In this section, we will provide a brief description of the LFG theory and its formalism, based on Kaplan and Bresnan (1982), Sells (1985), Kaplan (1989), and Huang (1989c). This description thus serves as the basis for the comparison between the conventional LFG and our vLFG discussed in the next section. The best-known feature of LFG theory is probably that its grammar assigns two types of syntactic representations to a sentence or phrase, c-structure to reflect its constituent structure and f-structure for its grammatical/functional structure. The idea of c- and f-structure division is similar to that of the ID/LP format (ID = immediate dominance; LP = linear precedence) of stating phrase structure rules in GPSG. The difference is that while the ID rules are an abstraction of pure constituency away from LP rules, which describe the linear ordering of constituents, f-structure is an abstraction of the grammatical, relational, or functional information away from both phrasal constituency and ordering. Therefore, c-/f-structure division and ID/LP format are totally compatible. Many LFG practitioners do adapt the ID/LP format in stating phrase structure rules (e.g., Huang and Mangione 1985).
The c-structure serves as the basis for phonological interpretation while the f-structure for semantic and discoursal interpretation. Lexical items have their functional information defined in the lexicon. The LFG context-free phrase structure rules are augmented with functional annotations. The c-structure formed by the PSR's is thus also annotated with functional expressions. The f-structure is then formed by instantiating the functional annotations on the c-structure.
1.3.1 The Lexicon
Capitalizing on the linguistic trend of having lexical information account for various grammatical phenomena, in LFG the lexicon plays an essential role. All the functional or grammatical information of a sentence comes from the words in it and the functional specifications on phrase structure rules. In the lexicon, all lexical entries are fully inflected and thus have complete grammatical information. A lexical entry contains its categorial specification and a set of functional expressions known as "schemata," which are to be
instantiated, or to take place, when the c-structure of the sentence is reached.
The English word 'forces', as in a construction like "Mary forces John to go"
would have the following entry:
1. forces V,
(↑ PRED) = 'force <(SUBJ) (OBJ) (XCOMP)>' (↑ OBJ) = (↑ XCOMP SUBJ)
(↑ SUBJ PERSON) =c 3rd (↑ SUBJ NUMBER) =c SG
For practical purposes, we can interpret ↑ as "the level of f-structure associated with my mother node in the c-structure" and ↓ as "the level of f-structure associated with my own node in the c-structure.” The syntactic category of this lexical entry is V. The first functional equation defines (indicated by =) this entry's semantic form and the predicate structure. It requires three arguments, or subcategorizes for three grammatical functions, SUBJ, OBJ, and XCOMP. The second equations defines the "control" relation between the matrix object (John) and the missing subject of the embedded non-finite clause XCOMP, with the former being the controller and the later the controlled. The subject of "to go" is therefore to be identified (unified) with "John." The third and fourth equations are functional constraints (indicated by =c). Unlike an equation of definition (=), where unification actually takes place, a constraint (=c), where no unification is performed, only checks whether such attribute-value pair exists or not. Thus the two constraints in this entry make sure that its subject has the attribute PERSON with value 3rd and the attribute NUMBER with value SG. If there is any constraint not satisfied, the functional structure is considered ill-formed. Many agreement features are checked in this manner. As we shall see later, the functional equations, or schemata, on a lexical entry are instantiated only after the c-structure is constructed.
1.3.2 The C-structure and Phrase Structure Rules
Basically an LFG grammar consists of a lexicon, a set of context-free phrase structure rules (PSR's) functionally annotated, and certain well-formedness conditions on f-structures. The PSR's describe the
LEXICALFUNCTIONAL GRAMMARANDAVARIANTFORMALISM 11
constituent structure of a sentence, and in fact they may also be viewed as constraints on the well-formedness of c-structures. Only the syntactic categories, not the functional equations, of the words contained in a word string are relevant to its c-structure. Let's see a simple example, "Mary loves John" assuming the following lexicon and PSR's.
2. a. Mary N,
(↑ PRED) = 'Mary' (↑ PERSON) = 3rd (↑ NUMBER) = SG
b. John N,
(↑ PRED) = 'John' (↑ PERSON) = 3rd (↑ NUMBER) = SG c. loves V,
(↑ PRED) = 'love <(SUBJ) (OBJ)>' (↑ SUBJ PERSON) =c 3rd
(↑ SUBJ NUMBER) =c SG 3. a. S → NP VP
(↑ SUBJ)=↓ ↑=↓
b. VP → V (NP) (NP)
↑=↓ (↑ OBJ)=↓ (↑ OBJ2)=↓
c. NP → (DET) (A) N ↑=↓ ↓ε(↑ ADJ) ↑=↓
If all we are concerned with is the c-structure of the sentence, both the functional equations on the lexical entries and the functional annotations, also known as "schemata," on the PSR's can be ignored. The only relevant feature is the lexical item's categorial specification indicating the preterminal category under which the lexical item may be inserted. Obviously then, the notion of c-structure is entirely compatible with that of the more commonly known tree
structure. These PSR's thus assign the following tree structure correspondence to the word string. In the tree representation of c-structures, we will borrow the Lexicase convention that a straight vertical line indicates that the lower node is the head of its mother node, but this does not mean that we assume the Lexicase position that all c-structure constructions have a lexical head.
