When the syntactic derivation of a cycle (a phase) is complete, at Spell-Out, it is sent to Phonological Form (PF) and Logical Form (LF). LF is the semantic interface where semantic interpretation is computed. To model that, we use different modes of composition: Function Application, Existential Closure, Predicate Modification, Event Identification and Predicate Restriction.
I will now show examples of different modes of composition. We start with Function Application and use it withdie, which is a verb that has a theme argument that needs to be saturated. The DP the actor does exactly that in the following.
(20) English
The actor died.
The verb die enters the derivation with an open argument variable (λx), whose domain is a set of individuals, and an open event variable (λe).
(21) λx.λe. [dying(e) ∧ theme(e,x)]
Here, λx binds all instances of x and λe binds all instances of e. When we apply the DP the actor to the function above, it replaces all instances of x (there is only one in (21)) and we remove λx; the actor combines with the verb and saturates its argument position.
(22) λx.λe. [dying(e) ∧ theme(e,x)](Jthe actorK) =λe. [dying(e) ∧ theme(e,the actor)]
The mode of composition used here is Function Application (FA), which is defined in (23):
(23) Function Application
If α is a branching node, {β,γ} is the set of α’s daugters, and JβK is a function whose domain contains JγK, then JαK =JβK(JγK).
(Heim and Kratzer 1998:44)
We draw the FA composition of (22) in the following tree, where vP equals α in (23) and β and γ equal v and DP, respectively.
(24) vP
Function Application
λe. [dying(e) ∧ theme(e,the actor)]
v
λx.λe. [dying(e) ∧ theme(e,x)]
v √die
DP
the actor
The second mechanism we need in this dissertation is Existential Closure (EC). To saturate the event variable, we existentially close it. In constructions like pas- sives, where there is an external argument which does not saturate the position, we also apply EC to saturate the external argument variable. For a construction like the passive, I assume that Asp(ect), which here is the participial head -ed, takes a property of the type he,hs,tiiand returns a proposition of the typehs,ti. (Asp takes a λx variable and returns it saturated, ∃x).
(25) a. The actor was fired.
b. AspP
Existential Closure
λe.∃x[agent(e,x)
∧ϕ(x) ∧ firing(e) ∧ theme(e,the actor)]
Asp
λphe,hs,tii.λe.∃x[p(x)(e)]
-ed
VoiceP
λx.λe. agent(e,x)
∧ firing(e) ∧ theme(e,the actor)
fire the actor
Here, the agent is not further specified in a by-phrase. Asp existentially closes the agent argument such that the interpretation of the sentence is: ‘Someone (or other) fired the actor’, i.e., there is some agent x which fired the actor. The way EC is presented here is a version of Function Application.
Another mode of composition is Predicate Modification (or Predicate Conjunc- tion) which takes two elements that are of the same type and returns that type.
(26) Predicate Modification
Ifα is a branching node, {β,γ} is the set of α’s daughters, and β and γ are both of type he,sti, then α is of type he,sti.
(adapted from Heim and Kratzer 1998:65)
(27) a red jacket
To describe the intersectivity of a red jacket is to say that we have two sets, one contains things that are red and the other contains jackets. The intersection is a set of things that are both a part of the set of things that are red and a part of the set of jackets.
We could use Function Application to get the composed meaning ofa red jacket
but as the two are of same type, red and jacket, we use Predicate Modification which captures well the intersective meaning.
(28) nP Predicate Modification λx.[red(x) ∧ jacket(x)] aP red λx.[red(x)] nP jacket λx.[jacket(x)]
Fourth, I assume Kratzer’s (1996) Event Identification when an element in at least SpecVoiceP and SpecApplP is introduced. Kratzer (see also Marantz 1984) assumes that the external argument is not part of the denotation of the verb. In- stead, it is introduced by Voice. The mechanism Kratzer introduces for this purpose is Event Identification. (It should be noted that it would also be possible to use Function Application here.)
(29) Event Identification
Ifα is a branching node, {β,γ} is the set of α’s daughters, and β is of type
he,hs,tii and γ is of type hs,ti, then α is of type he,hs,tii.
(adapted from Kratzer 1996:122)
Event identification combines a proposition of type hs,ti and a property of type
he,hs,tii with an open argument variable. Voice introduces an agent when it com- bines with vP. This is shown for (30a) in (30b).
(30) a. Mary danced.
b. VoiceP
Function Application
λe. agent(e,Mary) ∧ dancing(e)
DP
Mary
Voice0
Event Identification
λx.λe. agent(e,x) ∧ dancing(e)
Voice
λx.λe. agent(e,x)
vP
λe. dancing(e)
danced
As we see in (30b), Voice says that the agent of an event is x, but does not specify any further what kind of an event it is. When Voice combines with vP, Event
Identification ensures that whatever event x is the agent of, that event is the same as that of vP (here a dancing event) (see, e.g., Harley 2011).
Finally, Chung and Ladusaw (2004) introduce yet another mode of composition, predicate restriction (Restrict). Restrict targets an argument but, importantly, does not saturate it.
(31) Restrict
If α is a branching node, {β,γ} is the set of α’s daughters, and β is of type he,sti and γ is of type he,ti, then α is of type he,sti.
(adapted from Legate 2014:39)
When Voice introduces an argument via Event Identification, that argument can be saturated by a DP in SpecVoiceP via Function Application. In some cases, a bundle of ϕ-features, lacking D, may occupy the argument position, without saturating it. This is an important mode of composition for the analysis of the New Impersonal Passive (Legate 2014), the Impersonal Modal Construction and the Aspectual Passive, as we will see in §4.3.