This section is concerned with restriction in natural language. I provide two examples, one from the domain of events and the other from the domain of individuals. This ingre- dient will be concerned with a new compositional principle that represents the semantic glue in my analysis.
Chung & Ladusaw’s RESTRICT The restrict-operation aims, among other things, at capturing examples of noun incorporation like (54). These are cases of predicate restriction in which an argument must not be saturated, but has to be somehow incor- porated in the composition.
(54) *John dog-fed Fido. (Chung & Ladusaw 2004: 5) This example, of course, is not grammatical in English, but there are quite a few languages that have such structures. An example from Chamorro, an Austronesian language, is in (55). (55) Gaäi-[ga’] agr.have-pet yu’ I kätu, cat lao but matai. agr.die
‘I had a pet cat, but it died.’ (Chung & Ladusaw 2004: 104) In (55), the incorporated object can be doubled by an independent NP, i.e. we have an extra object (in boldface). The standard rules of composition cannot handle this. For examples like these the authors propose a mode of composition named restrict. I
apply it to the English example in (54). (56) a. JfedK = λy.λx.x fed y = f ed
0(y)(x)19
b. Jdog-fedK = λy.λx.x fed y ∧ y is a dog = f ed
0(y)(x)∧ dog0(y)
via restrict c. Jdog-fed FidoK = λx.x fed Fido ∧ Fido is a dog
= fed0(Fido)(x)∧ dog0(Fido)
via FA (Function Application), cf. (6-d) in Chapter 1 d. JJohn dog-fed FidoK = f ed
0(Fido)(John)∧ dog0(Fido)
= John fed Fido and Fido is a dog via FA
The important step of the composition via restrict is provided in (56-b). Note that the internal argument slot of the predicate does not get saturated by the predicate ‘dog’! The authors call (predicate) restriction20a “nonsaturating mode of composition” (Chung
& Ladusaw 2004: 2). The result of restricting the predicate with property p (‘dog’) is the original function with its domain restricted to the subdomain of its original domain to elements with the property p.
Kratzer’s Event Identification: RESTRICT with Events Kratzer (1994,1996) puts forward the idea that external arguments (i.e. subjects) are not arguments of the verb. External arguments are introduced by ‘Voice’ . She dubs the principle which is needed to compose the VP containing the internal argument with Voice Event Identifica- tion21. Event identification (EI) is a conjunction operation that works as follows:
(57) f g → h
he, hv, tii hv, ti → he, hv, tii
λxe.λev.f (x)(e)∧ g(e)
If we have as an input the functions f of type he, hv, tii and g of type hv, ti (order irrelevant) that we want to compose, we get the function h of type he, hv, tii as an output. The input function f and the output function h are of the same type. Event Identification
19Again, here as before already, I ignore the contribution of tense since it is not important for my
analysis.
20I mostly just call it “restriction”.
21A reminder for types: v is the type for events, e the type for individuals and t the type of truth values,
(EI) allows one to add various conditions to the event that the verb describes; Voice, for example, adds the condition that the event has an agent. Let us look at an example sentence and its composition.
(58) Mittie fed the dog.
(58) has the structure in (59). The lexical entries and the semantic composition are in (60-a) and (60-b). (59) VoiceP DP Mittie Voice’ Voice Agent VP V fed DP the dog (60) a. J f ed K = λxe.λev.f ed 0(x)(e)
J Agent K = λxe.λev.Agent(x)(e) J M ittie K = Mittie
b. J fed the dog K = λev.f ed
0 (the dog) (e)
J [Voice’Agent[VPfed the dog] ]K = λxe.λev.[Agent (x)(e) ∧ fed
0(the dog)(e)]
via Event Identification J [Mittie [Voice’Agent [VP fed the dog]]]K = λev.[Agent (Mittie)(e) ∧ fed
0(the
dog)(e)]
Event Identification makes it possible to chain together various conditions for the event described by a sentence. The agent argument of the VP is not an argument of the V, but is still identified with the same event. In the analysis that we will be adopting for Nenets, we will be using a very similar composition principle, this time in the domain of degrees.
Let us now compare restrict and Event Identification in the following table. So what does this “operation” do? In both cases, i.e. for restrict and Event Iden-
higher-type function f lower-type function g function after operation : h events he, hv, tii hv, ti he, hv, tii individuals he, he, tii he, ti he, he, tii
Table 4.2: Comparison between restrict and Event Identification
tification no saturation of an argument takes place. Basically, we have an elaborate type of conjunction where the operation allows us to tie together something of a higher type and a lower type. Assuming that the predicate is interpreted as a function g, the result is that the domain of the function g gets restricted by property p (which can be a property of individuals or a property of events) to a subdomain having that property p. The compositional principle that I will need for my analysis is parallel to both restrict and EI. I will need to compose something of a higher type, namely type hhd, hd, he, tiii, he, tii, with rkaabstract that has type hd, ti. I will generalize this principle
to a rule that I illustrate in (61). I call it Degree Restriction, i.e. DR. (61) Rule for Degree Restriction:
a. If α is a branching node and {β, γ} the set of its daughters, then for any assignment g, α is in the domain of J K
g if both β and γ are, and β is of
type hd, ti and γ is of type hhd, hd, he, tiii, he, tii, then: JαK g = λd d.λRhd, he, tii.λxe. Jγ K g(d)(R)(x)=1 ∧ Jβ K g(d)=1. b. shorter version: If α ={β γ}, and JβKg ∈ D hd, ti andJγ K g ∈ D
hhd, hd, he, tiii, he, tii, then:
JαK g = λd d.λRhd, he, tii.λxe. Jγ K g(d)(R)(x)=1 ∧ Jβ K g(d)=1.
This rule is designed specifically for phrasal comparatives using Heim’s degree operator. It can easily be accommodated for clausal or other phrasal comparatives:
(62) For any type α this will give us: hd, hα, tii + hd, ti = hd, hα, tii
The important part is that it allows us to combine a degree predicate (which will be ultimately the meaning of our protagonist -rka) with the meaning of a higher-type degree function the first argument of which is a differential degree that will be modified. As illustrated by Table 4.3, the following parallel to the two other conjunction operations, namely restrict and EI, can be drawn:
higher-type function f lower-type function g function after operation: h events he, hv, tii hv, ti he, hv, tii individuals he, he, tii he, ti he, he, tii degrees hd, hα, tii hd, ti hd, hα, tii
Table 4.3: Adding Degrees to the Picture
In this table, we see that the result of the composition is the higher-type function f we start out with, just restricted by g to a certain subdomain, in our case the domain of small degrees.