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We present our results regarding the automatic construction of a knowledge graph from historical documents related to the Chilean dictatorship period (1973-1990). Our approach consists on using LLMs to automatically recognize entities and relations between these entities, and also to perform resolution between these sets of values. In order to prevent hallucination, the interaction with the LLM is grounded in a simple ontology with 4 types of entities and 7 types of relations. To evaluate our architecture, we use a gold standard graph constructed using a small subset of the documents, and compare this to the graph obtained from our approach when processing the same set of documents. Results show that the automatic construction manages to recognize a good portion of all the entities in the gold standard, and that those not recognized are mostly explained by the level of granularity in which the information is structured in the graph, and not because the automatic approach misses an important entity in the graph. Looking forward, we expect this report will encourage work on other similar projects focused on enhancing research in humanities and social science, but we remark that better evaluation metrics are needed in order to accurately fine-tune these types of architectures., Comment: 11 pages, 1 figure, 2 tables. Paper submitted to KBC-LM 2024

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high interpretability. These models utilize trained architectures to execute atomic queries and integrate modules that mimic symbolic query operators. However, most neuro-symbolic query processors are constrained to tree-like graph pattern queries. These queries admit a bottom-up execution with constant values or anchors at the leaves and the target variable at the root. While expressive, tree-like queries fail to capture critical properties in knowledge graphs, such as the existence of multiple edges between entities or the presence of triangles. We introduce a framework for answering arbitrary graph pattern queries over incomplete knowledge graphs, encompassing both cyclic queries and tree-like queries with existentially quantified leaves. These classes of queries are vital for practical applications but are beyond the scope of most current neuro-symbolic models. Our approach employs an approximation scheme that facilitates acyclic traversals for cyclic patterns, thereby embedding additional symbolic bias into the query execution process. Our experimental evaluation demonstrates that our framework performs competitively on three datasets, effectively handling cyclic queries through our approximation strategy. Additionally, it maintains the performance of existing neuro-symbolic models on anchored tree-like queries and extends their capabilities to queries with existentially quantified variables.

Characterizing the separation power of graph neural networks (GNNs) provides an understanding of their limitations for graph learning tasks. Results regarding separation power are, however, usually geared at specific GNN architectures, and tools for understanding arbitrary GNN architectures are generally lacking. We provide an elegant way to easily obtain bounds on the separation power of GNNs in terms of the Weisfeiler-Leman (WL) tests, which have become the yardstick to measure the separation power of GNNs. The crux is to view GNNs as expressions in a procedural tensor language describing the computations in the layers of the GNNs. Then, by a simple analysis of the obtained expressions, in terms of the number of indexes and the nesting depth of summations, bounds on the separation power in terms of the WL-tests readily follow. We use tensor language to define Higher-Order Message-Passing Neural Networks (or k-MPNNs), a natural extension of MPNNs. Furthermore, the tensor language point of view allows for the derivation of universality results for classes of GNNs in a natural way. Our approach provides a toolbox with which GNN architecture designers can analyze the separation power of their GNNs, without needing to know the intricacies of the WL-tests. We also provide insights in what is needed to boost the separation power of GNNs., Comment: 43 pages, accepted as oral presentation at ICLR 2022: https://openreview.net/forum?id=wIzUeM3TAU

Various recent proposals increase the distinguishing power of Graph Neural Networks GNNs by propagating features between $k$-tuples of vertices. The distinguishing power of these "higher-order'' GNNs is known to be bounded by the $k$-dimensional Weisfeiler-Leman (WL) test, yet their $\mathcal O(n^k)$ memory requirements limit their applicability. Other proposals infuse GNNs with local higher-order graph structural information from the start, hereby inheriting the desirable $\mathcal O(n)$ memory requirement from GNNs at the cost of a one-time, possibly non-linear, preprocessing step. We propose local graph parameter enabled GNNs as a framework for studying the latter kind of approaches and precisely characterize their distinguishing power, in terms of a variant of the WL test, and in terms of the graph structural properties that they can take into account. Local graph parameters can be added to any GNN architecture, and are cheap to compute. In terms of expressive power, our proposal lies in the middle of GNNs and their higher-order counterparts. Further, we propose several techniques to aide in choosing the right local graph parameters. Our results connect GNNs with deep results in finite model theory and finite variable logics. Our experimental evaluation shows that adding local graph parameters often has a positive effect for a variety of GNNs, datasets and graph learning tasks.

