particular place. If we could simply dump knowledge in a known location (e.g. treat every instance of the word as simply a word) then this can be done with essentially zero cost6.

What this shows is that, from the perspective of someone wanting to contribute to knowledge, the presence of categorization adds a large cost deterrent to the activity. This is a plausible reason for the failure of ontology and semantic modelling so far today.

This need to choose a unique category is major hindrance to creating the model, and getting data into the model. What if I make a mistake? Every programmer knows that putting data into the wrong class or structure causes huge problems down the line, so you'd better get it right! But wouldn't it be nice if you didn't have to be so careful? Isn't the computer supposed to help us, not the other way around?

#### **7.4 The cost of knowledge maintenance: memory and repetition**

Repetition is a key tactic in learning and training. Repetition serves two goals: to gather experience about the consistency of information, as well as confirming and reinforcing a fixed message, thus increasing its value. The scientific method, for example, is based on the idea that verification of knowledge increases its value.

It will come as no surprise to anyone that merely documenting something cannot be viewed as an automatic strategy for increasing anyone's knowledge about it. Promising to write something does not imply an obligation on the part of a reader to read it. There must be a corresponding promise to read what has been written in order for it to be effective. Once read, knowledge must be remembered in order to be used. This suggests that there must be an approach for memory.

There are three kinds of memory:


In economics one uses dilemma games, to estimate the trade off between short and long term strategies, see Burgess & Fagernes (n.d.). I have no comments to make on that here. What this suggests is the following: if we are to improve the actual utility of knowledge over time, then we have

**Hypothesis 2** (Knowledge requires practice)**.** *Any knowledge management scheme must encourage user to interact with it regularly.*

Positive reinforcement is needed to turn information into knowledge, and this repetition incurs a cost.

#### **7.5 The Dunbar numbers**

It is worth mentioning, as an addendum to the economic question, some limitations we should expect to bump into in knowledge engineering. Science always throws up certain scales that need to be attended to in understanding organized phenomena. The Dunbar numbers could be such scales for Knowledge Management.

<sup>6</sup> This is the logic behind hash tables in computing.

And the Emergence of Ontology 17

What's Wrong with Knowledge Management? And the Emergence of Ontology 165

and jargon in special contexts. Context is therefore both highly important, and somewhat

Users further seek generalizations of things, because we all look for common patterns as a way of compressing a large number of special instances to a single representative category7. The danger is that we become obsessed with dividing and subdividing knowledge into precise categories, perhaps spurred on by a feeling that information will get lost if we don't put everything into exactly the right box. The problem with packing things into boxes, as many will have experienced, is how to find the right box again later as the number of boxes grows large. Moreover, we often change our minds about how to classify information so what was classified last year is not findable tomorrow unless we refresh our understanding of context. The first step in traditional classification schemes is to break things into a taxonomy. But a majority perhaps of concepts do not merely fall into just one category and so this artificial notion works against us once things go beyond the trivial. One has to either be an expert on a particular model of categorization or perform a brute-force search through the model to find

If we look more critically at the way humans think outside of what we've been taught in school, this is not what we do. Our minds tend to do the opposite: we generalize from little evidence into much broader categories, implying that we are not that consumed with

• Subject identifiers that point to explanatory documents and semantic relationships (*t*).

In my own testing of knowledge modelling, attempts to use typing of topics have proven excessively difficult, and have thrown up many conflicts and singletons from unnecessary repetition during modelling. The fixation on 'type', apparently shoehorned into ontology languages from the historical origins of database modelling, seems to have been both a red herring and an expensive hindrance to locating useful information. To see what we can replace

If knowledge is to be used and interacted with regularly, it will become the domain of a particular social group. Let's assume that such a group converges on a basic set of ideas.

**Definition 14** (Knowledge domain)**.** *An arbitrary set of topics used commonly by a group of users,*

Unlike the case of type annotation, there is no limitation on overlapping between different knowledge domains. The contention in topic map modelling is essentially that data-types model different cases. Again, this seems to flow more from a classic computer science dogma, based on some kind of entity relation model, rather than on a clear philosophy of the problem. In addition to a domain of knowledge, there is also the idea of usage in circumstances that are

**Definition 15** (Context)**.** *Any set of topics, either associated with one another or not, that describe*

A knowledge domain is then any set of topics claimed by a group of individuals.

governed by factors far outside of the domain itself, such as time and environment.

