Multi-Level Plurals and Distributivity

MULTI-LEVEL PLURALS AND DISTRIBUTIVITY Remko Scha and David Stallard BBN Laboratories Inc. 10 Moulton St. Cambridge, MA 02238 U.S.A. ABSTRACT We present a computational treatment of the semantics of plural Noun Phrases which extends an earlier approach presented by Scha [7] to be able to deal with multiple-level plurals ("the boys and the girls", "the juries and the committees", etc.) 1 We ar- gue that the arbitrary depth to which such plural struc- tures can be nested creates a correspondingly ar- bitrary ambiguity in the possibilities for the distribution of verbs over such NPs. We present a recursive translation rule scheme which accounts for this am- biguity, and in particular show how it allows for the option of "partial distributivity" that collective verbs have when applied to such plural Noun Phrases. 1 INTRODUCTION Syntactically parallel utterances which contain plural noun phrases often require entirely different semantic treatments depending upon the particular verbs (or adjectives or prepositions) that these plural NPs are combined with. For example, while the sen- tence "The boys walk" would have truth-conditions ex- pressed by: 2 Vxe BOYS: WALK[x] the very similar sentence "The boys gather" could not be translated this way. Its truth-conditions would in* stead have to be expressed by something like: GATHER[BOYS] since only a group can "gather', not one person by himself. It is common to call a verb such as "walk" a "distributive" verb, while a verb such as "gather" (or "disperse ~ or intransitive "meet*) is called a ~The wod( presented here was supported unOer DARPA contracts #N00014-85-C-0016 and #N00014-87.C-0085. The vmws and con- clusions contained in this document ere those of the authom and should not be intecpreted as neceeserily repr~tmg the official policies, e~ther expressed or implied, of the Defense Advanced Research Projects Agency or the United Statas Government. 2We ¢jnore here the diecourse ~sues that bear on the inter- pretation of definite NPs "collective" verb. The collective/distributive distinction raises an important issue: how to treat the semantics of plural NPs uniformly. An eadiar paper by Scha ("Distributive, Collective and Cumulative Quantification" [7], hereinafter "DCC") presented a formal treatment of this issue which ex- ploits an idea about the semantics of plural NP's which is due to Bartsch [1]: plural NP's are always interpreted as quantifying over sets rather than in- dividuals; verbs are correspondingly always treated as collective predicates applying to sets. Distributive verbs are provided with meaning postulates which re- late such collective applications to applications on the constituent individuals. The present paper describes an improved and ex- tended version of this approach. Two important problems are addressed. First, there is the problem of ambiguity: the need to allow for more than one distribution pattern for the same verb. Second, there is the problem of "multi-level plurality': the con- sequences which arise for the distributive/collective distinction when one considers conjoined plural NPs such as "The boys and the girls". Both issues are addressed by a two-level system of semantic interpretation where the first level deals with the …

Content truncated to 500 words