2. ALGEBRAIC SEMIOTICS
Communication is mediated by signs, which occur in structured systems.
Semiotic systems are axiomatic theories for sign systems, including
Context, including the settings of signs, is as important for meaning as signs.
For example, ``Yes'' can mean almost anything, given appropriate context.
Algebraic semiotics treats aspects of context with constructors that put signs in larger signs.
But interpretation is still needed for meaning in human sense.
Also, algebraic semiotics should be used flexibly, like music notation in performance.
Design often views some signs as representing other signs,
and asks what makes some representations better than others.
Semiotic morphisms are maps of semiotic spaces that preserve significant properties.
E.g., a book table of contents preserves structure and names of parts, but not content.
Design is massaging a source space, a target space, and a morphism, to achieve quality, subject to constraints.
This applies to managing an organization, and designing a website.
Design principles include:
These principles all have precise mathematical formulations.