Cumulative readings of "every" and leaks

Abstract

every surprisingly gives rise to cumulative readings (Schein 1993; Kratzer 2000). The distribution of these readings is governed by scope-related asymmetries (Champollion 2010; Haslinger & Schmitt 2018). In this work, I notice a third property of these readings: cumulative readings of every receive weaker "leaky" truth-conditions under negation, previously thought to be unattested (Bayer 2013). Exploiting this third property, I build an event semantics to deliver these "leaky readings" by default. Within this semantics, it becomes possible to account for cumulative readings of every and their properties, keeping to standard assumption about the denotation for every. I also show how the same analysis predict the scope-related asymmetries and their less studied interaction with overt movement.

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.…”

“…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.…”

“…There are two different types of semantic analyses of cumulativity asymmetries that can derive the data if semantically plural traces are permitted: The event-based approach (Schein, 1993;Kratzer, 2003;Ferreira, 2005;Zweig, 2008;Chatain, 2020Chatain, , 2022 and the so-called plural projection account of Haslinger andSchmitt (2018, 2020). An analysis capable of deriving the effects of the D-hypothesis within an event-based framework has been worked out by Chatain (2022) 35 , who proposes a generalization analogous to the D-hypothesis for the interaction of cumulativity asymmetries and covert QR.…”

“…Although Chatain does not claim that overt movement of an every-DP can block a previously available cumulative reading, we think his formal system could be expanded directly to our scrambling data. A different variant of the event-based analysis of cumulativity asymmetries, based on a weaker semantics for the thematic-role predicates, is developed in Chatain (2020). Unlike Chatain (2022), this system predicts that movement of a plural definite across an every-DP is not interpretable at all without reconstruction.…”