Knodules are not primarily designed to describe the world but to describe how people talk about the world. There is a common sense understanding that people sometimes use different words or expressions to meaning the same thing. Knodules are designed to articulate these human meanings and make them (partially) accessible to automated or interactive services and applications.
Every knodule applies to some limited domain of discourse and is organized around "disamgiguated terms" (dterms) that are just regular natural language words, phrases, or artificial compounds (like fish:animal). Knodules describe how words and phrases translate into dterms and describe relationships among dterms which can be used for search, inference, or other automatic processing.
Assertions about dterms are either synonyms (e.g. 'dog' can mean dog:animal), relations (e.g. labrador retriever is a kind of dog:animal), or asides (e.g. dog:animal is described by the wikipedia article "http://www.wikipedia.org/Dog".)
There are three core kinds of relations among dterms: logical relationships (e.g. 'a dog is an animal'), role relationships (e.g. 'Padme is the mother of Luke'), and associative relationships (e.g. 'gifts are often associated with birthdays' or 'mass is defined with respect to acceleration'). Knodule implementations can combine particular instances of these relations with one another to generate implied relationships, a process called inference.
Logical relationships are either 'identity relations' or 'subsumption relations'. Identity relations indicate that two dterms (possibly in different knodules) refer to the same thing (possibly in different aspects). Subsumption relations indicate a connection between the applicability of dterms: for example, if `X is a dog, X is always an animal'.
Identity relations have three flavors based on their degree of validity. Robust identity indicates identity relationships which can be used as logical equivalence for purposes of inference. Normal identity indicates identity which can be used in search and may be used for some inference. Dodgy identity indicates a relationship which can only be used in limited, speculative forms of inference or broad ranging searches.
Subsumption relations are loosely based on Aristotle's term logic and categorized into positive or negative relationships (e.g. 'dogs are always animals' or 'animals are never plants') and by three degrees of universality (e.g. 'dogs are always animals,' 'dogs are commonly pets', and 'dogs are sometimes big'). Negative relations are similarly categorized by universality (e.g. 'doctors are always people,' 'doctors are rarely criminals,' and 'doctors might not be rich'). There are simple rules for combining the logical relationships (in Aristotle's term logic, these are called syllogisms).
Role relationships are relationships which are described by dterms. Knodules are limited to two place relationships (such as 'Padme is the mother of Luke'). Some more complex relationships can be expressed by combining roles with subsumption, as in 'birth mother is a kind of mother' and 'Padme is the birth mother of Leia'. Role relationships can also be distinguished by whether they support multiple values (the default) and by the 'type' of their subjects and objects.
Associations represent relationships between concepts where the nature of the association does not correspond to a clearly defined role. There are three kinds of associations: differentiations are associations which define a dterm or distinguish it from other dterms; correlations are associations which are statistically significant; affiliations are distant associations which may not be statistically significant.
In addition to synonym (dterm/term) and structural (dterm/dterm) relationships, there are three additional properties which can be specified for a dterm: glosses, references, and drules.
Glosses are human-readble notes associated with particular dterms. Glosses are either definitive (they define the dterm), descriptive (they expand on the dterm, perhaps narrowing its scope or providing additional human-readable information), or incidental (any other kind of comment).
References are external references (typically URIs) which associated with particular dterms. They are also classified as definitive, descriptive, or incidental, along the same lines as glosses. For example, a definitive reference might point to a dictionary reference, a descriptive reference might point to an encyclopedia article, and an incidental reference might point to a site which refers to the concept.
DRules are rules for disambiguating human natural language into dterms. Every DRule consists of a natural language term (or set of terms) followed by other terms or dterms which indicate that the designated terms probably refer to a particular dterm. For example, a DRule might say that when 'dog' occurs with 'bark' it means dog:animal.