Closure and Telicity across Categories

One of the fascinating aspects of telicity is its relations with non-verbal categories. Whether a given predicate is telic or atelic does not only depend on the verb, but can also be affected by the count/mass quantification in the NP object, by the lexical semantics of related adjectives, and by the prepositions that the predicate may contain. The latter two factors are in the focus of this paper. For example, the telicity of the deadjectival verb straighten and the complex verb phrase jump into the water, is related to the semantic structures of the adjective straight or the preposition into. A mathematical notion that is relevant to semantic domains across different categories is the notion of closed intervals – intervals that include their limit points. This paper studies the relations that closure properties of adjectives and prepositions bear to the (a)telicity properties of verb phrases. Following Rotstein and Winter (2004), closure of adjectival scales is treated as the defining distinction between two kinds of adjectives (e.g. straight vs. bent) that affects their behavior with almost modifiers. This leads to a conception of