Semantic Entailment of Attribute-dependency Formulas and Their Non-redundant Bases

@inproceedings{Belohlvek2006SemanticEO,
  title={Semantic Entailment of Attribute-dependency Formulas and Their Non-redundant Bases},
  author={Radim Belohl{\'a}vek and Vil{\'e}m Vychodil},
  booktitle={JCIS},
  year={2006}
}
AD-formulas are simple formulas representing particular dependencies in data tables. We study AD-formulas from the logical point of view. In particular, we present results regarding the relationship of AD-formulas to attribute implications, models and entailment of AD-formulas, non-redundant bases, and computation of non-redundant bases. 

COMPLETENESS OF INFERENCE AND EFFICIENT COMPUTATION OF ATTRIBUTE-DEPENDENCY FORMULAS FOR TABULAR DATA

TLDR
Armstrong-like rules and a completeness theorem for reasoning with AD-formulas, and an efficient algorithm for extraction of a non-redundant basis of all AD- formulas from data, are presented.

Adding background knowledge to formal concept analysis via attribute dependency formulas

TLDR
The main aim is to make extraction of clusters from the input data more focused by taking into account the background knowledge, so that only clusters which are compatible with thebackground knowledge are extracted from data.

Fuzzy Implication and Functional Dependency on Formal Context

TLDR
This work shows difference and equivalence condition between fuzzy implication and fuzzy functional dependency and uses Armstrong's rule to define soundness and completeness of the implication and fuzzy functional dependency model.

FORMAL CONCEPT ANALYSIS WITH CONSTRAINTS BY EM OPERATORS

TLDR
The main aim is to make extraction of concepts from the input data more focused by taking into account the background knowledge, and only concepts which are compatible with the constraint are extracted from data.

Formal Concept Analysis with Constraints by EM Operators

TLDR
The main aim is to make extraction of concepts from the input data more focused by taking into account the background knowledge, and only concepts which are compatible with the constraint are extracted from data.

Formal Concept Analysis With Background Knowledge: Attribute Priorities

  • R. BelohlávekV. Vychodil
  • Computer Science
    IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)
  • 2009
TLDR
An approach to modeling background knowledge that represents user's priorities regarding attributes and their relative importance is presented, which means that the number of formal concepts presented to the user may get significantly reduced and the user is supplied with relevant formal concepts only and is not overloaded by a large number of possibly nonrelevant formal concepts.

Knowledge Spaces, Attribute Dependencies, and Graded Knowledge States

TLDR
A definition of dependencies and validity of dependencies in knowledge spaces with graded knowledge states, provide selected properties of the dependencies, and a lemma which serves as a bridge to existing results on so-called fuzzy attribute implications are proposed.

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