Characterization of Database Dependencies with FCA and Pattern Structures

Baixeries, Jaume; Kaytoue, Mehdi; Napoli, Amedeo

doi:10.1007/978-3-319-12580-0_1

Cited by 3 publications

(8 citation statements)

References 29 publications

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“…Horn Clauses / Implications [27], [7] Functional Dependencies [11], [2], [13], [30] [20], [24], [26], [22] Armstrong Dependencies Similarity Dependencies [12], [16] MVD Clauses [3] Degenerated MVD [8] [4], [5], [23], [25] Symmetric Dependencies Multivalued Dependencies [9] Acyclic Join Dependencies [6] this paper Acyclic Hypergraphs In this paper, we present the characterization of the axioms for AJD's in terms of FCA. This work complements that in [6], where a characterization of the AJD's that hold in a dataset (also in terms of FCA) was provided, and generalizes that in [4] and in [5], that presents a characterization of the axioms for MVD's, which are, as we previously mentioned, a special case of AJD's.…”

Section: Semantical Syntacticalmentioning

confidence: 99%

“…However, this implies as well that the computational advantages of this proposal will need to be accounted for. So far, evaluations of FCA-based characterizations of different dependencies in the RDBM have been presented in [13], [10] and [12].…”

Section: Semantical Syntacticalmentioning

confidence: 99%

“…This is why when we discuss properties based on those axioms, we use the term Armstrong Dependencies to refer to both FD's and implications. In fact, these are not the only kind of dependencies that can also be axiomatized with the Armstrong axioms: Similarity Dependencies [12,16] (a relaxation of FD's) also follow those axioms.…”

Section: Constraints In the Rdbmmentioning

confidence: 99%

See 2 more Smart Citations

A Formal Context for Closures of Acyclic Hypergraphs

Baixeries

2019

Formal Concept Analysis

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Database constraints in the relational database model (RDBM) can be viewed as a set of rules that apply to a dataset, or as a set of axioms that can generate a (closed) set of those constraints. In this paper, we use Formal Concept Analysis to characterize the axioms of Acyclic Hypergraphs (in the RDBM they are called Acyclic Join Dependencies). This present paper complements and generalizes previous work on FCA and databases constraints.

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Section: Semantical Syntacticalmentioning

confidence: 99%

Section: Semantical Syntacticalmentioning

confidence: 99%

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A Formal Context for Closures of Acyclic Hypergraphs

Baixeries

2019

Formal Concept Analysis

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“…Add a new row filled by 0s. More detailed tutorial on FCA and fuctional dependencies is given in [28].…”

Section: F M × F ×mentioning

confidence: 99%

“…In each row, replace empty cells by the row number starting from 1. More detailed tutorial on FCA and fuctional dependencies is given in [28].…”

Section: Examplementioning

confidence: 99%

Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields

Ignatov

2015

Communications in Computer and Information Science

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Abstract. This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. Originated in early 80s, during the last three decades, it became a popular human-centred tool for knowledge representation and data analysis with numerous applications. Since the tutorial was specially prepared for RuS-SIR 2014, the covered FCA topics include Information Retrieval with a focus on visualisation aspects, Machine Learning, Data Mining and Knowledge Discovery, Text Mining and several others.

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Decompositional Extraction and Retrieval of Conceptual Knowledge

Terletskyi

Yershov

2022

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An ability to extract hidden and implicit knowledge, their integration into a knowledge base, and then retrieval of required knowledge items are important features of knowledge processing for many modern knowledge-based systems. However, the complexity of these tasks depends on the size of knowledge sources, which were used for extraction, the size of a knowledge base, which is used for the integration of extracted knowledge, as well as the size of a search space, which is used for the retrieval of required knowledge items. Therefore, in this paper, we analyzed the internal semantic dependencies of homogeneous classes of objects and how they affect the decomposition of such classes. Since all subclasses of a homogeneous class of objects form a complete lattice, we applied the methods of formal concept analysis for the knowledge extraction and retrieval within the corresponding concept lattice. We found that such an approach does not consider internal semantic dependencies within a homogeneous class of objects, consequently, it can cause inference and retrieval of formal concepts, which are semantically inconsistent within a modeled domain. We adapted the algorithm for the decomposition of homogeneous classes of objects, within such knowledge representation model as object-oriented dynamic networks, to perform dynamic knowledge extraction and retrieval, adding additional filtration parameters. As the result, the algorithm extracts knowledge via constructing only semantically consistent subclasses of homogeneous classes of objects and then filters them according to the attribute and dependency queries, retrieving knowledge. In addition, we introduced the decomposition consistency coefficient, which allows estimation of how much the algorithm can reduce the search space for knowledge extraction and improves the performance. To demonstrate some possible application scenarios for the improved algorithm, we provided an appropriate example of knowledge extraction and retrieval via decomposition of a particular homogeneous class of objects.

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Characterization of Database Dependencies with FCA and Pattern Structures

Cited by 3 publications

References 29 publications

A Formal Context for Closures of Acyclic Hypergraphs

A Formal Context for Closures of Acyclic Hypergraphs

Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields

Decompositional Extraction and Retrieval of Conceptual Knowledge

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