Representational Purity
In the previous post, I said that
[attaching] linearization instructions to the individual features [..] contaminates the representation, combining true syntactic and merely interface information
To allay any confusion: I do not see this ‘representational contamination’ as a ‘real’ problem. It is simply notation. However, notation seems to have an ability to confuse humans, as we tend to confuse notation with some underlying reality. It is also sometimes useful for purposes of understanding to be able to cleanly separate different kinds of information in a representation. Our lexical items carry different kinds of information. They have information about what kinds of dependencies they will enter into (their features, with feature names, and feature polarity), the have information about the order in which they will enter into these dependencies (the linear order among features), and now they have information about the relative word order of the expressions with which they enter into dependencies with.
All of this information is logically distinct, and so we can attempt to seperate it all. Consider for example a lexical entry for the tense head will. Will takes a vP complement, assigns case, and is selectable as a TP, in that order. Using the notation from last time, we can write this as follows: \[\textsf{will}: \bullet\hspace{-.5pt}v.k\hspace{-.5pt}\bullet.t\] We can seperate the different kinds of information as shown below.
| feature | type | order | direction | polarity | strength |
|---|---|---|---|---|---|
| f | k | 2 | left | positive | strong |
| g | v | 1 | right | positive | strong |
| h | t | 3 | n/a | negative | n/a |
In the above table, the column feature expresses the information
that there is a feature. There are three different features in the
feature bundle, this is reflected in the feature column by there
being three distinct features f, g, and h. The type column
indicates the kind of feature that we have (i.e. is it a case (k)
relevant feature, or a v relevant feature, etc). The order column
indicates in which linear position the feature in question appears in
the feature bundle. The direction column indicates the
linearization information associated with a feature, and the
polarity column displays the polarity of the feature (governor or
governee). The strength column indicates whether a feature is
willing to host pronounced material. Of this information associated
with the feature bundle, the order information is of a different
kind than the others; of any given feature in isolation, it makes
sense to ask its type, its linearization information, its
polarity, and its strength. The order information on the other
hand is a relational property of features in a particular feature
bundle.
Given that there are these six types of information in a feature bundle, which are part of syntax proper, and which are part of something else? Syntax proper (i.e. to be able to decide whether an arbitrary dependency graph is well-formed) needs to make reference to:
- the features on a lexical item
- their relative order
- their type
- and their polarity
We need to know the type and polarity of a feature to determine whether the two ends of a dependency match, and we need to know the relative order of features to verify that a link was established at the correct time. (And we need to know that there is a feature there to verify that a link should be there at all.) Neither the directionality nor the strength of a feature is not needed to verify that a dependency graph is licensed by the grammar.
As we have defined it, linearization of a dependency structure works by performing three seemingly unrelated operations:
- turning dependency structure into constituency structure
- determining which chain link will be pronounced
- determining which side of a lexical item another is to be pronounced on
Each of these can be performed independently of the other. Crucially, not all information is relevant for each of these operations. The directionality information is only relevant for operation 3. Moreover, that is all that is relevant for operation 3. For operation 2, we need to have information about feature polarity (to determine which arcs link this expression to positions in the maximal projections of other items), about feature order (to determine which positions are higher than which others), and feature strength (to determine which arcs can host the expression). Type, on the other hand, is completely irrelevant. For operation 1, we again need information about polarity (to determine which arcs represent positions in the maximal projection of a head) and order (to determine which expressions in the maximal projections should c-command which others), but type, strengh, and direction are irrelevant.