  I explore some of the issues that arise when trying to establish a connection
between the underspecification hypothesis pursued in the NLP literature and
work on ambiguity in semantics and in the psychological literature. A theory of
underspecification is developed `from the first principles', i.e., starting
from a definition of what it means for a sentence to be semantically ambiguous
and from what we know about the way humans deal with ambiguity. An
underspecified language is specified as the translation language of a grammar
covering sentences that display three classes of semantic ambiguity: lexical
ambiguity, scopal ambiguity, and referential ambiguity. The expressions of this
language denote sets of senses. A formalization of defeasible reasoning with
underspecified representations is presented, based on Default Logic. Some
issues to be confronted by such a formalization are discussed.