Work on knowledge graphs and graph-based data management often focus either on declarative graph query languages or on frameworks for graph analytics, where there has been little work in trying to combine both approaches. However, many real-world tasks conceptually involve combinations of these approaches: a graph query can be used to select the appropriate data, which is then enriched with analytics, and then possibly filtered or combined again with other data by means of a query language. In this paper we propose a declarative language that is well suited to perform graph querying and analytical tasks. We do this by proposing a minimalistic extension of SPARQL to allow for expressing analytical tasks; in particular, we propose to extend SPARQL with recursive features, and provide a formal syntax and semantics for our language. We show that this language can express key analytical tasks on graphs (in fact, it is Turing complete), offering a more declarative alternative to existing frameworks and languages. We show how procedures in our language can be implemented over an off-the-shelf SPARQL engine with a specialised client that allows parallelisation and batch-based processing when memory is limited. Results show that with such an implementation, procedures for popular analytics currently run in seconds or minutes for selective sub-graphs (our target use-case) but struggle at larger scales., Comment: 14 pages, 1 figure

Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality we either need to build completely new indexes, or we must populate the database with several instantiations of indexes such as B$+$-trees. Either way, this means spending an extra amount of storage space that may be non-negligible. We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quad tree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal.

Assessing and improving the quality of data in data-intensive systems are fundamental challenges that have given rise to numerous applications targeting transformation and cleaning of data. However, while schema design, data cleaning, and data migration are nowadays reasonably well understood in isolation, not much attention has been given to the interplay between the tools that address issues in these areas. Our focus is on the problem of determining whether there exist sequences of data-transforming procedures that, when applied to the (untransformed) input data, would yield data satisfying the conditions required for performing the task in question. Our goal is to develop a framework that would address this problem, starting with the relational setting. In this paper we abstract data-processing tools as black-box procedures. This abstraction describes procedures by a specification of which parts of the database might be modified by the procedure, as well as by the constraints that specify the required states of the database before and after applying the procedure. We then proceed to study fundamental algorithmic questions arising in this context, such as understanding when one can guarantee that sequences of procedures apply to original or transformed data, when they succeed at improving the data, and when knowledge bases can represent the outcomes of procedures. Finally, we turn to the problem of determining whether the application of a sequence of procedures to a database results in the satisfaction of properties specified by either queries or constraints. We show that this problem is decidable for some broad and realistic classes of procedures and properties, even when procedures are allowed to alter the schema of instances.

Assessing and improving the quality of data are fundamental challenges for data-intensive systems that have given rise to applications targeting transformation and cleaning of data. However, while schema design, data cleaning, and data migration are now reasonably well understood in isolation, not much attention has been given to the interplay between the tools addressing issues in these areas. We focus on the problem of determining whether the available data-processing procedures can be used together to bring about the desired quality of the given data. For instance, consider an organization introducing new data-analysis tasks. Depending on the tasks, it may be a priority to determine whether the data can be processed and transformed using the available data-processing tools to satisfy certain properties or quality assurances needed for the success of the task. Here, while the organization may control some of its tools, some other tools may be external or proprietary, with only basic information available on how they process data. The problem is then, how to decide which tools to apply, and in which order, to make the data ready for the new tasks? Toward addressing this problem, we develop a new framework that abstracts data-processing tools as black-box procedures with only some of the properties exposed, such as the applicability requirements, the parts of the data that the procedure modifies, and the conditions that the data satisfy once the procedure has been applied. We show how common tasks such as data cleaning and data migration are encapsulated into our framework and, as a proof of concept, we study basic properties of the framework for the case of procedures described by standard relational constraints. While reasoning in this framework may be computationally infeasible in general, we show that there exist well-behaved special cases with potential practical applications.

