Articulated Homogeneity in Cumulative Sentences

Abstract

In this work, I use cumulative readings of every (Champollion, 2010, 2016a; Haslinger & Schmitt, 2018; Kratzer, 2003; Schein, 1993) as a tool to investigate homogeneity in cumulative readings in general. Based on a new observation about the homogeneity properties of cumulative readings of every, I argue that the homogeneity properties of cumulative readings arise from the interaction of multiple operators, each operator contributing one exhaustive participation inference which disappears in negative contexts. I identify these operators with the thematic role heads in a Neo-Davidsonian semantics. The resulting theory is able to predict the homogeneity properties of cumulative sentences from the homogeneity properties of their arguments and the position of these arguments.

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

“…2 By 'LF' we mean the syntactic level that forms the input for semantic interpretation, regardless of whether it differs from surface structure. 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.…”

“…Our final point (in Sect. 5) will thus be to show that this correlation can in fact be derived from semantic properties of the relevant structures: It suggests that semantic plurality and trace binding interact non-trivially (this claim also follows from Chatain's (2022) discussion of cumulativity asymmetries in English).…”

“…In the remainder of the paper, we will first present two new observations about cumulativity asymmetries in German, which correspond to the abstract schemata above and are correctly accounted for by the D-hypothesis. We will then discuss four other, simpler hypotheses that attribute the contrast to a scope asymmetry, a surface c-command asymmetry, thematic-role hierarchies (see Kratzer 2003 andChatain 2022 for discussion, although their actual systems are largely structure-based) and the special status of the subject position (see Drozd et al 2017), respectively. We will argue that, while each of these generalizations captures a part of the data pattern, none of them attains the empirical coverage of the D-hypothesis for the German data.…”

“…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.…”

“…Several works that aim for a compositional semantic analysis of cumulativity asymmetries, rather than a mere description (Ferreira 2005;Champollion 2010;Haslinger and Schmitt 2018;Chatain 2020Chatain , 2022 among others) ultimately predict that the distribution of the cumulative reading should be tied to a structural relation such as scope or c-command. 16 As cumulative readings are often considered to be 'scopeless' in the sense that there are no semantic asymmetries between the plurals involved, let us clar-ify what we mean by 'scope': The availability of a cumulative reading for an every-DP relative to another plural α in a syntactic configuration C would be linked to the scope relation that would hold between α and the every-DP in C on a distributive reading.…”