## 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?