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

Jaume Baixeries, José Luis Balcázar
2005 Lecture Notes in Computer Science  
We propose here a 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.  ... 
doi:10.1007/978-3-540-32262-7_11 fatcat:s33jof2a4zbzplm6d24chiv4gq

Characterizing functional dependencies in formal concept analysis with pattern structures

Jaume Baixeries, Mehdi Kaytoue, Amedeo Napoli
2014 Annals of Mathematics and Artificial Intelligence  
Considering the discovery of functional 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.  ... 
doi:10.1007/s10472-014-9400-3 fatcat:ckesjrsxe5fc5cvek5x35zondy

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Elmira Yu. Kalimulina
2021 Mathematics  
The 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.  ... 
doi:10.3390/math10010094 fatcat:w5y4a6bd4zfxxhqudii5rt4tiq

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.  ... 

Quantum groups and Nichols algebras acting on conformal field theories [article]

Simon D. Lentner
2021 arXiv   pre-print
The proof is based on a novel, intimate 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.  ... 
arXiv:1702.06431v2 fatcat:5otew6e3znczjh6tmfs6t2oeeu

Pairwise-definable subdirect decompositions of general database schemata [chapter]

Stephen J. Hegner
1991 Lecture Notes in Computer Science  
In this paper, we show that the thrust of these results is not specific to the 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.  ... 
doi:10.1007/3-540-54009-1_18 fatcat:bselxpzfgfdxzmtcldx2pvzumq

On the consistency problem for modular lattices and related structures [article]

Christian Herrmann, Yasuyuki Tsukamoto, Martin Ziegler
2016 arXiv   pre-print
The 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).  ... 
arXiv:1607.03315v1 fatcat:j6j2a2sqozfxvogv4ar35ki3vu

An object algebra for object-oriented database systems

Reda Alhajj, M. Erol Arkun
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 closure property for operations.  ...  Object algebra is as powerful as relational and nested relational algebra.  ...  relational representation.  ... 
doi:10.1145/173798.173800 fatcat:nl3z4mwqmbagvbxgpugiis3oq4

Decomposition of relational schemata into components defined by both projection and restriction

Stephen J. Hegner
1988 Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '88  
A generalized approach to the decomposition of 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.  ... 
doi:10.1145/308386.308434 dblp:conf/pods/Hegner88 fatcat:pjdmyyjomvcedpszoz5kdp7vku

An interval-based temporal logic in a multivalued setting [chapter]

Mathias Bauer
1992 Lecture Notes in Computer Science  
The DFKI conducts application-oriented basic research in the field of artificial intelligence 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.  ... 
doi:10.1007/3-540-55602-8_177 fatcat:eofta2eilzdh3af3apja25rfwq

Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion

Hagen Kleinert
2000 General Relativity and Gravitation  
An important consequence is a 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.  ... 
doi:10.1023/a:1001962922592 fatcat:3mx373hhpfavvd36f74fsfjkom

Inference for Multiplicative Models [article]

Ydo Wexler, Christopher Meek
2012 arXiv   pre-print
The paper ends with examples where using the 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 ∧.  ... 
arXiv:1206.3296v1 fatcat:5galygjqjngsvkhkth2bfgckze

Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion [article]

Hagen Kleinert
2002 arXiv   pre-print
As an important consequence, it yields a 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).  ... 
arXiv:gr-qc/0203029v1 fatcat:kwnemodnkrhjrjbrwumysbzhre

Theory of generalized annotated logic programming and its applications**A preliminary report on this research has appeared in [34]

Michael Kifer, V.S. Subrahmanian
1992 The Journal of Logic Programming  
First, we introduce a 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.  ... 
doi:10.1016/0743-1066(92)90007-p fatcat:6mrarcuturdtpkmdlli2nnulam

Multi-valued symbolic model-checking

Marsha Chechik, Benet Devereux, Steve Easterbrook, Arie Gurfinkel
2003 ACM Transactions on Software Engineering and Methodology  
We define the class of logics, present the theory of multi-valued sets 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.  ... 
doi:10.1145/990010.990011 fatcat:d22iidcvqzdbdcxocflpj6jtya
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