Dynamic Graph Queries

Graph databases in many applications - semantic web, transport or biological networks among others - are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries often combine first-order and navigational features. Motivated by recent results on maintaining dynamic reachability, we study the dynamic evaluation of traditional query languages for graphs in the descriptive complexity framework. Our focus is on maintaining regular path queries, and extensions thereof, by first-order formulas. In particular we are interested in path queries defined by non-regular languages and in extended conjunctive regular path queries (which allow to compare labels of paths based on word relations). Further we study the closely related problems of maintaining distances in graphs and reachability in product graphs. In this preliminary study we obtain upper bounds for those problems in restricted settings, such as undirected and acyclic graphs, or under insertions only, and negative results regarding quantifier-free update formulas. In addition we point out interesting directions for further research

Conjunctive Queries for Logic-Based Information Extraction

This thesis offers two logic-based approaches to conjunctive queries in the context of information extraction. The first and main approach is the introduction of conjunctive query fragments of the logics FC and FC[REG], denoted as FC-CQ and FC[REG]-CQ respectively. FC is a first-order logic based on word equations, where the semantics are defined by limiting the universe to the factors of some finite input word. FC[REG] is FC extended with regular constraints. The second approach is to consider the dynamic complexity of FC.Comment: Based on the author's PhD thesis and contains work from two conference publications (arXiv:2104.04758, arXiv:1909.10869) which are joint work with Dominik D. Freydenberge