Relations

Relationships are formed between concepts, forming a structural pattern among a collection of concepts. The entire background structure forms what we have termed a fabric.

Definition

A relationship in DSB maps two concepts to a third. N-ary mappings from n-concepts to n-concepts can be decomposed into many 2-1 concepts. Any pair of concepts will deterministically map to a third and therefore tail pairs are unique. This tail uniqueness gives concepts their identity.

Higher-order Relations

Each relationship can be defined using another collection of relations forming a tree structure. These relations can themselves be defined in such a manner, resulting in nth order relations. Instead of object hierarchies and decomposition (resulting in reductionism) there is a hierarchy of relations where first-order relations (plain hyperarcs) are the axioms in the current system.

Both first and nth order relations can be changed, corresponding to changes in the axioms or definitions. The system will then maintain all other existing relations to be compatible with the new changes, resulting in a live exploratory environment where questions and ideas about axioms and rules can be explored. It is the high-order relations that enable this capability.