In visual exploration and analysis of data, determining how to select and transform the data for visualization is a challenge for data-unfamiliar or inexperienced users. Our main hypothesis is that for many data sets and common analysis tasks, there are relatively few "data slices" that result in effective visualizations. By focusing human users on appropriate and suitably transformed parts of the underlying data sets, these data slices can help the users carry their task to correct completion. To verify this hypothesis, we develop a framework that permits us to capture exemplary data slices for a user task, and to explore and parse visual-exploration sequences into a format that makes them distinct and easy to compare. We develop a recommendation system, DataSlicer, that matches a "currently viewed" data slice with the most promising "next effective" data slices for the given exploration task. We report the results of controlled experiments with an implementation of the DataSlicer system, using four common analytical task types. The experiments demonstrate statistically significant improvements in accuracy and exploration speed versus users without access to our system.

Semantic Web, and its underlying data format RDF, lend themselves naturally to navigational querying due to their graph-like structure. This is particularly evident when considering RDF data on the Web, where various separately published datasets reference each other and form a giant graph known as the Web of Linked Data. And while navigational queries over singular RDF datasets are supported through SPARQL property paths, not much is known about evaluating them over Linked Data. In this paper we propose a method for evaluating property path queries over the Web based on the classical AI search algorithm A*, show its optimality in the open world setting of the Web, and test it using real world queries which access a variety of RDF datasets available online.

Despite the fact that JSON is currently one of the most popular formats for exchanging data on the Web, there are very few studies on this topic and there are no agreement upon theoretical framework for dealing with JSON. There- fore in this paper we propose a formal data model for JSON documents and, based on the common features present in available systems using JSON, we define a lightweight query language allowing us to navigate through JSON documents. We also introduce a logic capturing the schema proposal for JSON and study the complexity of basic computational tasks associated with these two formalisms.

We survey foundational features underlying modern graph query languages. We first discuss two popular graph data models: edge-labelled graphs, where nodes are connected by directed, labelled edges; and property graphs, where nodes and edges can further have attributes. Next we discuss the two most fundamental graph querying functionalities: graph patterns and navigational expressions. We start with graph patterns, in which a graph-structured query is matched against the data. Thereafter we discuss navigational expressions, in which patterns can be matched recursively against the graph to navigate paths of arbitrary length; we give an overview of what kinds of expressions have been proposed, and how they can be combined with graph patterns. We also discuss several semantics under which queries using the previous features can be evaluated, what effects the selection of features and semantics has on complexity, and offer examples of such features in three modern languages that are used to query graphs: SPARQL, Cypher and Gremlin. We conclude by discussing the importance of formalisation for graph query languages; a summary of what is known about SPARQL, Cypher and Gremlin in terms of expressivity and complexity; and an outline of possible future directions for the area.

Nested regular expressions (NREs) have been proposed as a powerful formalism for querying RDFS graphs, but research in a more general graph database context has been scarce, and static analysis results are currently lacking. In this paper we investigate the problem of containment of NREs, and show that it can be solved in PSPACE, i.e., the same complexity as the problem of containment of regular expressions or regular path queries (RPQs).

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if it is denoted by some regular expression obtained by replacing variables with letters; under the certainly semantics, the word must be denoted by every such expression. Such languages are regular, and we show that they naturally arise in several applications such as querying graph databases and program analysis. As the main contribution of the paper, we provide a complete characterization of the complexity of the main computational problems related to such languages: nonemptiness, universality, containment, membership, as well as the problem of constructing NFAs capturing such languages. We also look at the extension when domains of variables could be arbitrary regular languages, and show that under the certainty semantics, languages remain regular and the complexity of the main computational problems does not change.

In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For each of these proposals, we concentrate on the three following problems: the definition of the semantics of the operator, the language needed to express the operator, and the algorithmic issues associated to the problem of computing the operator. It should be pointed out that we primarily consider the formalization of schema mappings introduced in the work on data exchange. In particular, when studying the problem of computing the composition and inverse of a schema mapping, we will be mostly interested in computing these operators for mappings specified by source-to-target tuple-generating dependencies.