Quantifiers and Partiality

This paper investigates the behaviour of binary quantifiers in settings of incomplete information, i.e., in partial models. The framework to handle informational partiality that is presented in this paper is relevant for the behaviour of quantifiers in the natural language semantics of propositional attitudes and perception reports, for theories of vagueness in natural language and for semantic accounts of natural language fragments containing a truth predicate. First, the constraints on binary relations on a universe that make these relations qualify for the honorific title quantificational are generalized to the partial case. Special consideration is given to quantifiers defined via supervaluation from quantifiers on total models. Next, properties of partial quantifiers are studied, with particular emphasis on behaviour under growth of information and growth of domain. Quantifier interpretations for natural language determiners like all, some, most, exactly two, at least three and at most five, pick out binary relations on sets of individuals, on arbitrary universes E. Notation: QEAB