One Representation to Rule Them All?
Thinking after property-graphs-vs-reified-graphset-graphs, the reified graphset-graph is not sufficient to represent e.g. an AST, because we want to have two nodes with the same ‘identity’.
Consider a chart displaying a regression with data points and credible intervals. We could represent this as a table or a graph but it’s not useful! The representation and rendering of information is an essential component of how humans can understand and apply it.
This entails accessibility issues: if someone has aphantasia or blindness, how do we best represent information/data?
Is there a single ‘language’ we can use to: unambiguously represent data/information; in a way that is intuitive to humans; and has semantics allowing computers to operate on it?
Need to deconstruct the semantics of various existing representations, find commonalities, and then construct a new language for both describing a representation, and specifying the semantics associated with each element of that representation.
Notations are (semi-)formal methods for reifying abstract concepts. Notational elements are the components of a notation and the rules for composing them. Concepts are ‘stuff in your head’? Representations are instances of notations which bind notational elements to concepts, and provide a way for individuals to communicate ideas through an agreed relationship between concepts and notational elements.
| Representation | Concept | Notational element | Notation |
|---|---|---|---|
| Abstract syntax tree | Expression | Vertex | Graph |
| Parameter | |||
| Literal | |||
| Order of parameters | Horizontal position | ||
| Order of operations | Directed edge | ||
| Hierarchy | |||
| Flowchart | Step | Vertex | Graph |
| Type of step | Shape | ||
| Order of operations | Directed edge | ||
| Bland-Altman plot | Mean | Axis | Scatterplot |
| Horizontal position | |||
| Difference | Axis | ||
| Vertical position | |||
| Observation | Point | ||
| Histogram | Bin | Axis | Bar chart |
| Horizontal position | |||
| Count | Axis | ||
| Bar height | |||
| Category | Colour | ||
| Pattern | |||
| Restaurant menu | Course | Heading | ??? |
| Grouping | |||
| Dish | ??? | ||
| Ingredients | ??? | ||
| Dietary suitability | Icon | ||
| Colour | |||
| Grouping | |||
| Price | ??? | ||
| IKEA instructions | Inventory | Drawing | Diagram? |
| Order of steps | Sequence | ||
| Numbering | |||
| Assembly | Arrow | ||
| Construction blueprints | ??? | ??? | ??? |
| World map | Latitude | Axis | Map |
| Longitude | Axis | ||
| Country | Outline | ||
| Colour | |||
| Label | |||
| River | Line | ||
| Colour | |||
| Label |
How does a musical score work? Is it a representation or a notation, or both?