For example, newspapers are composed from articles, ads, cartoons, tables, etc., while articles are composed from headlines, paragraphs, photos, diagrams, etc., and paragraphs are composed of sentences. In many examples, some constructors for signs of a given sort are more important than others. For example, a warning popup window is more important than a virtual pet cat. This gives rise to an ordering on the constructors for signs of a given sort, which we call the priority ordering. This is a partial ordering rather than a total ordering, since given two distinct constructors r 1 and r 2, it is not necessary that either one has priority over the other.
Axioms are logical formulae built from constructors, predicates, functions, etc.
A huge, even infinite, number of signs are possible in some systems, including natural languages, due to the recursive nature of rules for combining signs. Numerous linguistic studies have shown that the context, including the speaker and setting of a given sentence, can be at least as important for meaning as the words that are used. For another example, artificial intelligence has found that contextual cues are essential for recognizing and disambiguating signs in speech understanding and machine vision systems. The concepts of sort, attribute, level, constructor, and priority can all be used to specify systematic differences among signs, in the sense that Saussure emphasized. We now take some first steps towards formalizing the ideas that have been sketched intuitively.