arXiv subjects
Publications and source records attributed to Piotr Wieczorek.
We propose KG-ER, a conceptual schema language for knowledge graphs that describes the structure of knowledge graphs independently of their representation (relational databases, property graphs, RDF) while helping to capture the semantics of the information stored in a knowledge graph.
We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema. Generic dominance, a classical notion for measuring information capacity, expresses that every instance of a schema can be uniquely represented in the dominating schema, through application of a deterministic, generic data transformation. Our investigation is motivated both by current interest in schema design for graph databases, as well as by intrinsic scientific interest. We also consider the ternary case, but without inclusion dependencies, and discuss how the notions change in the presence of object identifiers.
We propose a new approach to querying graph databases. Our approach balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of minimal (e.g. shortest) and maximal (e.g. most valuable) paths satisfying given criteria. To express complex properties in a modular way, we introduce labelling-generating ontologies. The resulting formalism is computationally attractive - queries can be answered in non-deterministic logarithmic space in the size of the database.
We consider the problem of constructing a Shape Expression Schema (ShEx) that describes the structure of a given input RDF graph. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound i.e., always producing a schema that validates the input RDF graph, and complete i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We study the case where the input graph is typed i.e., every node is given with its types. We limit our attention to a practical fragment ShEx0 of Shape Expressions Schemas that has an equivalent graphical representation in the form of shape graphs. We investigate the problem of constructing a canonical representative of a given shape graph. Finally, we present a sound and complete algorithm for shape graphs thus showing that ShEx0 is learnable from typed graphs.
We study the problem of containment for shape expression schemas (ShEx) for RDF graphs. We identify a subclass of ShEx that has a natural graphical representation in the form of shape graphs and their semantics is captured with a tractable notion of embedding of an RDF graph in a shape graph. When applied to pairs of shape graphs, an embedding is a sufficient condition for containment, and for a practical subclass of deterministic shape graphs, it is also a necessary one, thus yielding a subclass with tractable containment. While for general shape graphs a minimal counter-example i.e., an instance proving non-containment, might be of exponential size, we show that containment is EXP-hard and in coNEXP. Finally, we show that containment for arbitrary ShEx is coNEXP-hard and in coTwoNEXP^NP.
Querying graph databases has recently received much attention. We propose a new approach to this problem, which balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of minimal (e.g. shortest) and maximal (e.g. most valuable) paths satisfying given criteria. To express complex properties in a modular way, we introduce labelling-generating ontologies. The resulting formalism is computationally attractive -- queries can be answered in non-deterministic logarithmic space in the size of the database.
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational properties vary (from P to NP-complete). We present a thorough study of the complexity of the model checking problem i.e., is there an embedding of a given tree pattern in a given tree, and we investigate the impact of various restrictions imposed on the tree pattern: bound on the degree of a node, bound on the height, and type of allowed labels and edges.
We investigate the problem of learning XML queries, path queries and tree pattern queries, from examples given by the user. A learning algorithm takes on the input a set of XML documents with nodes annotated by the user and returns a query that selects the nodes in a manner consistent with the annotation. We study two learning settings that differ with the types of annotations. In the first setting the user may only indicate required nodes that the query must return. In the second, more general, setting, the user may also indicate forbidden nodes that the query must not return. The query may or may not return any node with no annotation. We formalize what it means for a class of queries to be \emph{learnable}. One requirement is the existence of a learning algorithm that is sound i.e., always returns a query consistent with the examples given by the user. Furthermore, the learning algorithm should be complete i.e., able to produce every query with a sufficiently rich example. Other requirements involve tractability of learning and its robustness to nonessential examples. We show that the classes of simple path queries and path-subsumption-free tree queries are learnable from positive examples. The learnability of the full class of tree pattern queries (and the full class of path queries) remains an open question. We show also that adding negative examples to the picture renders the learning unfeasible. Published in ICDT 2012, Berlin.