The paper introduces a model of the Web as an in nite, semistructured set of objects. We reconsider the classical notions of genericity and computability of queries in this new context and relate them to styles of computation prevalent on the Web, based on browsing and searching. We revisit several well-known declarative query languages rst-order logic, Datalog, and Datalog with negation and consider their computational characteristics in terms the notions introduced in this paper. In particular, we are interested in languages or fragments thereof which can be implemented by browsing, or by browsing and searching combined. Surprisingly, strati ed and well-founded semantics for negation turn out to have basic shortcomings in this context, while in ationary semantics emerges as an appealing alternative.