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Concepts
All distinguishable and identifiable "things" in DSB are called concepts. Individual concepts are defined entirely and only by the relationships they are involved in, they have no intrinsic properties or contents. Similarly, there is no single defined notion of reference; a concept may refer to any real world thing which fits with the relevant pattern of relations that the concept is involved in. Hence a concept is a variable, a universal or a place-holder in a structure. For a concept to refer to something, or be instantiated, there must be an interpreter who is interpreting the entire fabric or a sub-fabric and not just individual concepts.
- Created to mark a distinction.
- Have no intrinsic properties or contents (formal).
- Require an interpreter in order to refer.
- Can be an unbounded number of them (construction).
Within a single fabric, each concept must be involved in the tail of a relation that all others are not involved in for the concept to have been originally distinguished at all. Therefore, no concepts within a single connected fabric can be identical/equivalent except to themselves (Leibniz's Law). This notion relies on the uniqueness of relation tails. Equivalence of concepts is only meaningful between fabrics -- disconnected hypergraphs -- where again the notion of individual concept equivalence is impossible to determine without reference to the entire fabric. Concept equivalence can only be established by finding an isomorphism between one fabric and another. If one fabric is larger than the other then any such mapping is an extension and so the concept in the larger is an instance of that found in the smaller fabric. Only if two fabrics are identical in size and have an isomorphic mapping can the concepts -- and the entire fabric -- be said to be equivalent.
The process of interpretation involves the implicit and subjective addition of relations to a fabric. These relations are missing from the fabric being interpreted as they may have been considered irrelevant. However, the missing relations need to be added back in order to link this smaller fabric with a larger fabric. In effect, interpretation is the instantiation of a fabric into a larger fabric. This larger fabric may be the ``real world'' or may be another virtual fabric. Instantiation is the reverse of abstraction, both requiring an interpreter to add or remove relations from one fabric to another.
Concepts are implemented as Node IDs (NIDs). Each NID is a globally unique ID which is used when defining hyperarc relationships.