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The relational model of data and cylindric algebras

Tomasz Imieliński, Witold Lipski
1984 Journal of computer and system sciences (Print)  
model of data.  ...  It is shown, by using known facts from the theory of cylindric algebras, that a version of the relational algebra is not finitely axiomatizable and that the equivalence problem for certain relational expressions  ...  In this paper we shall be concerned with the relational model of data [Cod l] (see also [Ull] ).  ... 
doi:10.1016/0022-0000(84)90077-1 fatcat:b4jsdg6d2fduhif4cxlimccxt4

Cylindric structures and dependencies in relational databases

Ivo Düntsch, Szabolcs Mikulás
2001 Theoretical Computer Science  
In this paper, we explore the precise connection between dependencies in relational databases and variants of cylindric algebras, and apply recent algebraic results to problems of axiomatizing dependencies  ...  First, we will consider project-join dependencies and the corresponding class of (representable) cylindric semilattices.  ...  Due to the formulation of the data model with relational operators, there has always been an algebraic trend in the study of data dependencies in the sense that one looked for axioms for operators on relations  ... 
doi:10.1016/s0304-3975(01)00016-0 fatcat:dsb4edp7kfb67irwfnoixym2b4

Cylindric Algebras and Relational Databases [chapter]

Ivo Düntsch
2013 Bolyai Society Mathematical Studies  
An interpretation of the relational data model and various dependencies is given within the framework of cylindric algebras.  ...  It turns out that there is a natural translation of relational databases into cylindric set lattices, and that Codd's relational operators have a simple interpretation in these structures.  ...  The relational data model The two components of Codd's original concept of a relational database are objects and operators [4] : 1.  ... 
doi:10.1007/978-3-642-35025-2_15 fatcat:xj3jtcrjyzd7bjebhf2u6j7uya

Page 26 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
Sain [Mathematical logic in computer science, (Salgotarjan, 1978), 25-83, North-Holland, Amsterdam, 1981; see MR 83g:68007] and by Imielifski and Lipski [The relational model of data and cylindric algebras  ...  , Warsaw, 1981; per revr.] show that various nonclassical logic models and relational data models can be interpreted as set algebras.  ... 

Page 6767 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
This is pointed out in a final section, where we also briefly discuss the relation of this model to other models for spreaddata that have occurred in the literature.” Manukyan, S.  ...  We should mention that a different kind of generalization of Stone duality to cylindric algebras has been obtained (and success- fully applied to obtain new results in model theory) by S.  ... 

Page 4122 of Mathematical Reviews Vol. , Issue 85i [page]

1985 Mathematical Reviews  
(PL-PAN) The relational model of data and cylindric algebras. J. Comput. System Sci. 28 (1984), no. 1, 80-102.  ...  into Codd’s relational model of data.  ... 

Page 2772 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
and mixed algebras (263-285); Artur Wolinski, Cylindric algebras for partial relational systems.  ...  ; Ivo Diintsch, Contact relation algebras (113-133); Joachim Lambek, Relations old and new (135-147); Marek Szczerba, Rela- tional models for the nonassociative Lambek calculus (149-159); Stéphane Demri  ... 

Page 8761 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Another approach to the algebraization of first-order calculus uses Tarski cylindric algebras (TCAs) [see L. Henkin, J. D. Monk and A. Tarski, Cylindric algebras.  ...  of the number of relations and the size parameters of the network.  ... 

Page 2973 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
The authors’ main result is that every locally finite weak cylindric probability algebra A with |A| > 1 has a homomorphism onto a weak cylindric probability set algebra.  ...  The result then follows from the facts that a consistent set x in L has a model and that there is a homomorphism from Form, /= x onto the set algebra induced from the model. S.  ... 

Calculation of Transition State Energies in the HCN-HNC Isomerization with an Algebraic Model [article]

Jamil Khalouf-Rivera, Miguel Carvajal, Lea F. Santos, Francisco Pérez-Bernal
2019 arXiv   pre-print
Here, we show that the transition state of the bond breaking HCN-HNC isomerization reaction can also be achieved with the two-dimensional limit of the algebraic vibron model.  ...  We describe the system's bending vibration with the algebraic Hamiltonian and use its classical limit to characterize the transition state.  ...  , Junta de Andalucía and European Regional Development Fund (ERDF), ref.  ... 
arXiv:1907.07290v3 fatcat:al7i2uphurhlbhgxu4zs2peitq

Page 4413 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
It is known that we get classes of algebras with decidable equa- tional theories if we expand relativized relational set algebras or cylindric relativized set algebras by including the global count- ing  ...  The set of all relations which can be defined from C and the identity 1’ on W by using the (absolute) Boolean operators and the rela- tive operators ; and ~ is a contact relation algebra (CRA) on W 03G  ... 

Page 4672 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
Demetrovics, Mathematical analysis of the relational data model (pp. 65-73); E. Knuth, A survey of mathematical and software aspects of concurrent programming (pp. 75-84); L.  ...  Arnon and Scott McCallum, Cylindrical algebraic decomposition by quantifier elimination (pp. 215-222); Z. Lomecky, Algorithms for the computation of free lattices (pp. 223-230); L. Bordoni, A.  ... 

Page 2005 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
The authors discuss the role of Sahlqvist identities in the theory of Boolean algebras with operators, and exemplify their usefulness in the realm of cylindric algebras by showing that Henkin’s equation  ...  The propositions of linear logic are interpreted as games or dialogues between a server or provider of data and a client or consumer of data.  ... 

Page 3539 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
Peter Gumm, Continuations of logic programs (pp. 27-36); Istvan Németi, On cylindric algebraic model theory (pp. 37-75); Vaughan Pratt, Dynamic algebras as a well-behaved fragment of relation algebras  ...  Suchenek, Incremental models of updating data bases (pp. 243-271); Richard J.  ... 

From random Regge triangulations to open strings [article]

Mauro Carfora, Claudio Dappiaggi, Valeria L. Gili
2007 arXiv   pre-print
We show how Boundary Conformal Field Theory deformation techniques allow for a complete characterisation of the coupling between the discrete geometry inherited uniformizing a random Regge triangulations  ...  and open string theory.  ...  The above data allow us to discuss the extension of such a CFT on a given cylindrical end over M ∂ .  ... 
arXiv:hep-th/0702114v1 fatcat:ipvezfalfzeafhwqkejieaft4a
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