Goguen has proposed the use of semiotics to study the ways in which information is mediated in computer systems, particularly in user interfaces. His algebraic semiotics provides a formal tool for studying the systematic use of signs in computer systems, and for presenting formal comparisons of different interface designs. The formal elements of algebraic semiotics make it a kind of algebraic engineering for sign systems, and introduces an engineering rigour to interface design.This paper presents some applications of algebraic semiotics to the design of user interfaces. In particular, we study the kinds of signs used in interfaces, and how they work as signs. We present some basic notions from algebraic semiotics, namely sign systems and semiotic morphisms, and apply these concepts to the sign systems of user interfaces, which allows us to give rigorous argumentation why some representations are better than others.