*the current situation of an agent when using or searching for information.*

<sup>7</sup> This is the basic approach behind all data compression.

neglected in knowledge research, see Deutsche (2006).

an obsessive compulsion for semantic correctness.

Topics play a dual role in the topic map standard, as:

• Context 'containers' or categories for other subjects (*C*).

**8.2 Topic type, a redundant concept**

type with, we need to define some terms.

*forming a cultural body of knowledge.*

the appropriate category.

Studies by anthropologists, interested in the origin of human intelligence, have demonstrated statistical evidence for the idea that our capacity to perceive and know things and people well is limited by our brain size, see Dunbar (1996); Zhou et al. (2004). The evidence for this assertion comes from studies of inter-human relationships, but from there it is not a huge stretch to imagine that similar limitations apply to any kind of learned acquaintance, such as acquaintance with knowledge in its various forms.

The so-called Dunbar hierarchy identifies some key numbers that suggest economics limits on level of intimacy we can have to knowledge, because more intimate knowledge has a greater cognitive cost. The precise implications for knowledge management are, as far as I know, not fully understood, but the following numbers can be expected to appear if the hypothesis is correct (parentheses describe the original inference).


Table 1. Key numbers from the Dunbar hierarchy, relating cognitive cost.

These numbers might appear anywhere cognitive cost plays a role. When presenting knowledge, for instance, we can expect people to have difficulty in relating to large numbers of choices and interrelationships, e.g. returned search results, number ingredients in an idea, number of steps in a recipe, etc. It would not be right to speculate unduly on how the Dunbar numbers might apply to knowledge management, but it is worth flagging this subject as worthy of further study.

### **8. From type hierarchy to overlapping contexts-acheaper solution to encourage participation**

Experience seems to show that users rarely contribute their own expertise back to projects that attempt to build taxonomies or strongly typed ontologies. It costs them too much. The same applies to Wikis that are organized hierarchically, because users either cannot find the right place to put something or they put it in the 'wrong' place, creating little value. The problem lies in quickly knowing how things should be organized in relation to one another.

Why is it so hard to know what topics should be related and how, to see what information is going to be needed and in which context? The answer is simply that this decision involves creative design. It is not a matter of pre-determined fact, but an arbitrary choice – but we don't like arbitrariness, so we look for agreement within a group or permission from an authority, etc. What started out as a simply desire to share, becomes an exercise in multi-party logistics. There is thus a significant 'mental computation' involved in this.

Suppose we could add a topic wherever we pleased, with some context to explain our usage. Then the cost of adding would be reduced by the entire cost of searching for the right place. Instead of an *O*(*N*) search, we have an *O*(1) insertion, costing the user little effort. Let's examine this idea further.

#### **8.1 The meaning of domain and context**

Users embellish facts with contextual information and want to emphasize certain aspects of knowledge. This freedom must be allowed in any account of KM. Terminology might begin as a set of unique terms, but quickly becomes distorted by ordinary linguistic creativity into slang and jargon in special contexts. Context is therefore both highly important, and somewhat neglected in knowledge research, see Deutsche (2006).

Users further seek generalizations of things, because we all look for common patterns as a way of compressing a large number of special instances to a single representative category7. The danger is that we become obsessed with dividing and subdividing knowledge into precise categories, perhaps spurred on by a feeling that information will get lost if we don't put everything into exactly the right box. The problem with packing things into boxes, as many will have experienced, is how to find the right box again later as the number of boxes grows large. Moreover, we often change our minds about how to classify information so what was classified last year is not findable tomorrow unless we refresh our understanding of context.

The first step in traditional classification schemes is to break things into a taxonomy. But a majority perhaps of concepts do not merely fall into just one category and so this artificial notion works against us once things go beyond the trivial. One has to either be an expert on a particular model of categorization or perform a brute-force search through the model to find the appropriate category.

If we look more critically at the way humans think outside of what we've been taught in school, this is not what we do. Our minds tend to do the opposite: we generalize from little evidence into much broader categories, implying that we are not that consumed with an obsessive compulsion for semantic correctness.

