< jpreston.xyz

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
  Order of parameters Horizontal position  
  Order of operations Directed edge  
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  
Restaurant menu Course Heading ???
  Dish ???  
  Ingredients ???  
  Dietary suitability Icon  
  Price ???  
IKEA instructions Inventory Drawing Diagram?
  Order of steps Sequence  
  Assembly Arrow  
Construction blueprints ??? ??? ???
World map Latitude Axis Map
  Longitude Axis  
  Country Outline  
  River Line  

How does a musical score work? Is it a representation or a notation, or both?