SAGE maintains a formal symbolic representation of the graphics it creates, in order to support the physics of the information world. A graphic representation consists of a number of spaces, within which spatial location is used to encode data attributes. For example, in a histogram, there is a space in which the y-axis encodes quantity and the x-axis encodes a discrete independent variable. The axes are called encoders because they maintain the relationship between data values and graphical values. Besides axis encoders, SAGE also uses color, saturation, length, lettering, shape, size, map, and network encoders.

The graphical elements within a space that carry the graphical values specified by the encoders are called graphemes. For instance, the histogram contains vertical bar graphemes, whose length parameter encodes quantity. Other types of graphemes include text, marks (or points), gauges, horizontal bars, and lines.

A single grapheme has many parameters. For instance, vertical bars have length, horizontal position, color, saturation, and outline color. The set of graphemes that encode the same data attributes in the same way are called a grapheme set. For instance, the set of all vertical bars in the histogram constitutes a grapheme set.

Multiple graphemes can be clustered together, and the cluster is called a symbol. A symbol set is a set of symbols that encode the same attributes the same way. For instance, a labeled bar is a symbol.

A symbol class is a prototype symbol. Symbol classes are hand-constructed to be useful combinations of graphemes. Symbol classes may also restrict the kind of data attribute that can map to each graphical attribute. For instance, the left and right graphical parameters of a horizontal interval bar are restricted to map to two data attributes that form an interval. For instance, the asking and selling price of a house form an interval, but the asking price and the salary of the owner don't. This is because there is no meaning to the intermediate values conveyed by the interval bar when the two data attributes don't form an interval.

Symbol classes are the primitive graphical languages known to SAGE. Complex graphics are built up by composing symbol classes. We have hand constructed many composition rules. For instance, single axis composition allows two symbol sets which use the same x-axis or y-axis to be combined. The resultant graphic contains two spaces which will be aligned. This picture can then be further composed with other spaces or grapheme clusters, using another single axis composition, or another rule. In this way, there is no fixed limit to the variety of graphical designs SAGE can produce.