#### **8.2 Topic type, a redundant concept**

16 Will-be-set-by-IN-TECH

Studies by anthropologists, interested in the origin of human intelligence, have demonstrated statistical evidence for the idea that our capacity to perceive and know things and people well is limited by our brain size, see Dunbar (1996); Zhou et al. (2004). The evidence for this assertion comes from studies of inter-human relationships, but from there it is not a huge stretch to imagine that similar limitations apply to any kind of learned acquaintance, such as

The so-called Dunbar hierarchy identifies some key numbers that suggest economics limits on level of intimacy we can have to knowledge, because more intimate knowledge has a greater cognitive cost. The precise implications for knowledge management are, as far as I know, not fully understood, but the following numbers can be expected to appear if the hypothesis is

30 Daily working group size (tribe, workgroup, extended family, etc).

These numbers might appear anywhere cognitive cost plays a role. When presenting knowledge, for instance, we can expect people to have difficulty in relating to large numbers of choices and interrelationships, e.g. returned search results, number ingredients in an idea, number of steps in a recipe, etc. It would not be right to speculate unduly on how the Dunbar numbers might apply to knowledge management, but it is worth flagging this subject as

**8. From type hierarchy to overlapping contexts-acheaper solution to encourage**

Experience seems to show that users rarely contribute their own expertise back to projects that attempt to build taxonomies or strongly typed ontologies. It costs them too much. The same applies to Wikis that are organized hierarchically, because users either cannot find the right place to put something or they put it in the 'wrong' place, creating little value. The problem

Why is it so hard to know what topics should be related and how, to see what information is going to be needed and in which context? The answer is simply that this decision involves creative design. It is not a matter of pre-determined fact, but an arbitrary choice – but we don't like arbitrariness, so we look for agreement within a group or permission from an authority, etc. What started out as a simply desire to share, becomes an exercise in multi-party logistics.

Suppose we could add a topic wherever we pleased, with some context to explain our usage. Then the cost of adding would be reduced by the entire cost of searching for the right place. Instead of an *O*(*N*) search, we have an *O*(1) insertion, costing the user little effort. Let's

Users embellish facts with contextual information and want to emphasize certain aspects of knowledge. This freedom must be allowed in any account of KM. Terminology might begin as a set of unique terms, but quickly becomes distorted by ordinary linguistic creativity into slang

lies in quickly knowing how things should be organized in relation to one another.

There is thus a significant 'mental computation' involved in this.

acquaintance with knowledge in its various forms.

correct (parentheses describe the original inference).

worthy of further study.

examine this idea further.

**8.1 The meaning of domain and context**

**participation**

5 Detailed intimate interactions (close friends). 15 Team-level or frequent interaction (teams).

Table 1. Key numbers from the Dunbar hierarchy, relating cognitive cost.

100 Things we recognize and understand (acquaintances).

Topics play a dual role in the topic map standard, as:


In my own testing of knowledge modelling, attempts to use typing of topics have proven excessively difficult, and have thrown up many conflicts and singletons from unnecessary repetition during modelling. The fixation on 'type', apparently shoehorned into ontology languages from the historical origins of database modelling, seems to have been both a red herring and an expensive hindrance to locating useful information. To see what we can replace type with, we need to define some terms.

If knowledge is to be used and interacted with regularly, it will become the domain of a particular social group. Let's assume that such a group converges on a basic set of ideas. A knowledge domain is then any set of topics claimed by a group of individuals.

**Definition 14** (Knowledge domain)**.** *An arbitrary set of topics used commonly by a group of users, forming a cultural body of knowledge.*

Unlike the case of type annotation, there is no limitation on overlapping between different knowledge domains. The contention in topic map modelling is essentially that data-types model different cases. Again, this seems to flow more from a classic computer science dogma, based on some kind of entity relation model, rather than on a clear philosophy of the problem. In addition to a domain of knowledge, there is also the idea of usage in circumstances that are governed by factors far outside of the domain itself, such as time and environment.

**Definition 15** (Context)**.** *Any set of topics, either associated with one another or not, that describe the current situation of an agent when using or searching for information.*

<sup>7</sup> This is the basic approach behind all data compression.

