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Disjunctive Multiple-Conclusion Consequence Relations

100%
Nowak M.
Bulletin of the Section of Logic
|
2019
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tom 48
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nr 4
EN
The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r (dened on the power set of a set of all formulas of a given language) the least multiple-conclusion consequence relation containing r, is dened on the grounds of a natural Galois connection. It is shown that the very closure C is an isomorphism from the power set algebra of a simple binary relation to the Boolean algebra of all multiple-conclusion consequence relations.
2
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The Słupecki criterion by duality

100%
Horváth E.
Discussiones Mathematicae - General Algebra and Applications
|
2001
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tom 21
|
nr 1
5-11
EN
A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of $A^{k}$ only. We show how the method applies for proving Słupecki's classical theorem by generating diagonal relations from each pair of k-tuples.
3
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Clausal relations and C-clones

100%
Vargas E.
Discussiones Mathematicae - General Algebra and Applications
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2010
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tom 30
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nr 2
147-171
EN
We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = {0,1}. Finally we prove certain results about C-clones over a larger set.
4
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A comprehensive survey on formal concept analysis, its research trends and applications

88%
Singh P., Aswani Kumar C., Gani A.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 2
495-516
EN
In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.
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