PowerPoint Presentation 323 Morphology

3.2 The form of Morphological Rules

D = {the, this, these, that, those}
Q = {{a, an, one, ø}, some, few, a few, several, … }
A = {happy, red, large, petite, long, deep, fuzzy, …}
Some syntacticians question question whether rules such as the VP expansion rule is really necessary. For example, the lexical entry for DESTROY should include the fact that it requires a direct object (a complement):
E.g. [V DESTROY + ____ NP].
They query whether the rule ‘VP -> V + (NP)’ is really necessary.
I don’t like the idea that the VP ‘rule’ is really a rule. Rather, it is a statement of sets:
E.g. VP is a set that contains V and NP; V and NP are members of the set VP.
This is merely a statement of sets. I will go one step further and write it as:
E.g. {VP} <--> .
Note: In set theory notation, the comma enclosed in angled brackets indicates linear order: VP is a set that contains the ordered set V then NP. This notation is not normally used in linguistics; the plus ‘+’ denotes order as shown above.
Note: the curly braces can be omitted once it is understood that VP, V and NP are each a set.
The lexical expansion above is a statement that in essence says:
If one member of the set V is DESTROY, then the second set is NP, which is the complement of the verb.
What remains in question is how to account for an optional member. In reality, there are no optional members. Recall that ø as a phonological sign is permitted in set theory. An optional member actually exists; it merely has ‘ø’ as its sign:
The S ‘John likes to eat’ implies he likes to eat something. The pronoun may take on a zero form for certain verbs: [V EAT [NP ø]].

3.2 The form of Morphological Rules

The lexical entry for EAT now should be:
{V EAT, {complement, NP, {-ø, ø}.
By ‘-ø’ I mean it must have a phonetic sign.
Not all verbs take a zero complement such as DESTROY.
[V DESTROY, {complement, NP, -ø}].
The logic for the ø complement rests in set theory and the 3-component theory. The complement fills the function role, and its form is ø, and its sign is ø, in most cases anyway. If it has no form how can it have a sign? Each component constitutes a set, usually called the complement of the verb, or an argument of the verb:
E.g. :{COOK, {-ø}, {-ø, +ø}}. The first argument is the agent, the second the theme.
The fact that EAT takes a theme argument prompts this analysis. The function of the first ø is [-Pl] and that of the second one is [+Pl], or the reverse.
There are morphological forms that have no form, but they have a sign:
E.g.: {[+Pl] (of certain nouns),