Predicate logic, (sometimes extended with for example generalised quantifiers or discourse markers), is often used to represent the meaning of sentences. Due to its long tradition in describing semantics of natural languages it is now a well established and well understood technique. The main advantage of artificial languages like predicate logic is that they are unambiguous. An ambiguous natural language utterance will therefore correspond to more than one expression in predicate logic, one for each reading of the utterance. The disadvantage of this approach is that for very ambiguous inputs, expensive computations must be carried out to compute all readings. The alternative adopted in formalisms based on the idea of monotonic semantic interpretation (, see also  and ) is to represent ambiguity by means of under-specification and to postpone the computation of individual readings as long as possible.
Representing ambiguity by under-specification, and postponing the computation of individual readings, has at least two computational advantages. First, parsing can benefit significantly from the fact that ambiguities which are only semantic (i.e. do not have a syntactic counterpart) are represented by a single derivation. Second, ambiguity resolution can often proceed without enumerating all possible readings of an input separately. A striking example of the latter situation is the translation of QLF's that are ambiguous with respect to quantifier-scope into a domain-specific meaning representation as it is used by the dialogue manager of the OVIS-system. The utterance in (6a), for instance, gives rise to a single QLF (6b), which could be resolved (ignoring the existential quantification over events and the fact that it is a question) to either (6c) or (6d). The domain-specific reading of (6a) (which corresponds to (6c)) is computed on the basis of (6b) directly, and thus never needs to consider the two different readings of this QLF.