Information systems for the support of complex business processes are often equipped with web-based front-ends to allow convenient user access. To produce executable specifications of the users' interactions with such web-based applications, we use a visual language that enables developers to model their complex dialog structures. In this paper, we introduce the formal semantics of the core constructs of this Dialog Flow Notation: We define its syntax in terms of invariants about the permitted elements and their relations, and show how any words of the language (i.e. any syntactically correct dialog flow specifications) can be mapped to a deterministic pushdown automaton whose behavior defines the notation's semantics. This gives us and other tool developers a formal basis for the design and implementation of tools and frameworks that mirror the precise meaning of all DFN constructs.