Structured meanings have evolved as a well-suited tool to describe the semantics of focus constructions (cf. von Stechow 1990; Jacobs 1991; Krifka 1992). In this paper, I will show how structured meanings can be combined with a framework of dynamic interpretation that allows for a cogent expression of anaphoric relations and presuppositions. I will concentrate in particular on the semantics of the focusing particle only and discuss several phenomena that have gone unnoticed or unsolved so far, for example the introduction of discourse markers in the scope of only and alternatives that are anaphorically related to quantifiers. In particular, I will show that the proposed representation format can handle sentences with multiple occurrences of focusing particles. The paper also includes a discussion of the behavior of negation with respect to presuppositions, and of principles that govern the interpretation of focus on quantified NPs.
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