Section: New Results

Incomplete Databases

Participants : Nadime Francis, Cristina Sirangelo.

Incomplete databases appear in several different scenarios. Intuitively, pieces of information might not be available, or can get lost due to failures in storage or transmission. Alternatively, some complex data managements tasks, such as data integration or data exchange, use incomplete databases as a model for databases with missing or unspecified information. In the context of the Web, these tasks have become even more crucial, which increased the need to handle incomplete databases. Given an incomplete database, one of the first question to answer is that of consistency: can we make sure that the incomplete database can be completed as a real database conforming to some specified schema.

Together with Claire David and Filip Murlak, we have considered this problem when incomplete instances are represented as incomplete XML documents, where labels and nodes might be missing, and we additionally assume the DOM semantics, meaning that nodes never lose their identity (otherwise, they are considered completely lost). These are further modeled as injective tree patterns using child and descendant relations. In [17] , we close the question of the complexity of checking the consistency of such patterns with regards to a fixed regular tree language: it is polynomial for patterns that do not use child edges, and for patterns that use both, it is already NP-complete for patterns using at most two descendant edges per branch, the case for at most one descendant edge being already known to be polynomial.

In [12] we have studied the feasibility of query answering in the presence of incomplete information in data. In particular we have generalized conditions allowing classical query evaluation techniques to be applicable also in the presence of incompleteness. Our results show that conditions found in some of our previous work can be significantly relaxed so as to account for more complex semantics of incompleteness, originating in the fields of logic programming, programming semantics and data exchange.