**10. Emergence friendly rules for ontology**

22 Will-be-set-by-IN-TECH

user process of adding topics and associations converge to a graph that auto-selects a set of

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.

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

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

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

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

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'.

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

**Hypothesis 3** (Convergence of knowledge graph)**.** *A knowledge map will converge to a graph*

distribution of node degrees, see Barabási (2002); Newman et al. (2001).

*with a power-law degree distribution if a type-free context model is used.*

Let's sketch out how one might go about discovering whether this is possible.

attractors we might call popular 'well known concepts'?

(normation) takes place, see Burgess & Fagernes (2007a;b).

'attractor topics' in the manner of a hierarchy.

For a simple review, see , see Barabási (2002).

**9.1 Norms, swarms and attractors**

sketch out some of the issues.

user's perspective.

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

**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 existing universally as pure syntax.*

The beauty of this reinterpretation is that it does very little violence to existing technology, but extends the possible interpretation of the data in potentially valuable ways. Under this new regime, we can assume that:


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 simple syntactic fragments.

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

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 the cognitive cost for end users of information?

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

And the Emergence of Ontology 25

What's Wrong with Knowledge Management? And the Emergence of Ontology 173

The ability to replace a lot of complexity with a simple label brings great economic efficiency for end-users of knowledge, which one could measure in concepts per role. However, I believe that it is not the size of a group or role that is the best indicator for providing a reduction in perceived complexity, but rather the affinity that a receiver who promises to *use* this role's defining pattern feels for the concept. In other words, how well does a user identify with the

When things combine to play a collaborative role, a single recipient can use the promise as an entity, i.e. a 'black box'– and experience a cognitive simplification. The cost of understanding

The important point here, as we see repeatedly in this essay, is that it is the way that these terms are perceived by the user, i.e. the *usage* (not the definition) of these terms that is the crucial element here. If I talk about 'Mr Green' and understand this usage as a decription of the man's colour, and you interpret it to be a name, the intended implication will not be passed on. We therefore require a binding of terms or ontologies between different agents

**Definition 19** (Knowledge bindings)**.** *A binding occurs between the author of knowledge and the recipient when there is something in common between their promised interpretations. If the recipient's promised understanding of concepts about the original intention does not overlap at all with the*

The interpretation of knowledge made by a recipient clearly depends formally on both the original promised usage of terms by the author/promiser of the knowledge and whatever

It follows straightforwardly from promise theory that what is offered is only a pre-requisite. It is what is *accepted* or used by agents that is important. Clearly, it is true that knowledge that

How might we use this cost reduction approach by grouping things effectively for users? One approach might be to simply write down items, as suggested before, and wait for natural social processes to normalize usage into common knowledge, but this can take significant time and can lead to an explosion of new items. One would likely need to go back and re-organize the stored information later to eliminate redundancy. All this accomplishes, however, is to

While there might be optimum ways of approaching categorizations that reduce the cost of knowing everything, this suggests that there is an intrinsic cost to knowing something that is associated with the what the receiver of the knowledge has decided is an acceptable set of category bundles. This is such an important observation, it is worth turning it into a

**Hypothesis 5** (Knowledge has a minimum cost)**.** *There is an intrinsic minimum cost to comprehending information that depends on the complexity of the model used to interpret information*

This hypothesis harks of Shannon's entropy theorem for intrinsic information, and is almost certainly related through the definition of modelling 'alphabets', see Burgess (2004); Shannon & Weaver (1949). As Einstein remarked: everything should be made as simple as possible but

pattern?

this functional collaboration is greatly reduced.

*meaning promised by the author, then nothing will be communicated.*

delay the inevitable cost of organizing the information in the first place.

*by the recipient, i.e. the complexity of the recipient's use-promise.*

who engage in knowledge interactions.

terms the recipient has promised to accept.

**12. Making usage the knowledge enabler**

no one accepts or uses is valueless.

hypothesis

what I shall call *roles*, see Bergstra & Burgess (1994-now). A role is simply a group of things that identifies some pattern amongst knowledge items (agents). If these agents or topics make similar kinds of knowledge promises, then they must play a similar role in the scheme of things too. Put simply, a role is a bundle of topics that make similar knowledge promises.

Some examples help to make this clear. For instance, at a low level, different categories of words play certain roles in the construction of knowledge; e.g. some words promise to be verbs, some promise to be nouns or 'things', and so on. These roles are functional and therefore have a practical value. Next, one might have other roles, like 'colour' or 'animal', which are less clearly functional, but more an attempt to put a name on a perceived phenomenon.

We can define such roles simply in terms of the promises they make:

**Definition 16** (Promise role)**.** *A collection of agents or things that is assessed by a user as making the same kind of promise (or collection of promises).*

Patterns like this tie in with the use of repetition to emphasize learning, as mentioned before, and thus patterns are related to our notion of learning by rote.

Now, consider a different type of knowledge promise that is not about describing an intrinsic property of a single item, but is rather about interpreting the result of a collaboration between different promises that individuals might classify in very different ways. Take, for example, the concept of a radio. Someone might call a particular group of functional elements (e.g. electronic components) a radio. Each of the components promises certain properties like 'will act as a switch' or 'which store electric charge', if this collective set of components keeps the promise to play music from various radio stations, we might indeed call it a radio.

The attachment of a concept like 'radio' to a set of collaborating relationships is nothing like the naming that happens in a standard taxonomy: it is an interpretation, based on probably an incomplete understanding of the structure of the internal properties, based on a superficial evaluation of its behaviour. In a hierarchical decomposition one would separate the components into rigid categories like 'resistor', 'capacitor', 'transistor', or 'plastic' and 'metal', none of which say anything about what these parts contribute to.