4. S
NP VP
N V NP N Mary loves John
1.3.3 Unification: from C-structure to F-structure
Of course c-structure rules in LFG are different from simple context-free PSR's in that they are augmented with functional annotations; therefore, they assign to a sentence its c-structure with particular specifications to regulate the manner of unification in constructing the f-structure of the sentence. Again, let's look at our previous example. The functionally annotated PSR's would assign the following c-structure with functional schemata to the sentence.
LEXICALFUNCTIONAL GRAMMARANDAVARIANTFORMALISM 13
5. S
│ NP VP (↑ SUBJ)=↓ ↑=↓
N V NP (↑ NUMBER)=SG (↑ PRED)='love<...>' (↑ OBJ)=↓
(↑ PERSON)=3rd (↑ SUBJ NUMBER)=cSG (↑ PRED)='Mary' (↑ SUBJ PERSON)=c3rd N (↑NUMBER)=SG (↑PERSON)=3rd (↑PRED)='John'
Mary loves John
Note that the functional schemata originating in the lexicon are not formally distinct from the ones coming from the augmented PSR's. Through the instantiation of the functional schemata and the operation of unification, the f-structure of the sentences is then composed. Therefore, f-structure is constructed only after the c-structure is constructed. Readers interested in the formal, detailed procedures of deriving f-structure correspondence from c-structure through functional descriptions should refer to Kaplan and Bresnan (1982) or Wescoat (1987). We will now illustrate in the figure below the correspondence between the c- and f-structure, or the co-description of c- and f-structures, of the sentence "Mary loves John."
S PRED ‘<(SUBJ) (OBJ)>’
NP VP NUMBER SG SUBJ PERSON 3rd N V NP PRED ‘Mary’
N NUMBER SG OBJ PERSON 3rd Mary loves John PRED ‘John’
Figure 1.1 Co-description of C- and F-structure
As mentioned before, LFG also posits certain well-formedness conditions on f-structures. A final f-structure associated with a final c-structure still needs to satisfy all the well-formedness conditions. We will discuss these conditions together with grammatical functions in CHAPTER 2, since most of the conditions make reference to the notion of "subcategorizable functions."
Thus, in LFG, both phrase structure rules and information associated with lexical items contribute a local co-description of partial information to the final c- and f-structure of the sentence. The advantage of this division is that it allows separate encoding of external constituent structure, which varies across different languages, and the internal relational structure of grammatical functions which is largely invariable universally. The two structures are two independent but parallel planes associated to each other. Therefore, the mapping from a c-structure to an f-structure is purely procedural and not derivational, which is the crucial difference between c-/f-structure division and the bistratal deep/surface structure distinction.
1.3.4 From Form to Meaning
The notion of correspondence in LFG is an important one: it provides a general way of correlating different kinds of linguistic information in separate domains through modular specifications. We have seen that the word string,
LEXICALFUNCTIONAL GRAMMARANDAVARIANTFORMALISM 15
c-structure utterance
f-structure
discourse structure
meaning
mediation of PSR’s
semantic stucture anaphoric
structure
unification specified by functional annotations through the mediation of PSR's, first maps to a c-structure correspondence, which is then mapped to an f-structure correspondence by the instantiation of functional schemata and the operation of unification. Kaplan (1989) suggests that the correspondence idea may be extended for the entire mapping between the external form of an utterance and its internal representation of meaning, as shown in the following configuration.
Figure 1.2 Correspondence of Linguistic Representations in LFG By extending the same conceptual framework of description and correspondence, the same existing mathematical and computational techniques in mapping c- to f-structure can be applied to other systems of linguistic information. For the semantic component in LFG, refer to Halvorsen (1983).
1.3.5 Further Readings
The most important compilation of works in LFG to date is still Bresnan (1982), of which Chapter 4 (i.e., Kaplan and Bresnan 1982) describes
systematically LFG theory and formalism. Two other chapters that are also important in terms of theoretical significance are Chapter 1 (Bresnan 1982a), which justifies the advantages of lexical processes in a lexical theory over transformational analyses, in the case of passivization, and Chapter 5 (Bresnan 1982b) where a theory of control relations and complementation in LFG is presented. The section on LFG of Sells (1985) constitutes a well-balanced and comprehensive introduction to the theory and formalism.
Likewise, Chapter 4 of Horrocks (1987) is a clearly illustrated and explicated introduction on LFG. As for detailed, step-by-step instructions on working with LFG's formalism and unification process, Wescoat (1987) is a most practical manual.
Kaplan (1989) provides a description of LFG's formal architecture and a summary of the recent developments of LFG's formalism since Kaplan and Bresnan (1982): functional uncertainty, functional precedence, and the natural-class organization of grammatical functions (also known as the Lexical Mapping Theory). The Lexical Mapping Theory started with the pioneering work of Levin (1986) and was formally introduced in Bresnan and Kanerva (1989). The extended technique of functional uncertainty is described in Kaplan and Zaenen (1989a), and Kaplan and Zaenen (1989) present a discussion on functional precedence in LFG. For the operation of unification, Shieber (1986) is still the best reference.