- Scalarity in the verbal domain by Olga Kagan
A long-standing topic in the discussion of Slavic languages is the proper analysis of verbal prefixes. Verbal prefixes play a special role in the expression of grammatical aspect as well as in word formation. One of the more complex issues associated with verbal prefixes in the Slavic languages is that they seem to resist a systematic and uniform analysis. In her monograph, Olga Kagan proposes a unified analysis of Russian verbal prefixes. The overall goal of her book is, as she states (p. 21), "to provide a unified formal semantic analysis for individual prefixes as well as for the more general system that underlies verbal prefixation in Russian." The analysis Kagan proposes is couched in degree semantics. A scalar approach to verbal prefixes in Slavic languages is not novel and goes back to Filip's work on this topic (e.g., Filip 2000). Nevertheless, the extent to which Russian verbal prefixes are covered within this analysis is unique to Kagan's work.
Degree semantics originated in the analysis of gradable adjectives like English tall or expensive. The notion of a scale is at the heart of this approach. A scale, following Kennedy and McNally (2005), among others, is a linearly ordered set of values (or degrees) of a measurement dimension such as height, price, or width. A gradable adjective, for example, tall, maps its argument onto a scale (in this case a height scale) and states the argument's degree on that scale, i.e., its height. Each gradable adjective requires a comparison degree, which is often left implicit. Saying John is tall can be interpreted as meaning 'John is tall for a boy of his age' or 'John is tall for an average American'. The exact interpretation is often determined by the context. Thus, saying that John is tall is a comparison of his degree of tallness to an (implicit) comparison degree.
Kagan takes the essential ingredients of degree semantics—scales and their components as well as standards of comparison—and applies them to the analysis of verbal prefixes in Russian. The central hypothesis put forward by Kagan is called the "scale hypothesis." It states that all verbal prefixes are instantiations of the same template. Without going into the formal details, the basic idea is that verbal prefixes specify a relation between degrees. The degree of a gradable property associated with the verbal predicate can either be less than (<), more than (>) or equal to (=) a comparison degree. The template [End Page 131] Kagan proposes is shown below in (1).1 A prefix takes a gradable property Q, which is related to a predicate P, and specifies the relation R between the degree d of the gradable property and a comparison degree ds. The second degree argument in the template, d', is a degree related to the predicate P. In case P and Qp coincide, d' is equal to d. Kagan does not explain why the predicate needs to have a degree argument when the prefix applies to the gradable property Q which is related to P.2 f(e) is a function that restricts the degree to a stage of the event (i.e., its beginning or its end). The verbal prefix indicates whether d is less than, more than, or equal to the standard of comparison at, for example, the end of the event. Beside the relation R, verbal prefixes can also specify the type of gradable property Q, the standard of comparison ds, or the function f which relates the degree to a part of the event. Thus, the template contains a number of variables that can either be saturated by the verbal prefix or the linguistic context (e.g., the verb or one of its complements) and therefore leaves many options for variation among verbal prefixes.
(1). The scale hypothesis (Kagan 2016: 26)
If π is a verbal prefix in Russian, then [[π]] instantiates the following template:
λPλdsλdλd'λxλe.[P(d')(x)(e) ∧ Qp(d)(x)(f(e)) ∧ d R...