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Characterization and Armstrong Relations for Degenerate Multivalued Dependencies Using Formal Concept Analysis
[chapter]

2005
*
Lecture Notes in Computer Science
*

We propose here a

doi:10.1007/978-3-540-32262-7_11
fatcat:s33jof2a4zbzplm6d24chiv4gq
*new*Galois connection, based on any given*relation*, which gives rise to a formal concept*lattice*corresponding precisely to the degenerate*multivalued**dependencies*that hold in the*relation*... Then, we extend our approach so as to extract Armstrong*relations**for*the degenerate*multivalued**dependencies*from the concept*lattice*obtained; the proof of the correctness of this construction is nontrivial ... We are ready*for*the main result in this section: the*closure**operator*so constructed corresponds, in a precise sense, to the degenerated*multivalued**dependencies*that hold in the original*relation*r. ...##
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Characterizing functional dependencies in formal concept analysis with pattern structures

2014
*
Annals of Mathematics and Artificial Intelligence
*

Considering the discovery of functional

doi:10.1007/s10472-014-9400-3
fatcat:ckesjrsxe5fc5cvek5x35zondy
*dependencies*, it is indeed known that a*relation*can be*expressed*as the binary*relation*of a formal context, whose implications are equivalent to those*dependencies*... Computing functional*dependencies*from a*relation*is an important database topic, with many applications in database management, reverse engineering*and*query optimization. ... de Catalunya (2009-SGR-980*and*2009-SGR-1428)*and*AGAUR (grant 2010PIV00057) that allowed professor Napoli to visit the Universitat Politècnica de Catalunya. ...##
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Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

2021
*
Mathematics
*

The

doi:10.3390/math10010094
fatcat:w5y4a6bd4zfxxhqudii5rt4tiq
*closure**operators*R1*for*the functions that differ only by dummy variables are considered equivalent. This*operator*is withiin the scope of interest of this paper. ... The problem of the*lattice*of closed classes*for*the class of functions T2 preserving two is considered. ... In the next section, I prove the existence*and*possibility of constructing a*lattice**for*the*closure**operator*in several lemmas*and*theorems. ...##
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Page 8187 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

Castellini,

*Closure**operators**and*fuzzy connectedness (397-405); Yong-ming Li, Exponentiable objects in the category of topological molecular*lattices*(407-414); Yoon Jin Lee, Generalized fuzzy filter ... Special attention is paid to the*expressions**for*the images under the products of fuzzy*multivalued*mappings.*For*composition the properties of the images in terms of cuts are also studied. ...##
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Quantum groups and Nichols algebras acting on conformal field theories
[article]

2021
*
arXiv
*
pre-print

The proof is based on a novel, intimate

arXiv:1702.06431v2
fatcat:5otew6e3znczjh6tmfs6t2oeeu
*relation*between Hopf algebras, vertex algebras*and*a class of*multivalued*analytic special functions, which are generalizations of Selberg integrals. ... We prove that the zeroes of these special functions correspond to the algebra*relations*of the respective Nichols algebra, by proving an analytical quantum symmetrizer formula*for*the functions. ... I am indebted*and*grateful to A. Semikhatov,*for*hospitality in Moscow*and**for*countless hours of exposing me to the topic*and*his ideas, to C. ...##
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Pairwise-definable subdirect decompositions of general database schemata
[chapter]

1991
*
Lecture Notes in Computer Science
*

In this paper, we show that the thrust of these results is not specific to the

doi:10.1007/3-540-54009-1_18
fatcat:bselxpzfgfdxzmtcldx2pvzumq
*relational*model, but rather applies in a much more general context in which schemata are just sets*and*views are defined ... He wishes to thank in particular the members of the Computational Linguistics Group*for*their kind hospitality during his stay there. ... (S4) R has a monotone join*expression*. (S5) R has a sequential join*expression*. (S6) The join*dependency*1 [U 1 , U 2 , .., U n ] is equivalent to a set of*multivalued**dependencies*. ...##
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On the consistency problem for modular lattices and related structures
[article]

2016
*
arXiv
*
pre-print

The

arXiv:1607.03315v1
fatcat:j6j2a2sqozfxvogv4ar35ki3vu
*lattice*results are used to prove unsolvability of the consistency problem*for*(finite) rings*and*(finite)*representable**relation*algebras. ... These results in turn apply to equations between simple*expressions*in Grassmann-Cayley algebra*and*to functional*and*embedded*multivalued**dependencies*in databases. ... (finite)*relational*databases with conjunctions of functional*and*embedded*multivalued**dependencies*as constraints (Section 6). ...##
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An object algebra for object-oriented database systems

