Knowledge-preserving Certain Answers for SQL-like Queries

International audienceAnswering queries over incomplete data is based on finding answers that are certainly true, independently of how missing values are interpreted. This informal description has given rise to several different mathematical definitions of certainty. To unify them, a framework based on "explanations", or extra information about incomplete data, was recently proposed. It partly succeeded in justifying query answering methods for relational databases under set semantics, but had two major limitations. First, it was firmly tied to the set data model, and a fixed way of comparing incomplete databases with respect to their information content. These assumptions fail for reallife database queries in languages such as SQL that use bag semantics instead. Second, it was restricted to queries that only manipulate data, while in practice most analytical SQL queries invent new values, typically via arithmetic operations and aggregation. To leverage our understanding of the notion of certainty for queries in SQL-like languages, we consider incomplete databases whose information content may be enriched by additional knowledge. The knowledge order among them is derived from their semantics, rather than being fixed a priori. The resulting framework allows us to capture and justify existing notions of certainty, and extend these concepts to other data models and query languages. As natural applications, we provide for the first time a well-founded definition of certain answers for the relational bag data model and for valueinventing queries on incomplete databases, addressing the key shortcomings of previous approaches

Propositional and predicate logics of incomplete information

International audienceOne of the most common scenarios of handling incomplete information occurs in relational databases. They describe in-complete knowledge with three truth values, using Kleene’s logic for propositional formulae and a rather peculiar exten-sion to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and pred-icate logics?Our goal is to answer this question. Using an epistemic ap-proach, we first characterize possible levels of partial knowl-edge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connec-tives of the propositional logic, and prove that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For exten-sions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete informa-tion represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpreta-tion of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it

Coping with Incomplete Data: Recent Advances

International audienceHandling incomplete data in a correct manner is a notoriously hard problem in databases. Theoretical approaches rely on the computationally hard notion of certain answers, while practical solutions rely on ad hoc query evaluation techniques based on threevalued logic. Can we find a middle ground, and produce correct answers efficiently? The paper surveys results of the last few years motivated by this question. We reexamine the notion of certainty itself, and show that it is much more varied than previously thought. We identify cases when certain answers can be computed efficiently and, short of that, provide deterministic and probabilistic approximation schemes for them. We look at the role of three-valued logic as used in SQL query evaluation, and discuss the correctness of the choice, as well as the necessity of such a logic for producing query answers

Troubles with Nulls, Views from the Users

International audienceIncomplete data, in the form of null values, has been extensively studied since the inception of the relational model in the 1970s. Anecdotally, one hears that the way in which SQL, the standard language for relational databases, handles nulls creates a myriad of problems in everyday applications of database systems. To the best of our knowledge, however, the actual shortcomings of SQL in this respect, as perceived by database practitioners, have not been systematically documented, and it is not known if existing research results can readily be used to address the practical challenges. Our goal is to collect and analyze the shortcomings of nulls and their treatment by SQL, and to re-evaluate existing research in this light. To this end, we designed and conducted a survey on the everyday usage of null values among database users. From the analysis of the results we reached two main conclusions. First, null values are ubiquitous and relevant in real-life scenarios, but SQL's features designed to deal with them cause multiple problems. The severity of these problems varies depending on the SQL features used, and they cannot be reduced to a single issue. Second, foundational research on nulls is misdirected and has been addressing problems of limited practical relevance. We urge the community to view the results of this survey as a way to broaden the spectrum of their researches and further bridge the theory-practice gap on null values

On the Translatability of View Updates

Abstract We revisit the view update problem and the abstract functional framework by Bancilhon and Spyratos in a setting where views and updates are exactly given by functions that are expressible in first-order logic. We give a characterisation of views and their inverses based on the notion of definability, and we introduce a general method for checking whether a view update can be uniquely translated as an update of the underlying database under the constant complement principle. We study the setting consisting of a single database relation and two views defined by projections and compare our general criterion for translatability with the known results for the case in which the constraints on the database are given by functional dependencies. We extend the setting to any number of projective views, full dependencies (that is, egd’s and full tgd’s) as database constraints, and classes of updates rather than single updates.