This chapter proposes a generalized paradigm function (GPF), comprising four separate functions defined over each of the four attributes of the lexical entry, FORM, SYN, SEM, LI, and mapping a pairing of 〈LI, {feature set}〉 to some representation. In the case of vanilla inflectional morphology the GPF applies trivially to the SYN, SEM, LI attributes and introduces no change. It therefore reduces to the paradigm function of classical PFM. However, for regular and productive derivational morphology the generalized paradigm function introduces non-trivial changes to all four attributes, including the lexemic index, LI, thus defining a new lexeme in the lexical database. The GPF is also deployed to define the notion ‘lexical entry’ itself: the FORM, SYN, and SEM components are defined over a pairing of the LI and the empty or unspecified feature set, u, so for the two homophonous verb lexemes DRAW1 and DRAW2, the FORM is defined as FORM(DRAW1, u) = FORM(DRAW2, u) = /draw/, while the SEM functions deliver distinct semantic representations for the two lexemes. The model includes a default principle specific to lexeme(LI)-changing morphology, the Derived Lexical Entry Principle: where a generalized paradigm function defines a new LI, either the properties are specified directly by the appropriate component of the generalized paradigm function, or they are replaced by underspecified values. For instance, if DRIVER has a SEM value ‘person who drives (something)’, the SYN attribute and the inflectional properties of the derived lexeme are replaced by the empty property set u. By the ‘Default Cascade’ the derived word will default to a noun syntactically (since DRIVER is ontologically a Thing) and hence morphologically to a noun. Inflecting words are given a morpholexical signature, which defines their morphological category and the features they inflect for. By default, this signature is derived from the SYN representation, but that default can be overridden to account for mismatches (e.g. nouns that inflect like adjectives). The GPF can now be used to define all the intermediate types of lexical relatedness. For instance, a transposition introduces non-trivial changes to the FORM and SYN attributes without changing the SEM and LI attributes, while meaning-bearing (inherent) inflection changes the FORM and SEM attributes without changing the SYN and LI attributes.