# Alternative and extended formalisms

Even for exponence rules, there are nearly as many formats as there are realizational approaches. For the most part, the differences between formats reflect different ways of organizing thesamecontent. Thefollowing discussion thus summarizes the syntactic variation across rule formats then considers more substantive differences between the form and functioning of other rule types.

The information common to all exponence rule formats can be expressed as a triple (B,*X, o(X)),* where *B* is a bundle of features interpreted by the rule, *X *is an input form associated with B, and o(X) specifies an operation on X. The different formats simply group these elements in slightly different ways. The format in Matthews (1991) characterizes a rule as a relation between a feature-form pair (B,*X)* and an output form o(X), i.e. as ((B,X),o(X)). The formats in Anderson (1992) and Aronoff (1994) represent rules as relations between a bundle *B* and a ‘spell-out pair’ (X,o(X)), i.e. as (B, (X, o(X))). In the format proposed in Stump (2001), *X* occurs as an index on a rule that maps an input form-bundle pair (X, *a) *onto the output pair (o(X), *a*).