Browsing Semantics in the Tower Model

Users interact with a hyperdocument by means of browsing through its elements. This behavioral aspect of a hyperdocument is an integral part of its functionality. Hence, one needs a behavioral modeling construct that defines the browsing semantics of each kind of hyperdocument that can be defined within the model. To arrive at the desired general notion of a browsing semantics, observe that the browsing semantics of the familiar network hyperdocument is the set of allowed paths over the network. Hence, the browsing semantics of a particular type of hyperdocument is defined by the set of allowable paths within the hyperdocument. If one regards the familiar network hyperdocument as a finite automaton, the set of allowed paths is the language accepted by the automaton. Thus, a specification of the browsing semantics is a specification of a language of paths. Generally this path language would specify trajectories through composite objects. In some cases, the possible paths can be given extensionally by means of enumerating actual paths. However, in general one would specify the possible paths by giving (intensionally) mappings from time to elements of the composite node (or to coordinates in space).

Accordingly, trajectories are specified by means of space-time axioms: A trajectory (path) is a mapping from time to tower type, where the tower type is that of the elements in the composite object. The browsing semantics of a composite object is a set of trajectories over its elements. This set is specified through space-time axioms defining properties of the mappings used in trajectories. Different strategies for navigation in hyperdocument networks, depending on their topology [VDP89], can be regarded as intensional ways of space-time axioms for particular kinds of composite nodes, e.g. multi-dimensional movements along coordinate axis for a multi-dimensional hypercube.