Overt distributivity in algebraic event semantics

Abstract

This is the second in a pair of papers that aim to provide a comprehensive analysis of the semantic phenomenon of distributivity in natural language. This paper describes and explains observable cross-linguistic differences in overt distributive items in the framework of Neo-Davidsonian algebraic event semantics. The previous paper, Champollion 2016a, postulated two covert distributivity operators, D and Part, in the grammar, even though the semantic effects of D can be subsumed under the workings of Part. This paper motivates the split by arguing that distance-distributive items across languages are in essence overt versions of these operators. For example, English each lexicalizes D while German jeweils lexicalizes Part. For this reason, jeweils occurs in a wider range of distributive environments, including distribution over salient occasions. The proposed analysis explains why distributive items that can also be used as determiners, such as each and every, never allow distribution over occasions. It also accounts for the ability of these determiners to take part in cumulative readings and to interact with nondistributive event modifiers. The paper and its companion include an explicit proposal for the compositional process in event semantics.

Stratified reference: the common core of distributivity, aspect, and measurement

“…Distributivity operators, whether covert or overt, can be reformulated in ways that are very similar to stratified reference. The difference between atomic and nonatomic distributivity can then be recast as a difference in settings of the granularity parameter of stratified reference (Champollion 2014a(Champollion , 2014b. Certain overt modifiers, such as adverbial each and together, can also determine whether the predicate that they modify is understood distributively or collectively.…”

Covert distributivity in algebraic event semantics

“…This is useful from the point of view of algebraic semantics because it allows us to formulate cross-domain generalizations more easily (Champollion 2010b). Finally, it allows us to treat distance-distributive items uniformly no matter if they occur within verbal or within nominal projections (Champollion 2016). That said, it may be possible to reformulate much of the content of this paper and Champollion 2016 in other approaches than Neo-Davidsonian event semantics if one wishes to do so.…”

“…My operator in (45) is parametrized for the relevant thematic role. This thematic role can be supplied by coindexation with an appropriate θ role head (Champollion 2016). Maintaining the adjacency assumption would make it harder to build on the D operators to account for the phenomenon of distance distributivity, as I do in Champollion 2016.…”

Refining stratified reference

“…Each accepts only distributive predicates because it requires distribution to events with atomic participants such as smiling events, while all also accepts certain collective predicates because it merely requires distribution to events with small but potentially nonatomic numbers of participants, such as gathering events. The same core idea can also be brought to bear on the difference between atomic and nonatomic covert distributivity operators and on the behavior of indefinites in the scope of for-adverbials (Champollion 2015a), as well as on the crosslinguistic difference between atomic and nonatomic adnominal distance-distributive items, such as English each and German jeweils (Champollion 2015b). Divided reference is not well-suited for any of these purposes because it lacks a granularity parameter.…”

“…In Champollion (2015a), I use slight variations of (23) to redefine the atomic and nonatomic distributivity operators originally introduced in Link (1987) and Schwarzschild (1996). I argue there that they are modifiers as well, just like adverbial each and similar items in other languages, which can be analyzed in terms of these operators (Champollion 2015b). It is encouraging that the reformulation in (23) brings stratified reference even closer to these operators and items.…”