S UBCATEGORIZABILITY OF G RAMMATICAL F UNCTIONS AND

For any given f-structure to be well-formed, it must satisfy three conditions:

Consistency, Completeness, and Coherence. The concept of subcategorizable, or governable, functions is involved in the last two conditions.

6. a. Consistency (or Functional Uniqueness):

In a well-formed f-structure, any attribute may have at most one value.

b. Completeness

An f-structure is locally complete if and only if it contains all the subcategorizable grammatical functions that its predicate subcategorizes.

An f-structure is complete if and only if all its subsidiary f-structures are locally complete.

c. Coherence

An f-structure is locally coherent if and only if all the subcategorizable grammatical functions that it contains are subcategorized by a local predicate.

An f-structure is coherent if and only if all its subsidiary f-structures are locally coherent.

The one exception to the Consistency condition is the attribute ADJUNCTS, which may have more than one value, in a conglomerated list, which is indicated by curly brackets, {}, in an f-structure. For example, xiao3 hei1 gou3 'little, black dog' would have the following f-structure.

7. [ FORM 'gou3'

ADJ { [ FORM 'xiao3' ] [ FORM 'hei1' ] }

]

The conditions of Completeness and Coherence ensure that all subcategorizable functions an f-structure contains are indeed subcategorized by a local predicate, and that all subcategorized functions are all indeed present locally. Sub-functions of ADJUNCTS, i.e., ADJ and XADJ, being non-subcategorizable, may appear (or be absent) freely and thus are exempted from all the above three conditions. In our vLFG formalism we impose one more well-formedness condition: Comprehensibility.

8. Comprehensibility

In a well-formed f-structure, no attribute may have the value ANY.

ANY, along with OPT and NONE, are three special values that need to be explained. Both ANY and OPT are placeholders, meaning that they always succeed in unification (Shieber 1986:43-44). However, an f-structure with OPT value does not constitute any violation. NONE is quite the opposite in that it always fails if unified with any other value. We will give an example of violation of each of the four conditions.

9. a. Inconsistent: `unification fails because the [ NUMBER SG ] = `result would assign more than one [ NUMBER PL ] `value, SG and PL, to NUMBER

b. Incomplete: `incomplete because PRED [ PRED < SUBJ , OBJ > `subcategorizes two functions but FORM 'construct' `one of them, OBJ, is not contained SUBJ [ FORM 'I' ] `in the f-structure locally

]

c. Incoherent: `incoherent because PRED only [ PRED < SUBJ > `subcategorizes one function and FORM 'sleep' `yet the f-structure contains SUBJ [ FORM 'I' ] `another subcategorizable function, OBJ [ FORM 'mary' ] `OBJ, not subcategorized by the

] `local PRED

GRAMMATICALFUNCTIONSANDANLFGGRAMMAROFMANDARINCHINESE 41

d. Incomprehensible [ PRED < SUBJ >

FORM 'swam'

SUBJ [ FORM 'deer' `incomprehensible because in SUBJ NUMBER ANY `the value of number is ANY

DEFINITE +

] ]

We can see that the condition of Functional Uniqueness or Consistency can be viewed as a general constraint on unification: whenever an attribute has conflicting values, unification fails. However, Completeness, Coherence, and Comprehensibility are constraints on the linguistic well-formedness of an f-structure. In conventional LFG, since the c-structure expanding the whole string has to be built first and then the corresponding f-structure is built, Completeness and Coherence are checked only when an f-structure corresponding to a final c-structure is built. In our vLFG formalism, similarly the Functional Uniqueness is always checked whenever unification takes place and the Completeness Condition and Comprehensibility Conditions are checked only after a final f-structure associated with the entire word string is reached. However, the important difference here is that in vLFG Coherence is checked whenever a partial f-structure containing a subcategorizable function is reached, while in LFG the Coherence Condition, like Completeness Condition, is checked only when a final f-structure is reached. This difference has significant psycholinguistic and computational implications. Although we will not discuss, nor justify, these implications in any detail and will simply note that statistical and psycholinguistic studies will need to be done to substantiate our claims, we will show some examples that intuitively indicate some advantages of the vLFG over LFG formalism.

