A unified semantics for exceptive-additive 'besides'

Abstract

Exceptive expressions like 'except' and 'but' are known to contribute an inference of exception when they occur with universal quantifiers and not to be compatible with non-universal quantifiers. Similarly to exceptives, exceptive-additive expressions like 'besides' contribute an exceptive inference in universal statements. They, however, differ from exceptives in being able to co-occur with non-universal quantifiers. In such contexts they contribute an inference of addition. We propose a unified semantic treatment of exceptive-additives that derives their interaction with universal and non-universal quantifiers from independently motivated mechanisms. We extend the treatment of exceptives in terms of 'Exh' (Gajewski 2013; Hirsch 2016; Crnič 2021) to exceptive-additives and propose that the difference between the two types of constructions lies in the way the alternatives are constructed. By reducing the set of alternatives, we can capture the additive inference of 'besides' with 'exactly n'-numerals. We extend this account to all other instances of modified numerals and existentials by adopting a decompositional approach to their semantics.