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i broadly recognize six ways in which information systems (including persons) represent knowledge.
type 1: monistic. monism is the absence of categorization of knowledge about something. in a given field, no categories are given, and criteria of the one present thing are assumed to be fundamentally universal. the book "Gödel, Escher, Bach" argues that zen buddhism prescribes favoring this type of knowledge, or absence thereof. this corresponds to the unit type with its single possible value. given this correspondence, it may or may not be useful to talk of a "type 0" corresponding to the bottom type and its absence of values, but here i am deciding against it, as informational structures with a bottom value by definition cannot exist.
type 2: multiplicity. a discrete collection of loose alternatives items are recognized, with no particular relation between any two items. this corresponds to booleans or enums.
type 3: spectrum. a continuous (or functionally continuous) range of items is recognized, or items are arranged linearly according to some scalar criteria. this corresponds to number ranges and other total orders.
type 4: multidimensional. items are no longer mapped along just one characteristic, but along a collection of characteristics. this could correspond to vectors in n-space, with a component on each dimension.
type 5: labelled graph. items are no longer related by a fixed number of criteria, but instead can be related by an arbitrary set of binary relations; edges between two nodes can be directed and labelled, but they are always either from one node to another or from one node to itself. a subset of labelled graphs is trees (which formats JSON, XML, or S-expressions are descriptions of), but there are many other types of graphs.
type 6: relational. the relation between multiple items are no longer strictly binary, but can apply to any discrete amount of items. i believe this to be the most general and powerful representation of knowledge; subsets of it can meaningfully encode another other type of knowledge representation. this is pretty equivelant to wolfram's directed hypergraphs (but not wikipedia-defined directed hypergraphs).
this post is of type 3: spectrum: i propose a discrete collection of possibilities, ordered by generality. i believe each type to be strictly more general than the ones before it.
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