3.2.1 Formation rules and typed variables
Formation rulesspecify how lexical items are to be combined into larger units, and how these larger units in turn are
combined into still larger units. Phrase structure rules are the prototypical formation rules. An example is the rule for
Englishnoun phrases thatpermits theconstructionof unitslikethe little star. In the traditional notationit is writtenlike
this:^15
This is traditionally read“Noun Phrase goes to (is expanded as) a Determiner followed by an Adjective Phrase
followed by a Noun.”The application of this rule is reflected in two places within Fig. 1.1, shown by the circled parts
of the syntactic tree structure shown in (3).
The traditional way of reading (2) suggests that the construction of utterances is to be conceived as proceeding from
thetopdown: onestarts withS, expands itto NP followed by VP, and so on. Studentsare always reminded thatthisis
just an abstract way of characterizing a class of structures, and therefore rules like (2) are to be understood non-
directionally. Nevertheless, the aura of directionality remains in the notation, if only because of the arrow.
A more neutral notation for the same formation rule might be the tree fragment (4) (Janet Fodor has suggested the
term“treelet”).
COMBINATORIALITY 41
(^15) This rule is meantonly as a sampleand is heavilyoversimplified. As in Ch. 1. I a massu ming NP has aflat structure in whichits constituentsare simplyconcatenated. If the
structureis morecomplex,as isstandardlyassumed, thephrasestructure rulesmustbeadjustedaccordingly. I am alsoignoringthedistinctionbetween optionalconstituents
(the Det and the AP) and obligatory constituents (the N) as well as further possible constituents of NP such as postnominal PPs and relative clauses.