Scope-related cumulativity asymmetries and cumulative composition

Abstract

Some elements in German and English, e.g. every DPs, give rise to cumulativity asymmetries: They allow for cumulative readings only if they occur in the scope of another semantically plural expression. We present a surface-compositional and event-less analysis of this pattern, expanding Schmitt's (2017) 'plural projection' framework. In this system, any constituent containing a semantically plural subexpression denotes a set of (possibly higher-type) pluralities. Cumulativity is built into the rules implementing this 'projection' of semantic plurality.

Pluralities across categories and plural projection

“…This shows that we must rethink quantificational elements not only in terms of their first arguments (taking plural sets as their arguments and thus blocking plural early access projection from their restrictor), but also in terms of their values: Examples like (107) show that quantifiers partake in cumulative readings, but that the projecting plurality cannot simply be a quantifier plurality. We address some aspects of this problem in Haslinger & Schmitt 2018, but it is an open question which elements exactly block plural projection and whether this particular behavior is correlated with the unexpected construals of conjunction just witnessed.…”

“…A number of configurations -including those with collective predicates and cases where a plural expression is embedded by quantificational material as in ( 8) -will require an expansion of the system. I believe such an expansion to be possible (see Haslinger & Schmitt 2018), but since a proper account would not only warrant a technical discussion, but also a detailed empirical investigation of the phenomena (see e.g., Heycock & Zamparelli 2005, Champollion 2016), I only give a general indication of what such an expansion could look like.…”

Contextual restrictions on cumulativity

“…The ontological assumption underlying Schmitt's (2019) approach is that semantic plurality is a cross-categorial notion, so that there are pluralities of predicates or propositions. These pluralities can be thought of as standing in a one-to-one correspondence to nonempty sets of predicates or propositions (see Haslinger & Schmitt 2018 for details). Thus, a predicate conjunction like sitting and cooking essentially contributes a predicate plurality, sitting ⊕ cooking , with the atomic parts sitting and cooking , to the semantic composition.…”

Syntactic conditions on cumulative readings of German jeder ‘every’ DPs

“…3 The structural view is compatible with several accounts of the semantics of cumulative every that differ radically in their assumptions: While Champollion (2010) employs cumulation operators that combine with predicates denoting relations between individuals, Ferreira (2005) and Chatain (2020Chatain ( , 2022 exemplify an event-based approach, on which cumulativity is introduced via thematic-role relations relating individuals to events. Haslinger and Schmitt's (2018) account, which attributes cumulativity to special composition rules rather than cumulation operators or thematic roles, also predicts the relevant factors to be structural. 4 In our semantic analysis in Sect.…”

“…But this traditional meaning, when combined with the standard e, e, t interpretation of transitive verbs, actually fails to account for a cumulative reading of every-DPs regardless of the syntactic configuration. As alluded to above, there are different semantic analyses that are compatible with a structural approach to cumulativity asymmetries, and each of them deviates in some way from the assumptions about LF syntax that lead to a type mismatch: Event-based approaches (Ferreira, 2005;Chatain, 2020Chatain, , 2022 analyze lexical verbs as denoting unary predicates of events regardless of their arity, and every-DPs as operators on such predicates (possibly mediated by a thematic-role operator); Champollion (2010) analyzes every-DPs not as quantifiers, but as simple type e plurals that must stand in a certain syntactic relation to a cumulation or distributivity operator; and Haslinger and Schmitt (2018) interpret predicates as sets of pluralities (as opposed to simple relations between individuals) and provide a cross-categorial schema to interpret every-DPs as operators on such sets. Finally, in Sect.…”