EISS 12 A Finer-grained Typology of Perfective Operators On Existential Closure, the Perfective Aspect and Divi-sive Reference

Abstract

We argue that completion and maximality (defined through the notion of self-connectedness) both need to be taken into account as potential parameters in analyses of perfectives. Stative predicates in the French passé composé and passé simple require self-connected maximality and completion , while event (including activity) predicates require event completion only. Event-semantic analyses commonly assume that a (non-quantified) sentence expresses existential quantification over events, typically realized by existential closure in the derivation (e.g., Kratzer 1996), often assumed to be introduced by tense or aspect, especially in neo-Reichenbachian accounts and formalizations of Klein 1994. A typical neo-Reichenbachian definition of the perfective operator (PFV) is as follows (Bohnemeyer 2014), where P is a variable for an eventuality predicate, t T a variable for the topic time, and g the variable assignment function parameter with respect to a model M: (1) [[PFV]] M,g = λP∃e[τ(e) ⊆ t T ∧ P(e)] The imperfective operator (IMPF) is assumed to express the inverse