Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate Functions

Klug, Anthony C.

doi:10.1145/322326.322332

Cited by 234 publications

(71 citation statements)

References 4 publications

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“…Figure 1 shows a simple database instance in the E-R format (Domingos and Richardson 2007) and the ground atoms in functor notation. The results in this paper extend to functors built with nested functors, aggregate functions (Klug 1982), and quantifiers; for the sake of notational simplicity we do not consider more complex functors explicitly. A table join of two or more tables contains the rows in the Cartesian products of the tables whose values match on common fields.…”

Section: Bayes Nets For Relational Datamentioning

confidence: 96%

Learning directed relational models with recursive dependencies

Khosravi

Man

2012

Mach Learn

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Recently, there has been an increasing interest in generative models that represent probabilistic patterns over both links and attributes. A common characteristic of relational data is that the value of a predicate often depends on values of the same predicate for related entities. For directed graphical models, such recursive dependencies lead to cycles, which violates the acyclicity constraint of Bayes nets. In this paper we present a new approach to learning directed relational models which utilizes two key concepts: a pseudo likelihood measure that is well defined for recursive dependencies, and the notion of stratification from logic programming. An issue for modelling recursive dependencies with Bayes nets are redundant edges that increase the complexity of learning. We propose a new normal form format that removes the redundancy, and prove that assuming stratification, the normal form constraints involve no loss of modelling power. Empirical evaluation compares our approach to learning recursive dependencies with undirected models (Markov Logic Networks). The Bayes net approach is orders of magnitude faster, and learns more recursive dependencies, which lead to more accurate predictions.

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Section: Bayes Nets For Relational Datamentioning

confidence: 96%

Learning directed relational models with recursive dependencies

Khosravi

Man

2012

Mach Learn

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“…We express the relations using relational algebra based upon the work of Codd [9]. We use an extention of the relational algebra [12,13] that offers aggregation and grouping functionalites. The symbol ξ groups the output according to specifed atribute(s).…”

Section: Top-level Relationsmentioning

confidence: 99%

Ontology-Based Identification of Research Gaps and Immature Research Areas

Beckers¹,

Eicker²,

Faßbender³

et al. 2012

Lecture Notes in Computer Science

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Abstract.Researchers often have to understand new knowledge areas, and identify research gaps and immature areas in them. They have to understand and link numerous publications to achieve this goal. This is difficult, because natural language has to be analyzed in the publications, and implicit relations between them have to be discovered. We propose to utilize the structuring possibilities of ontologies to make the relations between publications, knowledge objects (e.g., methods, tools, notations), and knowledge areas explicit. Furthermore, we use Kitchenham's work on structured literature reviews and apply it to the ontology. We formalize relations between objects in the ontology using Codd's relational algebra to support different kinds of literature research. These formal expressions are implemented as ontology queries. Thus, we implement an immature research area analysis and research gap identification mechanism. The ontology and its relations are implemented based on the Semantic MediaWiki+ platform.

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“…Almost as quickly, the subtleties of unnesting became apparent. The first bugs in the original approach were detected -among them the famous count bug [20]. Retrospectively, we can summarize the problem areas as follows:…”

Section: Introductionmentioning

confidence: 99%

“…They have been corrected by different approaches [7,14,18,20,23,24]. -If the nested query contains grouping, special rules are needed to pull up grouping operators [4].…”

Section: Introductionmentioning

confidence: 99%