1993
*
ACM SIGMIS Database the DATABASE for Advances in Information Systems
*

The result of a query possesses the properties of an operand, thus providing the

doi:10.1145/173798.173800
fatcat:nl3z4mwqmbagvbxgpugiis3oq4
*closure*property*for**operations*. ... Object algebra is as powerful as*relational**and*nested*relational*algebra. ...*relational**representation*. ...##
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Decomposition of relational schemata into components defined by both projection and restriction

1988
*
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '88
*

A generalized approach to the decomposition of

doi:10.1145/308386.308434
dblp:conf/pods/Hegner88
fatcat:pjdmyyjomvcedpszoz5kdp7vku
*relational*schemata is developed in which the component views may be defined using both restriction*and*projection*operators*, thus admitting both horizontal ... It is shown that there are two major types, the bidimensional join*dependencies*, which are tuple generating*and*allow tuple removal by implicit encoding of knowledge,*and*splitting*dependencies*, which ... (iii) J has a monotone join*expression*. (iv) J is semantically equivalent to a set of bidirectional*multivalued**dependencies*. ...##
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An interval-based temporal logic in a multivalued setting
[chapter]

1992
*
Lecture Notes in Computer Science
*

The DFKI conducts application-oriented basic research in the field of artificial intelligence

doi:10.1007/3-540-55602-8_177
fatcat:eofta2eilzdh3af3apja25rfwq
*and*other*related*subfields of computer science. ... From its beginning, the DFKI has provided an attractive working environment*for*AI researchers from Germany*and*from all over the world. ... Acknowledgements I'd like to thank Caby l\1erziger*and*Dietmar Dengler*for*fruitful discussions*and*Jana hohler*for*her comlllent.s OIl an earlier version of this paper. ...##
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Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion

2000
*
General Relativity and Gravitation
*

An important consequence is a

doi:10.1023/a:1001962922592
fatcat:3mx373hhpfavvd36f74fsfjkom
*new*action principle*for*determining the equation of motion of a free spinless point particle in such spacetimes. ... The geometric origin of the torsion force is a*closure*failure of parallelograms. The torsion force changes the covariant conservation law of the energy-momentum tensor whose*new*form is derived. ... Pelster*for*many stimulating discussions,*and*to Drs. G. Barnich, H. von Borzeszkowski, C. Maulbetsch,*and*S.V. Shabanov*for*useful comments. ...##
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Inference for Multiplicative Models
[article]

2012
*
arXiv
*
pre-print

The paper ends with examples where using the

arXiv:1206.3296v1
fatcat:5galygjqjngsvkhkth2bfgckze
*new*models*and*algorithm is computationally beneficial. ... An inference algorithm*for*multiplicative models is provided*and*its correctness is proved. ... Output: A*representation*ρ = {S , Γ }. Figure 3 : 3 Algorithm*for*computing the*operation*M (V, {ρi}). R i is the*closure*of S i under the*operator*∧. ...##
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Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion
[article]

2002
*
arXiv
*
pre-print

As an important consequence, it yields a

arXiv:gr-qc/0203029v1
fatcat:kwnemodnkrhjrjbrwumysbzhre
*new*action principle*for*determining the equation of motion of a free spinless point particle in such spacetimes. ... I explain the geometric basis*for*the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature*and*torsion from those in flat spacetime, thus ... A proper construction will require a field version of the*new*variation formula (237) caused by the*closure*failure. This is in fact necessary*and*nontrivial even*for*the Schrödinger action (89). ...##
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Theory of generalized annotated logic programming and its applications**A preliminary report on this research has appeared in [34]

1992
*
The Journal of Logic Programming
*

First, we introduce a

doi:10.1016/0743-1066(92)90007-p
fatcat:6mrarcuturdtpkmdlli2nnulam
*new*semantics*for*such programs based on ideals of*lattices*. ... As an interesting byproduct of the investigation, we obtain a*new*result concerning*multivalued*logic programming: a model theory*for*Fitting's bilattice-based logic programming, which until now has not ... We thank Mel Fitting*and*Raymond Ng*for*useful suggestions on preliminary versions of this paper. S. Morishita pointed out a mistake in an earlier version of Theorem 6. ...##
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Multi-valued symbolic model-checking

2003
*
ACM Transactions on Software Engineering and Methodology
*

We define the class of logics, present the theory of multi-valued sets

doi:10.1145/990010.990011
fatcat:d22iidcvqzdbdcxocflpj6jtya
*and*multi-valued*relations*used in our model-checking algorithm,*and*define the multi-valued extensions of CTL*and*Kripke structures ... Properties are*expressed*in χ CTL, our multi-valued extension of the temporal logic CTL. ... We are also indebted to Albert Lai*for*his help with several aspects of*lattice*theory presented in this paper. ...
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