And the Emergence of Ontology 19

What's Wrong with Knowledge Management? And the Emergence of Ontology 167

Underlying hierarchies and networks is the concept of *sets*. A set or *collection* of something is just a number of instances that satisfy some property. For example, the *set of all vending machines*, or the *set of times between 2 and 3 o'clock*. Sets can be thought of as networks in which the elements are all joined to each other by a common relationship 'in the same set as'. We often write subset membership using a membership '.' character, e.g. if linux is the set of hosts with property 'linux', then a subset (or sub-class) of these hosts is 'debian' (see figure). The class *64 bit hosts* is not a subset of linux, as part of it lies outside. It is a subset of *hosts*.

i.e. the commutativity of membership ordering. Hierarchies do not have this property. Sets can be made hierarchical when every subset is contained entirely by one and only one parent set, and in turn contains zero or more whole subsets which it does not share with any other. The problem with hierarchical sets is that they are too restrictive. If you design them incorrectly in the first place, you shut parts of the organization inside a box that prevents other

With sets, we can perform filtering based on logical reasoning, just as with search languages – but in a very efficient way. We can promise to association meanings by set-computation:

Thus the English speakers promise to identify themselves as those entities belonging to the

Henceforth, I will use the notation 'context::topic', e.g. 'X::Y' to mean a mention of a topic Y

Consider a slightly different case of 'homonyms', i.e. words that have multiple meanings in different contexts. As an example, I shall borrow from the Topic Map literature a fascination with opera as a knowledge domain, see Pepper (2009), by examining the topic "Peter Grimes" which is a character from a poem made famous through Benjamin Britten's acclaimed opera. What type or types should this topic have? We might interpret a mention of the name in

• One or more persons with the same name, e.g. 'names.friends::Peter Grimes',

usa.finance usa AND finance usa ∩ finance

Context sets have the property that usa.finance = finance.usa

parts from accessing them.

"english\_speaking"

**8.4 Topics in multiple contexts**

• As a name, e.g. 'names::Peter Grimes'.

'names.tv\_show::Peter Grimes'. • An opera, e.g. 'opera::Peter Grimes'.

expression => "(usa|uk).!legal";

USA 'OR' to the UK, excepting the legal department (! means NOT).

• A libretto from an opera, e.g. 'opera.libretto::Peter Grimes'. • A character from an opera, e.g. 'names.opera::Peter Grimes'.

classes:

in context X.

multiple ways:

Contexts are words and phrases we attach to a topic to disambiguate its usage. A context need not be either semantically or categorically related to the topic it describes. For example, the knowledge about 'tea' can be in the context of 'flavours', 'botany', 'drinking', 'suppliers', or even 'afternoon' none of which has any particular affinity to tea other than by association.

As mentioned above, it seems that, more by habit than reason, one has used a hierarchy of non-overlapping category types to disambiguate usage in different contexts. This seems to be a simple error of modelling. The problem is that it mixes up two different models unnecessarily: a description of generalizations or 'type' (which is forced unnaturally to be unique) and a model of brainstorming relationships to related things. We do not need a type to disambiguate usage, just another existing topic within the model, with no special status.

#### **8.3 Contextualization is not strongly ordered**

To illustrate why context is not at all hierarchical, consider this example of a geographically distributed organization, with finance, engineering and legal departments in three countries. Let us suppose that the organization has headquarters in 'usa', 'uk' and 'norway', and each branch has departments for 'finance', 'engineering' and 'legal' matters.

We have now two choices when making a hierarchy for the organization, depending on what we happen to think is of primary importance. In the first version, we treat geography as the primary distinction, and can express the full hierarchy like this:

```
usa.finance
usa.engineering
usa.legal
uk.finance
uk.engineering
uk.legal
norway.finance
norway.engineering
norway.legal
```
In this notation, the dot has the apparent interpretation of 'member' because the departments are smaller than the countries and are contained within them.

A different agent might feel that this model is upside down and that one should consider the finance department to be a unified global entity, with branches in three different countries. In that case, you would write

```
finance.uk
finance.usa
finance.norway
```
and so on. This example highlights the fact that we often want to slice and dice complex concepts in different ways, and attending too closely to a single hierarchical model prevents that.

If we think technically for a moment, the key observation is to notice that the '.' (dot) operator is really an intersection of sets (AND)8, and that this is a much more flexible notion than hierarchy.

