When the restrictor of a quantifier is not overtly given, as in example (1b) below, an inference must be made in order to assign a full interpretation to the sentence. In such cases, many interpretations are possible in principle, but perceivers are rarely aware of this and usually do not experience any processing difficulty.

1. a. An army doctor examined five boys for military service.
     b. From the file it appeared that three were passed as fit.

Our presentation focuses on this type of semantic ambiguity resolution. Two interrelated questions are addressed, (1) How is the ambiguity resolved, i.e., what principles guide the selection of a restrictor (i.e., set to which the quantifier refers)? We hypothesize that the processor prefers selecting the restrictor defined by all relevant information in the preceding discourse. (2) At what moment does the processor make a decision? We assume that semantic processing, like parsing, takes place on a word-by-word basis. The results of two questionnaire studies provide preliminary support for our hypotheses. An on-line (eye-tracking) study, aimed at further exploring the time course of semantic processing, is currently underway.