A radio is thus an emergent property of a collaborative network of properties that has no place in a taxonomic categorization related to its parts. A radio is not more than the sum of its parts, as we sometimes like to say, but rather it forms a collaboration which comes alive and takes on a new interpretation at a different level. Typical taxonomic decompositions are reductionistic, leaving no room for the understanding of this as a collective phenomenon. This defect can really only be repaired if we understand that it is the *observer* or recipient, not the designer, that ultimately makes the decision whether to accept the assessment of a set of component promises is a radio or not.

#### **Definition 17** (Collective role)**.** *A collection of agents that is assessed to form a collaborative role, if the agents work together to keep a promise that requires the participation of all the agents collectively.*

The concept of a radio is clearly much cheaper to maintain as a new and separate entity than a detailed understanding of how the components collaborate to produce the effect. We frequently use this kind of information hiding to reduce the cost of knowledge, but clearly knowledge gets lost in this process.

**Definition 18** (Black box)**.** *The purposeful forgetting or discarding of knowledge in order to reduce the cost of accepting a collective role.*

24 Will-be-set-by-IN-TECH

what I shall call *roles*, see Bergstra & Burgess (1994-now). A role is simply a group of things that identifies some pattern amongst knowledge items (agents). If these agents or topics make similar kinds of knowledge promises, then they must play a similar role in the scheme of things too. Put simply, a role is a bundle of topics that make similar knowledge promises. Some examples help to make this clear. For instance, at a low level, different categories of words play certain roles in the construction of knowledge; e.g. some words promise to be verbs, some promise to be nouns or 'things', and so on. These roles are functional and therefore have a practical value. Next, one might have other roles, like 'colour' or 'animal', which are less clearly functional, but more an attempt to put a name on a perceived

**Definition 16** (Promise role)**.** *A collection of agents or things that is assessed by a user as making*

Patterns like this tie in with the use of repetition to emphasize learning, as mentioned before,

Now, consider a different type of knowledge promise that is not about describing an intrinsic property of a single item, but is rather about interpreting the result of a collaboration between different promises that individuals might classify in very different ways. Take, for example, the concept of a radio. Someone might call a particular group of functional elements (e.g. electronic components) a radio. Each of the components promises certain properties like 'will act as a switch' or 'which store electric charge', if this collective set of components keeps the

The attachment of a concept like 'radio' to a set of collaborating relationships is nothing like the naming that happens in a standard taxonomy: it is an interpretation, based on probably an incomplete understanding of the structure of the internal properties, based on a superficial evaluation of its behaviour. In a hierarchical decomposition one would separate the components into rigid categories like 'resistor', 'capacitor', 'transistor', or 'plastic' and

A radio is thus an emergent property of a collaborative network of properties that has no place in a taxonomic categorization related to its parts. A radio is not more than the sum of its parts, as we sometimes like to say, but rather it forms a collaboration which comes alive and takes on a new interpretation at a different level. Typical taxonomic decompositions are reductionistic, leaving no room for the understanding of this as a collective phenomenon. This defect can really only be repaired if we understand that it is the *observer* or recipient, not the designer, that ultimately makes the decision whether to accept the assessment of a set of component

**Definition 17** (Collective role)**.** *A collection of agents that is assessed to form a collaborative role, if the agents work together to keep a promise that requires the participation of all the agents collectively.* The concept of a radio is clearly much cheaper to maintain as a new and separate entity than a detailed understanding of how the components collaborate to produce the effect. We frequently use this kind of information hiding to reduce the cost of knowledge, but clearly

**Definition 18** (Black box)**.** *The purposeful forgetting or discarding of knowledge in order to reduce*

promise to play music from various radio stations, we might indeed call it a radio.

'metal', none of which say anything about what these parts contribute to.

We can define such roles simply in terms of the promises they make:

and thus patterns are related to our notion of learning by rote.

*the same kind of promise (or collection of promises).*

phenomenon.

promises is a radio or not.

knowledge gets lost in this process.

*the cost of accepting a collective role.*

The ability to replace a lot of complexity with a simple label brings great economic efficiency for end-users of knowledge, which one could measure in concepts per role. However, I believe that it is not the size of a group or role that is the best indicator for providing a reduction in perceived complexity, but rather the affinity that a receiver who promises to *use* this role's defining pattern feels for the concept. In other words, how well does a user identify with the pattern?

When things combine to play a collaborative role, a single recipient can use the promise as an entity, i.e. a 'black box'– and experience a cognitive simplification. The cost of understanding this functional collaboration is greatly reduced.

The important point here, as we see repeatedly in this essay, is that it is the way that these terms are perceived by the user, i.e. the *usage* (not the definition) of these terms that is the crucial element here. If I talk about 'Mr Green' and understand this usage as a decription of the man's colour, and you interpret it to be a name, the intended implication will not be passed on. We therefore require a binding of terms or ontologies between different agents who engage in knowledge interactions.

**Definition 19** (Knowledge bindings)**.** *A binding occurs between the author of knowledge and the recipient when there is something in common between their promised interpretations. If the recipient's promised understanding of concepts about the original intention does not overlap at all with the meaning promised by the author, then nothing will be communicated.*

The interpretation of knowledge made by a recipient clearly depends formally on both the original promised usage of terms by the author/promiser of the knowledge and whatever terms the recipient has promised to accept.

It follows straightforwardly from promise theory that what is offered is only a pre-requisite. It is what is *accepted* or used by agents that is important. Clearly, it is true that knowledge that no one accepts or uses is valueless.