<sup>8</sup> It is a commutative operator, which is why it makes sense to write both usa.finance and finance.usa.

Underlying hierarchies and networks is the concept of *sets*. A set or *collection* of something is just a number of instances that satisfy some property. For example, the *set of all vending machines*, or the *set of times between 2 and 3 o'clock*. Sets can be thought of as networks in which the elements are all joined to each other by a common relationship 'in the same set as'. We often write subset membership using a membership '.' character, e.g. if linux is the set of hosts with property 'linux', then a subset (or sub-class) of these hosts is 'debian' (see figure). The class *64 bit hosts* is not a subset of linux, as part of it lies outside. It is a subset of *hosts*.

usa.finance usa AND finance usa ∩ finance

18 Will-be-set-by-IN-TECH

Contexts are words and phrases we attach to a topic to disambiguate its usage. A context need not be either semantically or categorically related to the topic it describes. For example, the knowledge about 'tea' can be in the context of 'flavours', 'botany', 'drinking', 'suppliers', or even 'afternoon' none of which has any particular affinity to tea other than by association. As mentioned above, it seems that, more by habit than reason, one has used a hierarchy of non-overlapping category types to disambiguate usage in different contexts. This seems to be a simple error of modelling. The problem is that it mixes up two different models unnecessarily: a description of generalizations or 'type' (which is forced unnaturally to be unique) and a model of brainstorming relationships to related things. We do not need a type to disambiguate usage, just another existing topic within the model, with no special status.

To illustrate why context is not at all hierarchical, consider this example of a geographically distributed organization, with finance, engineering and legal departments in three countries. Let us suppose that the organization has headquarters in 'usa', 'uk' and 'norway', and each

We have now two choices when making a hierarchy for the organization, depending on what we happen to think is of primary importance. In the first version, we treat geography as the

In this notation, the dot has the apparent interpretation of 'member' because the departments

A different agent might feel that this model is upside down and that one should consider the finance department to be a unified global entity, with branches in three different countries. In

and so on. This example highlights the fact that we often want to slice and dice complex concepts in different ways, and attending too closely to a single hierarchical model prevents

If we think technically for a moment, the key observation is to notice that the '.' (dot) operator is really an intersection of sets (AND)8, and that this is a much more flexible notion than

<sup>8</sup> It is a commutative operator, which is why it makes sense to write both usa.finance and

branch has departments for 'finance', 'engineering' and 'legal' matters.

primary distinction, and can express the full hierarchy like this:

are smaller than the countries and are contained within them.

**8.3 Contextualization is not strongly ordered**

usa.finance usa.engineering

usa.legal uk.finance uk.engineering

uk.legal

norway.finance norway.engineering

that case, you would write

norway.legal

finance.uk finance.usa finance.norway

that.

hierarchy.

finance.usa.

Context sets have the property that

```
usa.finance = finance.usa
```
i.e. the commutativity of membership ordering. Hierarchies do not have this property. Sets can be made hierarchical when every subset is contained entirely by one and only one parent set, and in turn contains zero or more whole subsets which it does not share with any other. The problem with hierarchical sets is that they are too restrictive. If you design them incorrectly in the first place, you shut parts of the organization inside a box that prevents other parts from accessing them.

With sets, we can perform filtering based on logical reasoning, just as with search languages – but in a very efficient way. We can promise to association meanings by set-computation:

```
classes:
 "english_speaking"
     expression => "(usa|uk).!legal";
```
Thus the English speakers promise to identify themselves as those entities belonging to the USA 'OR' to the UK, excepting the legal department (! means NOT).

Henceforth, I will use the notation 'context::topic', e.g. 'X::Y' to mean a mention of a topic Y in context X.

