Conservativity: a necessary property for the maximization of witness sets
Livio Robaldo · Logic Journal of IGPL · 2013
It is generally assumed that Conservativity is a necessary ingredient for interpreting collective and cumulative predicates or, more in general, for interpreting—what I termed as—Independent Set (IS) readings (a.k.a. Scopeless readings). Under this assumption, several approaches aiming at formally providing logical representations of collective/cumulative readings implement Conservativity. This is done also in the frameworks defined in Winter (2001, Flexibility Principles in Boolean Semantics: Coordination, Plurality, and Scope in Natural Language, MIT Press) and in Robaldo (2011, J. Logic Lang. Infor., 20, 233–271). This article investigates further the role played by Conservativity in the interpretation of IS readings, and argues that its need is not specifically due to the use of collective/cumulative predicates. Rather, it serves to maximize witness sets for quantifiers thereby guaranteeing correct truth conditions in several cases.