(Modal) Logics for Semistructed Data

The area of semistructured data includes collections of data items which have in some ways similar but not identical structure. Examples of semistructured data range from heterogeneous databases to the World Wide Web Abi97]. The area is obviously quite heterogeneous itself. However there are some important features common to all kinds of semistructured data, namely: data is represented as an edge labelled graph; querying data involves traversing paths in a graph. Both features suggest that modal logic techniques can be successfully used for analysing logical properties of semistructured data. The reason for believing this is that modal logics were successfully applied to express similar properties over similar graphs, for example transition systems and feature structures. Logical issues involved in working with semistructured data (the list below contains mutually dependent items!) are: which operations should a query language have; expressive power and complexity of query evaluation ; how precisely do we want to describe structures (what is the right notion of equivalence); how do we express information available about the format of data (what is the right description language). The talk will contain an overview of work on semistructured data and advocate the use of`modal frag-ments' of transitive closure logic Imm87] as a formal basis for query and description languages for semistruc-tured data. By a modal fragment of some language containing rst order quantiiers 8 and 9 we mean a fragment where the range of quantiiers is restricted to elements which arèaccessible' from the parameters of the quantiied formula Ale95]. In the context of rst order logic extended with transitive closure operator, accessibility means existence of a path. We believe that this restriction reeects the spirit of navigational query languages such as Lorel AQM97].