#### **8.4 Topics in multiple contexts**

Consider a slightly different case of 'homonyms', i.e. words that have multiple meanings in different contexts. As an example, I shall borrow from the Topic Map literature a fascination with opera as a knowledge domain, see Pepper (2009), by examining the topic "Peter Grimes" which is a character from a poem made famous through Benjamin Britten's acclaimed opera. What type or types should this topic have? We might interpret a mention of the name in multiple ways:


And the Emergence of Ontology 21

What's Wrong with Knowledge Management? And the Emergence of Ontology 169

represents => { ''The complete score of the opera''};

In our new set interpretation, the sub-set operation '.' is commutative and reflexive. So it doesn't matter if we consider peter\_grimes to the the superset or opera to be the super-set. Suppose however that the first book contains the complete text of the libretto and the etymology of the name, an explanation of the poem, etc. Then it is relevant to all these contexts, or indeed in a generic context 'any' and should appear in the results of any search. If we interpreted opera,libretto,poem,name as type categories that do not overlap (e.g. as a conventional topic map) then it would be necessary to register this book as an occurrence in every single category – i.e. with multiple registrations; that is because the combination type+topic is a unique entity, and thus multiple types significantly increases the cost of documenting this information for users. The overlapping set model collapses all these registrations into one, but is not broken by multiple references, so we achieve two things: a

Using context sets, we have many more possible ways to give useful information. Suppose we search for peter\_grimes.opera, returning results for peter grimes in any category is generally more helpful than unhelpful to a human being. The issue then becomes for whom are the results intended? If we admit that humans play a role in the process (because they are far superior reasoning agents than software) then a freer interpretation is the correct one. This

Conversely if machines are to do all the work, users must have access to a complete and mathematically correct technical ontology, with type-correct documentation to yield precise search results. The only way to address this is the Topic Maps standard is the introduction of a search language, which pushes the complexity back onto the user, violating the first principle. The user is forced to fight the logic of the system rather than using it for inspiration. In practice it is rare that we want to restrict information so stringently as through a logic of types – and when we do so, we often end up finding nothing because the data are so over-constrained that the intersection of all constraints is the empty set. We need to simplify all this structure

An interesting and highly relevant question is thus the following: given a free approach to ontology, based on context rather than a pre-arranged taxonomy of types, would a free

represents => { ''Book about the opera''};

represents => { ''The origin of the name''};

reduction in cost of inserting data, and robustness to inserting multiple times.

**9. Emergent norms and common knowledge – the recipient's view**

requires less expertise to set up and leads to better results.

occurrences:

drastically.

peter\_grimes.opera::

peter\_grimes.name::

''http://names.com''

''http://onlinebooks.com''

''http://onlinescores.com''

• A character in a poem (The Borough) on which the opera was based, e.g. 'names.poem::Peter Grimes'.

And so on. The list is potentially infinite.

Fig. 4. A single topic, like 'Peter Grimes' is really a linguistic element, that has usage in many different contexts. Arranging topics in a tree confuses context with parent-node, which is wrong.

The desire for simplicity and parsimony encourages people to think about topics as falling into neat, mutually exclusive categories, but what we see is really something with a much more linguistic freedom: a single phrase 'Peter Grimes' used in a wide variety of overlapping contexts, with slightly different meanings.

At this point, most people feel an uncomfortable need to anchor the righteous place of each usage in their model by making an exclusive choice. Suppose this is to place this name within the category of opera, along with Aida and The Ring cycle, etc, but what criterion does one have for deciding on types? In fact, a type is just a topic itself, and the entire type notion could be eliminated in favour of an association: Aida "is an" opera, as one does in an object oriented model approach.

#### **8.5 Reasoning about categories in searches**

Consider occurrence of text for different interpretations of Peter Grimes. There is a book of the libretto

20 Will-be-set-by-IN-TECH

• A character in a poem (The Borough) on which the opera was based, e.g.

Things

Man

Art Names

Poems Books Operas Mark Peter Grimes

Fig. 4. A single topic, like 'Peter Grimes' is really a linguistic element, that has usage in many different

The desire for simplicity and parsimony encourages people to think about topics as falling into neat, mutually exclusive categories, but what we see is really something with a much more linguistic freedom: a single phrase 'Peter Grimes' used in a wide variety of overlapping

At this point, most people feel an uncomfortable need to anchor the righteous place of each usage in their model by making an exclusive choice. Suppose this is to place this name within the category of opera, along with Aida and The Ring cycle, etc, but what criterion does one have for deciding on types? In fact, a type is just a topic itself, and the entire type notion could be eliminated in favour of an association: Aida "is an" opera, as one does in an object oriented

Consider occurrence of text for different interpretations of Peter Grimes. There is a book of

contexts. Arranging topics in a tree confuses context with parent-node, which is wrong.

