The paper presents a constraint based semantic formalism for HPSG. The
advantages of the formlism are shown with respect to a grammar for a fragment
of German that deals with (i) quantifier scope ambiguities triggered by
scrambling and/or movement and (ii) ambiguities that arise from the
collective/distributive distinction of plural NPs. The syntax-semantics
interface directly implements syntactic conditions on quantifier scoping and
distributivity. The construction of semantic representations is guided by
general principles governing the interaction between syntax and semantics. Each
of these principles acts as a constraint to narrow down the set of possible
interpretations of a sentence. Meanings of ambiguous sentences are represented
by single partial representations (so-called U(nderspecified) D(iscourse)
R(epresentation) S(tructure)s) to which further constraints can be added
monotonically to gain more information about the content of a sentence. There
is no need to build up a large number of alternative representations of the
sentence which are then filtered by subsequent discourse and world knowledge.
The advantage of UDRSs is not only that they allow for monotonic incremental
interpretation but also that they are equipped with truth conditions and a
proof theory that allows for inferences to be drawn directly on structures
where quantifier scope is not resolved
