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Conjunction & Plurality:
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Work in formal semantics of natural language and work in generative syntax have often looked at the same phenomena from mutually unenlightening perspectives. Syntax has typically dealt with a wider set of data and languages, but has often overlooked issues of interpretation. Conversely, a number of longstanding syntactic notions (e.g. empty categories, functional projections) have never been widely used in semantic analysis; furthermore, the semantic relevance of important syntactic hypotheses such as the Internal Subject Hypothesis has never been investigated beyond some basic scope facts.
The overall goal of our research is to show that it is both possible and advantageous to combine syntactic and semantic approaches to language. The particular issue we will focus on is the interpretation of conjunction and what it reveals about the syntactic and semantic structure of predicates and nominal arguments across languages. In the last year we have looked at a specific aspect of this issue, coordination of material inside the noun phrase. The data from this little-studied domain have led us to propose a novel semantics for the conjunction of nominals and an important cross-linguistic difference in the way languages obtain the denotation of plural and singular nominals, which makes crucial use of syntactically motivated functional projections as a way to obtain a compositional meaning. Our project is now to provide an account of the different behaviour of mass nouns, to extend the analysis of conjunction from argumental to predicate nominals, and then to predicates in general. The ultimate goal is a unified analysis of coordination which can then serve as a more sophisticated probe for the functional structure of categories.
In English and Dutch, the conjunction of two singular Ns under a singular Det may refer either to two individuals (split interpretation), or to a single individual with two (compatible) properties (joint interpretation).
| 1. | a. | That soldier and sailor were good friends | |
| b. | John's friend and colleague was here. |
Most other languages (we exemplify with Italian) allow only the joint reading in the singular:
| 2. | a. | * |
Quel soldato e marinaio erano buoni amici. |
| b. | L'amico e collaboratore di Gianni è stato qui. |
In the plural however, N-N conjunction allows a split reading in many and perhaps all languages.
Current semantic analyses of conjunction treat it either as set-theoretic intersection (e.g. (Winter 1996) or as ambiguous between intersection and union/sum-formation (Link 1984, Hoeksema 1983 and others). While intersection can yield the joint reading in (1b) and (2b), neither union or intersection can render the split reading in (1a), as we argue in Heycock & Zamparelli 2000. Moreover, no analysis known to us would predict any particular cross-linguistic difference in this domain.
Our proposal is that, cross-linguistically, "and'' unambiguously denotes the operation of set product, defined as the set of unions over each possible n-tuple across n conjuncts. To exemplify:
| 3. | a. | ||friend|| = {{a}, {b}, {c}}, ||colleague||= {{c}, {d}} | |
| b. | ||friend and colleague|| = {{a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {c}} |
Note that (3b) contains pairs of distinct individuals, one a friend, the other a colleague: the appropriate denotation for the split reading of "a friend and colleague''. But it also contains one individual, ({c}), who is both a friend and a colleague: the joint, intersective reading of (1b).
The lack of a split reading in the singular in some languages derives from a difference in the way languages realise the semantics of number. We base our analysis on the following DP structure:
| 4. | [DP D [NumP Num [PlP Pl [NP N ]]]] |
We take each functional head to denote a function over the denotation of its syntactic complement, and assume that (singular and plural) NPs denote sets of singletons. In Italian, Pl computes the closure under union of the NP denotation, obtaining a join semi-lattice. Num checks the PLUR features of N, and filters this lattice accordingly, excluding singularities (N[+PLUR]) or pluralities (N[-PLUR]). The result provides a restrictor for D. Applied to a denotation such as (3b) with N singular, this operation will leave only {{c}}, hence the unambiguously joint interpretation of (2). In the plural, however, it can be shown that the same semantics preserves the split reading (Heycock & Zamparelli 2000).
English differs from Italian in that singularity and plurality are not obtained by doing closure-under-union and filtering the result, but rather by doing or not doing closure-under-union itself. Only if +PLUR is present does Pl compute the closure; otherwise the NP denotation remains unaltered. Since the semantic effect of plur is exhausted at PlP, PLUR never has any semantic effect at NumP, and no filtering of the lattice takes place. Consequently, even in the singular a denotation such as (3b) will reach D, making available both joint and split readings. Independent evidence for this difference comes from the existence of plural "no'' and dependent plurals ("Unicorns have horns'') in English but not in Italian.
Our semantics for conjunction can be shown to work correctly for whole DPs in argument position, via a generalized quantifier analysis. However, we now need to explore how it extends to predicate nominals and to predicates of other categories. It is clear that conjoined predicates can apply to temporally distinct stages of an individual (5); moreover, some predicates can apply to different subgroups of the subject's denotation (6):
| 5. | John was (first) single and (then) married. |
| 6. | a. | My grandparents were Scots and Italians. | |
| b. | The children are in the bathroom and in the living room. | ||
| c. | Those two men are a doctor and a lawyer. |
However, cross-linguistically, not all predicates behave in this way:
| 7. | a. | ?? |
My grandparents were very tall and quite short. |
| b. | ?? |
The documents were mailed out last week and were written today. |
Similar facts in ATB-extracted Wh-DPs lead us to the hypothesis that the impossibility for a predicate to "split'' the subject may be typical of categories for which an internal subject has been proposed: VPs and AdjPs but not DPs (and possibly PPs). In the first stage of our research we plan to address the following questions:
| a. | How exactly does the SIH block the possibility of ``splitting'' a plural subject? |
| b. | How do expressions such as ``respectively'' work in this context? |
| c. | Can split conjunction be used to test for internal subjects in other domains (e.g.relative clauses, attributive adjectives, comparatives)? |
| d. | Does predicate conjunction exhibit cross-linguistic differences related to those found in the DP-internal domain? |
| e. | Can examples like (5) be subsumed under the same analysis? |
Answering questions (b--d) requires the collection of multilingual judgements and corpus data. For this purpose we plan to use the tools developed at the Human Communication Research Centre. We plan to investigate (e) in consultation with researchers currently working on the semantics of discourse structure at the School of Cognitive Science, University of Edinburgh
Preliminary searches on the British National Corpus have revealed that the most common type of DP-internal split coordination involves abstract mass nouns ("their fitness and concentration,'' "this information and knowledge''). Strikingly, similar examples are grammatical also in Italian:
| 8. | La corruzione e lentezza del tribunale era/erano nota/e a tutti. the corruption and slowness of-the court was/were known[sg]/[pl] to everyone. |
The contrast between (8) and the ungrammatical (2a) bolsters the close relation between mass nouns and plurals advanced on semantic grounds since Link 1983. However, with concrete mass nouns the divergence between English and Italian re-emerges; i.e. these nouns appear to behave like count nouns. Thus (9) is ungrammatical, just like (2a):
| 9. | * |
Il burro ed olio sono freschi. the butter and oil are fresh |
This distinction prompts a reevalution of the unitary status of the class of mass nouns, which we propose to address in the second stage of the project. This will involve further corpus work across languages, since at present not even the data are available in this area. We then propose to test the resulting classes against current theories of mass noun semantics (in particular Link 1983, Chierchia 1998) and to investigate their interaction with measure phrases and classifiers.