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On Desirable Semantics of Functional Dependencies over Databases with Incomplete Information

Badia A., Lemire D.

Fundamenta Informaticae

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2018

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Vol. 158, nr 4

327--352

EN

Codd’s relational model describes just one possible world. To better cope with incomplete information, extended database models allow several possible worlds. Vague tables are one such convenient extended model where attributes accept sets of possible values (e.g., the manager is either Jill or Bob). However, conceptual database design in such cases remains an open problem. In particular, there is no canonical definition of functional dependencies (FDs) over possible worlds (e.g., each employee has just one manager). We identify several desirable properties that the semantics of such FDs should meet including Armstrong’s axioms, the independence from irrelevant attributes, seamless satisfaction and implied by strong satisfaction. We show that we can define FDs such that they have all our desirable properties over vague tables. However, we also show that no notion of FD can satisfy all our desirable properties over a more general model (disjunctive tables). Our work formalizes a trade-off between having a general model and having well-behaved FDs.

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Selected Relationships between Process Magnitudes during Surface Grinding with and without Cooling

Rutkiewicz T, Urbaniak M., Wajszczyk P

Mechanics and Mechanical Engineering

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2012

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Vol. 16, nr 2

117--125

EN

The paper contains a comparison of surface grinding process run and its outcomes contingent on cooling and greasing lotion used. On this basis relationships were established between process magnitudes and a new way of predicting their values during grinding processing with cooling was proposed.

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Computing Supports of Conjunctive Queries on Relational Tables with Functional Dependencies

Jen T-Y., Laurent D.

Fundamenta Informaticae

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2010

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Vol. 99, nr 3

263-292

EN

The problem of mining all frequent queries on a relational table is a problem known to be intractable even for conjunctive queries. In this article, we restrict our attention to conjunctive projection-selection queries and we assume that the table to be mined satisfies a set of functional dependencies. Under these assumptions, we define and characterize two pre-orderings with respect to which the support measure is shown to be anti-monotonic. Each of these pre-orderings induces an equivalence relation for which all queries of the same equivalence class have the same support. The goal of this article is not to provide algorithms for the computation of frequent queries, but rather to provide basic properties of pre-orderings and their associated equivalence relations showing that functional dependencies can be used for an optimized computation of supports of conjunctive queries. In particular, we show that one of the two pre-orderings characterizes anti-monotonicity of the support, while the other one refines the former, but allows to characterize anti-monotonicity with respect to a given table, only. Basic computational implications of these properties are discussed in the article.

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Counter-Free Keys and Functional Dependencies in Higher-Order Datamodels

Sali A., Schewe K-D.

Fundamenta Informaticae

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2006

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Vol. 70, nr 3

277-301

EN

We investigate functional dependencies (FDs) in the presence of several constructors for complex values. These constructors are the tuple constructor, list-, set- and multiset-constructors, an optionality constructor, and a disjoint union constructor. The disjoint union constructor implies restructuring rules, which complicate the theory. In particular, they do not permit a straightforward axiomatisation of the class of all FDs without a detour via weak functional dependencies (wFDs), i.e. disjunctions of functional dependencies, and even the axiomatisation of wFDs is not yet completely solved. Therefore, we look at the restricted class of counter-free functional dependencies (cfFDs). That is, we ignore subattributes that only refer to counting the number of elements in sets or multisets or distinguish only between empty or non-empty sets. We present a finite axiomatisation for the class of cfFDs. Furthermore, we study keys ignoring again the counting subattributes. We show that such keys are equivalent with certain ideals called HL-ideals. Based on that we introduce an ordering between key sets, and investigate systems of minimal keys. We give a sufficient condition for a Sperner family of HL-ideals being a system of minimal keys, and determine lower and upper bounds for the size of the smallest Armstrong-instance.