The Semantics of Determiners

1.3.3 Dynamic approaches
Part of the impetus that led to differentiating quantificational DPs from all the others came, as mentioned above, in Kamp (1981) and Heim (1982), works that were essential to the development of dynamic approaches to semantics. The former is the founding stone for the framework known as D(iscourse) R(epresentation) T(heory); the latter is the source of dynamic approaches to semantics known under the name of C(ontext) C(hange) S(emantics). Both views pay particular attention to how the interpretation of a linguistic expression affects and is affected by its context. The dynamic nature of the system resides in treating linguistic utterances as occurring against the background of an input D(iscourse)R(epresentation)S(tructure) or context and causing a series of changes that lead to an output DRS or context. The system is compositional in as much as the changes a particular expression brings about are determined by the immediate constituents of that expression and the way they are composed.

The engine that drove early work in DRT is the need to provide a uniform account of definite pronouns. One issue at the root of Heim (1982) is to account for the differences between indefinite and definite DPs the one hand and those DPs whose determiner is a universal or proportional quantifier on the other. This is what is behind the distinction in Figure 3. The other core issue in Heim (1982) is the proper characterization of the difference between ordinary indefinites (a DPs) and ordinary definites (the DPs) in English. We return to this latter distinction in Section 2.

Both DRT and CCS assume an intermediate level of representation that mediates between linguistic expressions and semantic interpretation, called D(iscourse) R(epresentation) S(tructure) in DRT . For our purposes, the two approaches can be seen as equivalent. We will use DRT terminology below.

An ingredient of DRSs that is crucial for our purposes is the notion of discourse referent (or variable), an entity that mediates between a nominal used as an argument (of type e or < < e, t >, t > in type-theoretical terms) and its interpretation.¹¹ (The notion of discourse referent and, with it, the notion of context change, was first introduced in Karttunen (1976), a classic paper on the role of (in)definite DPs.)

Crucial here is the idea that at the level of DRS, non-quantificational nominals introduce a discourse referent (or free variable) accompanied by a restrictive expression, while quantificational DPs, besides doing this, also introduce a complex structure that ends up determining the quantificational force of the DP. The discourse referents introduced by non-quantificational DPs acquire existential force by default, as it were, via the truth conditions associated with the representations in which they appear. To exemplify with a simple case, assume the sentence in (18) is added to an empty context.

(18) A student came in.

The DRS resulting after the processing of (18) against an empty input context is of the form in (19), where the contribution of the DP is bold-faced:

(19)
x

student(x)
came in(x)

Simple discourse representations like the one in (19) (those that do not involve structures introduced by quantification for instance) are made up of a set of discourse referents (in this case, {x}) and a set of conditions placed on them (in this case {student(x), come in(x)}). Specific ‘construction rules’ specify the way DRSs are constructed based on particular linguistic expressions.

Interpretation rules connect DRSs to their truth conditions relative to a model. By general rules, a DRS K is true in a model M just in case one finds a function from the set of discourse referents in K to the entities in D such that this function meets all the conditions imposed by K. A function f that meets the conditions imposed by a DRS K relative to a model M is an embedding function for K in M. A DRS K is true in M iff there is an embedding function for K in M. The contents of the DRS are, in essence, constraints on the embedding function. For the DRS in (19) this amounts to requiring there to be an entity d in D that is a student and that came in. Existential force is treated here as a default, conferred on discourse referents by general truth conditions.

A quantificational determiner such as fiecare/every is responsible for the introduction of a complex structure made of two DRSs linked by an operator. The first DRS is the Restrictor, the second, the Nuclear Scope and the connecting operator is determined by the nature of the determiner. The DRS resulting after interpreting (20) relative to an empty input DRS is given in (21):

(20) Every student came in.

( 21)
x
∀x came in(x)
student(x)
K’ K”
K

The DRS K’ is the Restrictor; the DRS K” is the NS. The complex conditions associated with such complex DRSs say that a function f is an embedding function for K in M just in case every f’ that extends f and is an embedding function for K’ can be extended to a function f” that is an embedding function for K”.¹² Crucial for dynamic issues concerning inter- and intra-sentential pronominal reference, the Restrictor is processed prior to the NS and therefore information provided in the Restrictor is accessible to the NS but not the other way around. Furthermore, note that the quantificational DP has not contributed a discourse referent in the main DRS K (unlike what happens in the case of non-quantificational nominals). This property is responsible for the fact that such DPs cannot normally act as antecedents for discourse pronouns.

Non-quantificational nominals simply introduce a discourse referent and a condition on that referent, but do not create extra structure. A special condition may require the introduced discourse referent to be identical to some discourse referent present in the input DRS in which case no actual increase in discourse referents is involved. The effect of introducing a discourse referent (whether novel or not) is the equivalent of being an e-type nominal. Quantificational DPs (those of type < < e,t >, t > ) have the complex effect just sketched. The effect of nominals acting as predicative nominals is to simply introduce a predicative condition, as exemplified in (22) and its DRS in (23):

(22) John is a doctor.

( 23)
x
x = John
doctor(x)

These nominals then (of type < e, t >) do not introduce a discourse referent independently of their syntax; their contribution is the same as that of a predicate such as leave.

Going into the details of how nominals make their contribution to DRSs, it has been suggested that when it comes to CN-headed argumental nominals in languages with articles and number marking, discourse referents are introduced by D in the structures in (7), while the material at the NP level contributes predicative conditions on the discourse referent introduced by the higher projections. Farkas and de Swart (2003) further suggest that the feature [Pl] also introduces a discourse referent which has to be identified with the discourse referent introduced by D within a single DP. This lack of independence of the discourse referent introduced by [Pl] is connected, in this approach, with the special properties of bare plurals across languages. Explicit rules are given in Farkas and de Swart for combining a D with its NP and for combining an argumental nominal with its predicate, which we don’t repeat here.

The crucial question that arises if we are interested in the semantics of determiners within this framework is how to further distinguish between types of non-quantificational nominals of various sorts. The distinctions can be made at the level of the properties of the discourse referent introduced (such as whether it refers to an ordinary entity or a kind-level entity), as well as at the level of the conditions the nominal brings along. Furthermore, distinctions may involve the properties of the discourse structure that serves as input to the relevant expression or the properties of the output structure. Finally, we can consider only the content of the DRSs involved or we may look at more complex properties concerning their connection with the model. In what follows we concentrate on non-quantificational Ds (the ‘existential’ determiners of Figure 2) and discuss the various subtypes we find in Romanian. Given that we are interested in finer-grained distinctions than what type-theory (even if flexible) is giving us we will be phrasing our observations in the DRT framework just sketched.