1 On subjects and explanation
1.4 The formal framework
The subject-as-grammatical-function approach, and the consequent mixed formal-functional conceptualization of syntax, is most typical of the theoreti-cal framework of Lexitheoreti-cal-Functional Grammar (LFG), a theoretitheoreti-cal framework originally developed by Joan Bresnan and Ron Kaplan in the late 1970s, and described in Bresnan (2001), Falk (2001), and Dalrymple (2001). The formal portions of the present study will therefore be couched in the notation and terminology of LFG. In this section, we will outline most of the aspects of the LFG formalism which will be relevant in this study. We will not relate to subjecthood-related issues here.
LFG is based on a parallel-architecture model of language, in which con-stituent structure and grammatical functions are represented as distinct dimen-sions of linguistic structure. The functional structure in (38) is a simplified ver-sion of the formal LFG representation of grammatical functions: the f-structure.
F-structure is an “attribute-value matrix” (AVM), a table-like representation of “attributes” (grammatical functions and grammatical features) and their values.
(39)
As we have done in (38), where the internal structure of an f-structure element is unimportant, an orthographic representation of the element enclosed in double quotes can be used. This is the f-structure equivalent of a constituent structure triangle.
Unlike in structurally based theories, the structure–function mapping is taken to be defined by language-specific constraints (albeit constrained by univer-sal principles; Bresnan 2001). It is these constraints which form the heart of the descriptive power of LFG. Consider the c-structure and f-structure of the sentence (40a).
On subjects and explanation 25 (40) a. The baby will put a book on the shelf.
b.
c.
Elements of the c-structure and elements of the f-structure are in a relation of correspondence with each other. The correspondence function mapping from c-structure to f-structure is usually called, and the mapping relation from f-structure to c-structure is its inverse,−1.
The DP the baby corresponds to a functional element which is the value of the attribute subj, while the DP a book corresponds to a functional element which is the value of the attribute obj. Or, informally, the baby is the subj and a book is the obj. This is because the baby is a daughter of the IP node and a book is a daughter of the VP node, and the grammar of English asso-ciates each of these structural positions with a particular grammatical function.
Similarly, the PP under VP is associated with an oblique argument function.
Unlike constituent-structure-based theories, these associations of structural positions with grammatical functions are not assumed to be universal; this
26 Subjects and their properties
allows for languages with different associations between structure and func-tion, as in non-configurational languages.
The grammar of English therefore must include constraints of the following nature:13
(41) a. An IP node may dominate a DP, which functions as the value of the attribute subj in the f-structure of the IP, and/or a head I.
b. A VP node may dominate any or all of: a head V, a DP which functions as the value of the attribute obj in the f-structure of the VP, a PP which functions as the value of the attribute obl in the f-structure of the VP,14 etc.
The formal expression of constraints licensing c-structure configurations has traditionally been the phrase structure rule. In LFG, this is enriched by adding functional annotations to the elements on the right-hand side of the phrase struc-ture rule. These annotations use the symbols↑, indicating the f-structure cor-responding to the mother node, and↓, indicating the f-structure corresponding to the daughter node.15For example, the DP daughter of IP will be annotated with the functional constraint (42a), which means (42b) or, more precisely, (42c).
(42) a. (↑ subj) = ↓
b. The f-structure corresponding to the mother node (IP) includes the attribute subj. The value of this attribute is the f-structure corresponding to the daughter node (DP).
c. The f-structure corresponding to the mother node (IP) includes the attribute subj. There is also an f-structure corresponding to the daughter node (DP). Traversing a path through the f-structure from the f-structure corresponding to the mother node through the attribute subj leads to the same f-structure element as (i.e. is equal to) the f-structure corresponding to the daughter node.
13 All c-structure positions are optional, including structural heads. Missing heads in LFG corre-spond roughly to empty heads in transformational theory.
14 Oblique arguments are more complicated than suggested by this characterization, since the exact oblique function (goal, benefactive, locative, etc.) is determined by the preposition. This is irrelevant for the present study. The full formal expression can be found in the standard LFG references mentioned at the beginning of this section.
15 The symbols↑ and ↓ are technically defined in terms of the mapping function: if the current node of the tree is represented by *, and each of the surrounding nodes is represented by an arrowhead pointing in the appropriate direction of the tree (i.e. the mother node is ˆ∗, the left sister is<∗, and the right sister is ∗>), ↓ is (*) and ↑ is ( ˆ∗). For more on the technical details of the formalism, see Dalrymple (2001).
On subjects and explanation 27 Similarly, a head, like I, is annotated (43), which expresses part of what is meant by “head.”
(43) a. ↑ = ↓
b. The f-structure corresponding to the mother node (IP) is identical (equal) to the f-structure corresponding to the daughter node (I).
The full formal version of (41) is thus (44):
(44) a. IP→ DP I
(↑ subj) =↓ ↑ = ↓
b. VP→ V DP PP . . .
↑=↓ (↑ obj)=↓ (↑ obl)=↓
As shown in (42c), the parenthesized expressions formally express paths through the f-structure. We will return to this in Chapters 3 and 4.
Functional constraints also appear in lexical entries. For example, the lexical entry of the word baby includes the following constraints:
(45) (↑ pred) = ‘baby’
(↑ num) = sg
The pred feature is a representation of the meaningfulness of syntactic ele-ments, which is one aspect of their functionality. For most lexical items, the value of this feature is an atomic expression, conventionally represented as the word in single quotes. Pronouns have a special value for the pred feature,
‘ p r o . ’In the case of argument-taking predicates, the value of the pred feature includes a specification of the arguments selected. The lexical entries of forms of the verb put, for example, include:
(46) (↑ pred) = ‘put (↑ subj)(↑ obj)(↑ oblLoc)’
The list of selected arguments is a projection of the verb’s argument struc-ture; we will discuss some aspects of LFG’s theory of argument structure in Chapter 2. The↑ in the specification of each argument function is a formal indi-cation that the arguments must be local: the obj of put must be in put’s local f-structure, while the obj of on must be in on’s local f-structure. In general, each of the argument functions specified in the value of the pred feature must be present in the local f-structure. The principle that specifies this is called the Com-pleteness Condition. Conversely, the principle that disallows other (unlicensed) argument functions from appearing is called the Coherence Condition. Taken together, the Completeness and Coherence Conditions enforce the selectional
28 Subjects and their properties
properties of the predicate, and correspond approximately to the Criterion of Government/Binding theory.
In addition to argument functions, LFG hypothesizes adjunct functions (pri-marily adj) and grammaticized discourse functions (such as focus and t o p i c).16These elements are not selected, but must still be licensed as specified in an extension of the Coherence Condition. The Extended Coherence Condi-tion requires adjuncts to modify meaningful elements. For the grammaticized discourse functions, the Extended Coherence Condition specifies that any item bearing one of those functions must also bear an argument or adjunct function.
For example, in our example (38) the same item that bears the focus function also bears the argument obj function. An element that bears only the focus function is ruled out by the Extended Coherence Condition.
The f-structure in (38) is more standardly drawn as follows:
(47)
Here, a curved line is used to show that one element has two different functions (or, more formally, is the value of two different attributes). It is more useful than the bracket we used informally earlier, as it can be used when the two functions are in two different clauses.
Formalism in linguistics provides a way to express descriptive generaliza-tions precisely. In addition, if the formalism is well designed, properties of the formalism can themselves turn out to be part of the explanation of linguistic phenomena.