10. a.*John slept Mary the bed.

b.*John slept Mary the bed, I slept in the chair, and Cindy slept in the sofa.

Given the intransitive "sleep" which subcategorizes <SUBJ> only, the conventional LFG formalism would assign a well-formed c-structure to 10a

which is then ruled out only because when the f-structure is built it is found incoherent due to the existing unsubcategorized OBJ and OBJ2.

10a-f-LFG: `[John slept Mary the bed.]

[ SUBJ [ PRED 'John' ]

PRED 'sleep <(SUBJ)>'

OBJ [ PRED 'Mary' ] `incoherent OBJ2 [ PRED 'bed' `incoherent

DEFINITE +

NUMBER SG

]

TENSE PAST

]

However, in the vLFG formalism, there is no well-formed c-structure assigned to the entire string of 10a, because when "slept" is combined with

"Mary" and "the bed" to form a VP, an f-structure is being built simultaneously to correspond to it and this f-structure will then be found incoherent due to the unsubcategorized OBJ and OBJ2 in relation to "sleep"

and therefore the VP category expanding "slept Mary the bed" or "slept Mary" will never be built. Thus, in the process of the vLFG analysis, there is no c-structure nor f-structure assigned to the entire string of 10a.

10a-f-vLFG: `[John slept][Mary][the bed]

[ SUBJ [ FORM 'John' ] PRED <SUBJ>

TENSE PAST FORM 'sleep' ]

[ FORM 'Mary' ] [ FORM 'bed'

DEFINITE + NUMBER SG ]

GRAMMATICALFUNCTIONSANDANLFGGRAMMAROFMANDARINCHINESE 43

Our approach, again, is more similar to a lexicalist word-dependency theory, e.g., Lexicase, in that the c-structure of a word string is intrinsically tied with the idiosyncratic dependency requirements of words in that string.

Which approach reflects native psychological processing more faithful is a matter for empirical study, but sentences like 10b might give some indication that our approach is more favorable. Conventional LFG would predict that native speakers detect the ungrammaticality of 10b only when they finish reading or listening to the whole string, which is composed of three clauses and the part that is ill-formed is the very first one. Our approach, along with that of dependency grammars, predictS that the ungrammaticality is detected before the end of the string, which is intuitively more correct.

For the following sentences, the conventional LFG would assign c-structures that would not be allowed in vLFG. From a computational point of view, our formalism is thus intuitively more efficient.

11. a. When John slept Mary left.

`c-structure allowed in LFG

b. When John slept Mary Lou left.

`c-structures allowed in LFG

These c-structures with incoherent f-structures would not be allowed in the vLFG formalism and thus such paths would not be pursued further. For 11b, for example, two final c-structures are possible in LFG, one with incoherent f-structure, the other with its f-structure well-formed. In vLFG formalism, again similar to dependency grammars, only one c-structure with a well-formed f-structure is allowed for 11b. We will list below the two f-structures of 11b allowed in LFG.

11b-f-LFG-1: `[[When John slept Mary] Lou left.]

[ SUBJ [ PRED 'Lou' ] PRED 'leave <(SUBJ)>' TENSE PAST

ADJ { [ CFORM 'when' SUBJ [ PRED 'John' ] PRED 'sleep <(SUBJ)>'

OBJ [ PRED 'Mary' ] `incoherent

TENSE PAST

] } ]

11b-f-LFG-2: `[[When John slept] Mary Lou left.]

[ SUBJ [ PRED 'Mary Lou' ] PRED 'leave <(SUBJ)>'

TENSE PAST

ADJ { [ CFORM 'when' SUBJ [ PRED 'John' ]

PRED 'sleep <(SUBJ)>' ]

} ]

Recall that LFG theory imposes the Direct Syntactic Encoding Principle which bans syntactic rules from deleting or replacing any grammatical function. Given this constraint, an incoherent function, once having come to existence in an f-structure, will always be there, and therefore the f-structure is bound to be incoherent. To allow the analysis process to pursue paths that are doomed to failure is counter-intuitive and reduces efficiency. Based on this observation, vLFG formalism checks coherence whenever a subcategorizable function enters an f-structure.

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