Monotonicity and Relative Scope Entailments 1

This paper explores the hypothesis that simple monotonicity properties of quantiiers in natural language determine to a large extent the entailment relations between their wide/narrow scope readings. We prove that the disjunctive normal form of upward monotone quanti-ers using principal ultraalters correlates with whether an object narrow scope reading entails an object wide scope reading. This result naturally extends the familiar entailment relations between 98 and 89 quantiication in rst order logic into arbitrary \\nitely based" upward monotone determiners (over possibly innnite models), which are precisely deened. Given a simple sentence of the form Subject-Verb-Object, we are interested in the logical relations between the object narrow scope (ONS) and the object wide scope (OWS) readings of the sentence. In 4], Zimmermann (1993) fully characterizes the class of "scopeless" object quantiiers { those for which the ONS and OWS readings are equivalent for any subject. Zim-mermann shows that this class is closely related to the class of (principal) ultraalters (names). In 3], Westerst ahl (1996) fully characterizes the class of "self-commuting" quantiiers, i.e. the quantiiers Q for which ONS and OWS readings are equivalent when Q is substituted for both subject and object. However, as far as we know, the more general problem of characterizing (possibly one-way) entailment relations between ONS and OWS readings has not been given serious attention. Global determiners (see 2]) are functors that map any non-empty domain