Composition and Inversion of Schema Mappings

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

Enhanced Inversion of Schema Evolution with Provenance

Long-term data-driven studies have become indispensable in many areas of science. Often, the data formats, structures and semantics of data change over time, the data sets evolve. Therefore, studies over several decades in particular have to consider changing database schemas. The evolution of these databases lead at some point to a large number of schemas, which have to be stored and managed, costly and time-consuming. However, in the sense of reproducibility of research data each database version must be reconstructable with little effort. So a previously published result can be validated and reproduced at any time. Nevertheless, in many cases, such an evolution can not be fully reconstructed. This article classifies the 15 most frequently used schema modification operators and defines the associated inverses for each operation. For avoiding an information loss, it furthermore defines which additional provenance information have to be stored. We define four classes dealing with dangling tuples, duplicates and provenance-invariant operators. Each class will be presented by one representative. By using and extending the theory of schema mappings and their inverses for queries, data analysis, why-provenance, and schema evolution, we are able to combine data analysis applications with provenance under evolving database structures, in order to enable the reproducibility of scientific results over longer periods of time. While most of the inverses of schema mappings used for analysis or evolution are not exact, but only quasi-inverses, adding provenance information enables us to reconstruct a sub-database of research data that is sufficient to guarantee reproducibility

The Inverse of a Schema Mapping

The inversion of schema mappings has been identified as one of the fundamental operators for the development of a general framework for data exchange, data integration, and more generally, for metadata management. Given a mapping M from a schema S to a schema T, an inverse of M is a new mapping that describes the reverse relationship fromT to S, and that is semantically consistent with the relationship previously established by M. In practical scenarios, the inversion of a schema mapping can have several applications. For example, in a data exchange context, if a mapping M is used to exchange data from a source to a target schema, an inverse of M can be used to exchange the data back to the source, thus reversing the application of M. The formalization of a clear semantics for the inverse operator has proved to be a very difficult task. In fact, during the last years, several alternative notions of inversion for schema mappings have been proposed in the literature. This chapter provides a survey on the different formalizations for the inverse operator and the main theoretical and practical results obtained so far. In particular, we present and compare the main proposals for inverting schema mappings that have been considered in the literature. For each one of them we present their formal semantics and characterizations of their existence. We also present algorithms to compute inverses and study the language needed to express such inverses

Integrated data model and DSL modifications

Companies are increasingly more and more dependent on distributed web-based software systems to support their businesses. This increases the need to maintain and extend software systems with up-to-date new features. Thus, the development process to introduce new features usually needs to be swift and agile, and the supporting software evolution process needs to be safe, fast, and efficient. However, this is usually a difficult and challenging task for a developer due to the lack of support offered by programming environments, frameworks, and database management systems. Changes needed at the code level, database model, and the actual data contained in the database must be planned and developed together and executed in a synchronized way. Even under a careful development discipline, the impact of changing an application data model is hard to predict. The lifetime of an application comprises changes and updates designed and tested using data, which is usually far from the real, production, data. So, coding DDL and DML SQL scripts to update database schema and data, is the usual (and hard) approach taken by developers. Such manual approach is error prone and disconnected from the real data in production, because developers may not know the exact impact of their changes. This work aims to improve the maintenance process in the context of Agile Platform by Outsystems. Our goal is to design and implement new data-model evolution features that ensure a safe support for change and a sound migration process. Our solution includes impact analysis mechanisms targeting the data model and the data itself. This provides, to developers, a safe, simple, and guided evolution process

Conjunctive Queries and Mappings With Unequalities

We study conjunctive queries with unequalities (x ≠ y) and we identify cases when query containment can still be characterized by the existence of homomorphisms. We also identify a class of GLAV-like database schema mappings with unequalities, for which the chase theorem holds, and thus data exchange has the same complexity as for GLAV mappings. Finally, we define a notion of consistency and provide an algorithm to check whether a set of mappings is consistent

Answering Complex Questions by Joining Multi-Document Evidence with Quasi Knowledge Graphs

Direct answering of questions that involve multiple entities and relations is a challenge for text-based QA. This problem is most pronounced when answers can be found only by joining evidence from multiple documents. Curated knowledge graphs (KGs) may yield good answers, but are limited by their inherent incompleteness and potential staleness. This paper presents QUEST, a method that can answer complex questions directly from textual sources on-the-fly, by computing similarity joins over partial results from different documents. Our method is completely unsupervised, avoiding training-data bottlenecks and being able to cope with rapidly evolving ad hoc topics and formulation style in user questions. QUEST builds a noisy quasi KG with node and edge weights, consisting of dynamically retrieved entity names and relational phrases. It augments this graph with types and semantic alignments, and computes the best answers by an algorithm for Group Steiner Trees. We evaluate QUEST on benchmarks of complex questions, and show that it substantially outperforms state-of-the-art baselines

Primitive recursion in the abstract

International audienceRecurrence can be used as a function definition schema for any non-trivial free algebra, yielding the same computational complexity in all cases. We show that primitive-recursive computing is in fact independent of free algebras altogether, and can be characterized by a generic programming principle, namely the control of iteration by the depletion of finite components of the underlying structure

Query Rewriting with Disjunctive Existential Rules and Mappings

We consider the issue of answering unions of conjunctive queries (UCQs) with disjunctive existential rules and mappings. While this issue has already been well studied from a chase perspective, query rewriting within UCQs has hardly been addressed yet. We first propose a sound and complete query rewriting operator, which has the advantage of establishing a tight relationship between a chase step and a rewriting step. The associated breadth-first query rewriting algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive query that has no UCQ-rewriting. It follows that the notion of finite unification sets (fus), which denotes sets of existential rules such that any UCQ admits a UCQ-rewriting, seems to have little relevance in this setting. Finally, turning our attention to mappings, we show that the problem of determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping is undecidable. We conclude with a number of open problems.Comment: This report contains the paper accepted at KR 2023 and an appendix with full proofs. 24 page