'names.poem::Peter Grimes'. And so on. The list is potentially infinite.

Peter Grimes

contexts, with slightly different meanings.

**8.5 Reasoning about categories in searches**

model approach.

the libretto

```
occurrences:
  peter_grimes.opera::
    ''http://onlinebooks.com''
        represents => { ''Book about the opera''};
    ''http://onlinescores.com''
        represents => { ''The complete score of the opera''};
  peter_grimes.name::
     ''http://names.com''
        represents => { ''The origin of the name''};
```
In our new set interpretation, the sub-set operation '.' is commutative and reflexive. So it doesn't matter if we consider peter\_grimes to the the superset or opera to be the super-set. Suppose however that the first book contains the complete text of the libretto and the etymology of the name, an explanation of the poem, etc. Then it is relevant to all these contexts, or indeed in a generic context 'any' and should appear in the results of any search.

If we interpreted opera,libretto,poem,name as type categories that do not overlap (e.g. as a conventional topic map) then it would be necessary to register this book as an occurrence in every single category – i.e. with multiple registrations; that is because the combination type+topic is a unique entity, and thus multiple types significantly increases the cost of documenting this information for users. The overlapping set model collapses all these registrations into one, but is not broken by multiple references, so we achieve two things: a reduction in cost of inserting data, and robustness to inserting multiple times.

Using context sets, we have many more possible ways to give useful information. Suppose we search for peter\_grimes.opera, returning results for peter grimes in any category is generally more helpful than unhelpful to a human being. The issue then becomes for whom are the results intended? If we admit that humans play a role in the process (because they are far superior reasoning agents than software) then a freer interpretation is the correct one. This requires less expertise to set up and leads to better results.

Conversely if machines are to do all the work, users must have access to a complete and mathematically correct technical ontology, with type-correct documentation to yield precise search results. The only way to address this is the Topic Maps standard is the introduction of a search language, which pushes the complexity back onto the user, violating the first principle. The user is forced to fight the logic of the system rather than using it for inspiration. In practice it is rare that we want to restrict information so stringently as through a logic of types – and when we do so, we often end up finding nothing because the data are so over-constrained that the intersection of all constraints is the empty set. We need to simplify all this structure drastically.

#### **9. Emergent norms and common knowledge – the recipient's view**

An interesting and highly relevant question is thus the following: given a free approach to ontology, based on context rather than a pre-arranged taxonomy of types, would a free

And the Emergence of Ontology 23

What's Wrong with Knowledge Management? And the Emergence of Ontology 171

We are not able to say what result a graph will converge to as users add associations and

We identify semantic 'votes' for discrete subjects, although many of the concepts might view things less precisely, living only in the suburbs of these concept's centra. Any suitable model must account for this uncertainty, and multiplicity of viewpoints (a town can have many

Let's summarize what minor changes to, say Topic Maps, are needed to encourage spontaneous ontology, and lower the cost of knowledge development. The data model for topic maps contains no major errors or omissions, but it contains one unnecessary constraint that makes topic maps hard to build models with. That is the constraint that topic types

**Hypothesis 4** (Correction of Topic Maps)**.** *We replace non-overlapping types with overlapping contexts so that a topic can belong to more than one contexts. Topic types become contexts, and topic names are registered only once, with associations and occurrences belonging to contexts, and topics*

The beauty of this reinterpretation is that it does very little violence to existing technology, but

• Only topic associations need be explicitly promised, including in which context they are

• The context of a topic (i.e. the usage of the term or phrase) explains its semantics, not a

The 'current context' in a topic search, for instance, can be assumed from the path taken by the user through the history of topics, etc. This also motivates the idea of stories below. The transition from selection by taxonomic classification to selecting topics by usage is subtle but wide ranging. It's not what the topic is, but how the term is used that is important. In other words, topics themselves are reinterpreted from labelled semantic concepts to being

The Dunbar numbers, mentioned previously, suggest that cognitive complexity is related to the number of things we need to (promise to) know at different levels of intimacy. So a relevant economic question is: how can we reduce this number of items, and thereby reduce

Categories are clearly an attempt to do reduce the numbers by providing umbrella concepts, but their introduction is often overwhelmed by hiearchical design issues. I believe that too great an emphasis is placed on the hierarchical aspect of the taxonomic category trees. Promise theory's basic tenets lead to a suggestion for this reduction that is simpler: spanning sets – or

extends the possible interpretation of the data in potentially valuable ways.

relevant, i.e. in which context a topic promises certain properties.

classification of its type within a separate ontological spanning tree.

