Reasoning in higraphs with loose edges

Harel (1988) introduces the notion of zooming out as a useful operation in working with higraphs. Zooming out allows one to consider less detailed versions of a higraph by dropping some detail from the description in a structured manner. Although this is a very useful operation it seems it can be misleading in some circumstances by allowing the user of the zoomed out higraph to make false inferences given the usual transition system semantics for higraphs. We consider one approach to rectifying this situation by following through Harel's suggestion that, in some circumstances, it may be useful to consider higraphs with edges that have no specific origin or destination. We call these higraphs loose higraphs and show that an appropriate definition of zooming on loose higraphs avoids some of the difficulties arising from the use of zooming. We also consider a logic for connectivity in loose higraphs