Generating Plans from Proofs: The Interpolation-based Approach to Query Reformulation

Benedikt, Michael; Leblay, Julien; Cate, Balder ten; Tsamoura, Efthymia

doi:10.2200/s00703ed1v01y201602dtm043

Cited by 40 publications

(115 citation statements)

References 58 publications

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“…This result is true even without result bounds, and follows from results in [13]: we give a self-contained argument here. Satisfiability for equality-free first-order constraints is undecidable [1].…”

Section: General First-order Constraintssupporting

confidence: 56%

“…Plans. We use plans to describe programs that use the access methods, formalizing them using the terminology of [14,13]. A monotone plan PL is a sequence of commands that produce temporary tables.…”

Section: Preliminariesmentioning

confidence: 99%

“…To prove the other direction of Theorem 4.2, we first recall the result that corresponds to Theorem 4.2 in the case without result bounds: 13,14]). For any CQ Q and schema Sch (with no result bounds) whose constraints Σ are expressible in active-domain first-order logic, the following are equivalent:…”

Section: Reducing To Query Containmentmentioning

confidence: 99%

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When Can We Answer Queries Using Result-Bounded Data Interfaces?

Amarilli

Benedikt

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g., because of pagination or rate limits. We thus study result-bounded methods, which may return only a limited number of tuples. We study how to decide if a query is answerable using result-bounded methods, i.e., how to compute a plan that returns all answers to the query using the methods, assuming that the underlying data satisfies some integrity constraints. We first show how to reduce answerability to a query containment problem with constraints. Second, we show "schema simplification" theorems describing when and how result bounded services can be used. Finally, we use these theorems to give decidability and complexity results about answerability for common constraint classes.

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Section: General First-order Constraintssupporting

confidence: 56%

Section: Preliminariesmentioning

confidence: 99%

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When Can We Answer Queries Using Result-Bounded Data Interfaces?

Amarilli

Benedikt

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…A first result we could prove in this direction is that every monotone boolean query expressible as a containment of N (all ) expressions is in fact expressible as the nonemptiness of an N (all ) expression. This may be seen as a preservation theorem, similar to, say, the theorem that the monotone first-order boolean queries are those expressible by positiveexistential sentences (allowing nonequalities) [23].…”

Section: Discussionmentioning

confidence: 99%

The primitivity of operators in the algebra of binary relations under conjunctions of containments

Surinx

Bussche

Gucht

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Abstract-The algebra of binary relations provides union and composition as basic operators, with the empty set as neutral element for union and the identity relation as neutral element for composition. The basic algebra can be enriched with additional features. We consider the diversity relation, the full relation, intersection, set difference, projection, coprojection, converse, and transitive closure. It is customary to express boolean queries on binary relational structures as finite conjunctions of containments. We investigate which features are primitive in this setting, in the sense that omitting the feature would allow strictly less boolean queries to be expressible. Our main result is that, modulo a finite list of elementary interdependencies among the features, every feature is indeed primitive. I. INTRODUCTIONThe algebra of binary relations (aka the calculus of relations) was created by De Morgan, Peirce, and Schröder, and popularized and further developed by Tarski and his collaborators [1]- [3]. These developments gave rise to the rich field of relation algebras [4]- [6]. In the present paper, however, we are focusing on the algebra of binary relations as a language for expressing properties of binary relational structures. This focus comes very naturally in the context of query languages for graph data. Indeed, a binary relational structure really is a directed graph, with the different binary relation names playing the role of edge labels. Not surprisingly, the algebra of binary relations lies at the basis of query languages for graph databases [7]-[12].But also more fundamentally, the algebra of binary relations originated in the desire to have a principled language for expressing properties (axiomatizing classes) of relational structures. (In this respect, the algebra of binary relations actually predates first-order logic [13].) This paper is part of our ongoing work [9], [14]-[17] to understand the expressive power, in particular the primitivity or interdependencies, among different operators considered in the realm of binary relational algebra. Since we include projection, coprojection, transitive closure, intersection, and converse, our investigation is also relevant to propositional dynamic logic, multi-dimensional modal logic [18] and to the relational interpretation of Kleene algebras with tests, and of Kleene allegories [19], [20].There are indeed many different operators that have been considered. Our choice of operators is a natural one and motivated by the applications to graph database query languages. We always start from union ∪ and composition •,

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“…Related is also query answering under access patterns, which require a relation to be accessed only by providing certain combinations of attributes [10,32,34]. This work differs from the prior work as follows.…”

Section: Introductionmentioning

confidence: 99%

Data driven approximation with bounded resources

Cao

Fan

2017

Proc. VLDB Endow.

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This paper proposes BEAS, a resource-bounded scheme for querying relations. It is parameterized with a resource ratio α ∈ (0, 1], indicating that given a big dataset D, we can only afford to access an α-fraction of D with limited resources. For a query Q posed on D, BEAS computes exact answers Q(D) if doable and otherwise approximate answers, by accessing at most α|D| amount of data in the entire process. Underlying BEAS are (1) an access schema, which helps us identify and fetch the part of data needed to answer Q, (2) an accuracy measure to assess approximate answers in terms of their relevance and coverage w.r.t. exact answers, (3) an Approximability Theorem for the feasibility of resource-bounded approximation, and (4) algorithms for query evaluation with bounded resources. A unique feature of BEAS is its ability to answer unpredictable queries, aggregate or not, using bounded resources and assuring a deterministic accuracy lower bound. Using real-life and synthetic data, we empirically verify the effectiveness and efficiency of BEAS.

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Generating Plans from Proofs: The Interpolation-based Approach to Query Reformulation

Cited by 40 publications

References 58 publications

When Can We Answer Queries Using Result-Bounded Data Interfaces?

When Can We Answer Queries Using Result-Bounded Data Interfaces?

The primitivity of operators in the algebra of binary relations under conjunctions of containments

Data driven approximation with bounded resources

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