**11. Roles and collective promises – user-perceived black boxes**

• An arbitrary choice by policy of a desired outcome for the meaning of a norm. • An attractor or potential surface with a unique minimum, e.g. based on popularity.

topics.

districts).

**10. Emergence friendly rules for ontology**

*existing universally as pure syntax.*

simple syntactic fragments.

Under this new regime, we can assume that: • All topics exist, whether defined or not.

the cognitive cost for end users of information?

should be non-overlapping categories, see Kipp (2003).

user process of adding topics and associations converge to a graph that auto-selects a set of attractors we might call popular 'well known concepts'?

It is tempting to answer: yes, this must be so, since our natural language evolves in basically this way, and seems to have achieved just that. However, we also know from natural language that, when a sufficient number of individuals is involved, languages fragment and sub-cultures emerge. All of these things are natural from a network point of view however. Let's sketch out how one might go about discovering whether this is possible.

#### **9.1 Norms, swarms and attractors**

We would like to know if a group of agents, making no promises to obey a predetermined ontology, would effectively promise to follow an emergent ontology after a sufficient amount of time. Understanding this hypothesis fully goes beyond the scope of this essay, but we can sketch out some of the issues.

The concept of emergent behaviour is tied to so-called swarm intelligence, see Bonabeau et al. (1999) and has enjoyed a fashionable period over the past 20 years. It has brought both insight and a lot of hype to modelling. Let us focus on a simple promise model of swarming that attempts to bring a simple but clear meaning to how swarming and emergent norm-formation (normation) takes place, see Burgess & Fagernes (2007a;b).

A swarm is simply a flock of agents (birds, insects, etc) that seem to exhibit collectively organized behaviour, even though each of the agents is a free entity with only weak links to its nearest neighbours. Swarms often come together to minimize costs of some kind, e.g. the cost of protecting each agent against predators. We call such behaviour 'emergent' because it is not explicitly designed, but is perceived as a side effect of something else, by a particular user's perspective.

In promise theory, emergent behaviour is explained by noting the indistinguishability of certain collections promises from others. Without getting into details, we say that a system has emergent properties if it seems to promise something, from the viewpoint of an external observer who in scope, that in fact it does not explicitly promise, see Burgess & Fagernes (2007a) In the same way, it is possible for a knowledge model to make no explicit design promises about category and yet still form a structure that appears to cluster around certain 'attractor topics' in the manner of a hierarchy.

The spontaneous formation of hierarchies is a relatively well-known phenomenon in network science, see Newman et al. (2001); Watts (1999) and is related to the 'small worlds' phenomenon. This could provide an explanation for the preponderance of attention given to hierarchical organization. Put simply, what happens is that certain early-defined topics acquire an economic advantage to being used. Topics that have the most associations and usage tend to attract even more attention, and therefore acquire the status of an anchor point or emergent category for knowledge. This phenomenon is called 'preferential attachment'. For a simple review, see , see Barabási (2002).

What is exciting about this model is that it can be tested by looking at the statistics of the graphs that result from such a free collaboration. Preferential attachment leads to long-tailed or power-law distributions in the node degree *k* of the association graph, of the form *<sup>N</sup>*(*k*) <sup>∼</sup> 1/*kn*, for some *<sup>n</sup>*, whereas a designed hierarchy would likely show a much sharper distribution of node degrees, see Barabási (2002); Newman et al. (2001).

**Hypothesis 3** (Convergence of knowledge graph)**.** *A knowledge map will converge to a graph with a power-law degree distribution if a type-free context model is used.*

We are not able to say what result a graph will converge to as users add associations and topics.


We identify semantic 'votes' for discrete subjects, although many of the concepts might view things less precisely, living only in the suburbs of these concept's centra. Any suitable model must account for this uncertainty, and multiplicity of viewpoints (a town can have many districts).
