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Algebraic Databases [article]

Patrick Schultz, David I. Spivak, Christina Vasilakopoulou, Ryan Wisnesky
2016 arXiv   pre-print
Databases have been studied category-theoretically for decades. The database schema---whose purpose is to arrange high-level conceptual entities---is generally modeled as a category or sketch.  ...  In the present work, we propose an extension of the set-valued functor model, making use of multisorted algebraic theories (a.k.a. Lawvere theories) to incorporate concrete data in a principled way.  ...  What we call (algebraic) databases straddle what are traditionally known as relational databases and the more modern graph databases.  ... 
arXiv:1602.03501v2 fatcat:h3562zannbgeplfe2sjchi4z4i

Plan Databases: Model and Algebra [chapter]

Fusun Yaman, Sibel Adali, Dana Nau, Maria L. Sapino, V. S. Subrahmanian
2004 Lecture Notes in Computer Science  
We then propose a set of operators similar to the relational algebra to query such databases of plans. Definition 4. Suppose α(t) is an action instance.  ...  In this paper, we first propose a formal model of plan databases. We describe important notions of consistency and coherence for such databases.  ...  We then present a relational-algebra style plan algebra to query plan databases.  ... 
doi:10.1007/978-3-540-24627-5_20 fatcat:ansvhrva5feyreihljc4z5g27u

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 two main examples of these are concrete algebras of n-ary relations on the one hand, and algebras of first order sentences on the other.  ... 
doi:10.1007/978-3-642-35025-2_15 fatcat:xj3jtcrjyzd7bjebhf2u6j7uya

Probabilistic temporal databases, I: algebra

Alex Dekhtyar, Robert Ross, V. S. Subrahmanian
2001 ACM Transactions on Database Systems  
Next, we present a Temporal Probabilistic Algebra (TPA).  ...  As noted in [53] , past attempts to deal with uncertainty in databases have been restricted to relatively small amounts of uncertainty in attributes.  ...  Then, in Section 6, we will show how these operations can be implemented in the TP-Algebra in such a way that the TP-Algebra operations implement the annotated algebra operations on the implicit (smaller  ... 
doi:10.1145/383734.383736 fatcat:xqswmh2frbgpznbrg6sekyhlhm

An algebra of database preferences

Bernhard Möller, Patrick Roocks
2015 Journal of Logical and Algebraic Methods in Programming  
Preferences allow more flexible and personalised queries in database systems.  ...  We present a point-free calculus of such preferences and exemplify its use in proving algebraic laws about preferences that can be used in query optimisation.  ...  This concept of typed relations also appears in the relation-based logical, but not primarily algebraic, approach to database notions of [14] . We will generalise it in Section 3.2.  ... 
doi:10.1016/j.jlamp.2015.01.001 fatcat:ofsy4n7jvnhu7iyzxxx7jcmuum

An algebra for probabilistic databases

M. Pittarelli
1994 IEEE Transactions on Knowledge and Data Engineering  
The probabilistic algebra is developed in such a way that (restricted to α -acyclic database schemes) the relational algebra is a homomorphic image of it.  ...  IndexT erms − Bayes and Markov networks, data models, decision support, probability, relational algebra.  ...  very stimulating year.Iam grateful to Martin Zwick for mentioning in 1982 that someone should do something about the obvious correspondence between results in (general) system theory and (relational) database  ... 
doi:10.1109/69.277772 fatcat:3x7mo6roq5dg5fnybaoy4lefjq

An extended algebra for constraint databases

A. Belussi, E. Bertino, B. Catania
1998 IEEE Transactions on Knowledge and Data Engineering  
The de nition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology.  ...  Then, we introduce two distinct classes of constraint algebras, one based on the relational algebra, and one based on the nested relational algebra, and we present an algebra of the latter type.  ...  The de nition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology.  ... 
doi:10.1109/69.729722 fatcat:ilma452c45dslfyht2j7yobg6i

On Query Algebras for Probabilistic Databases

Christoph Koch
2009 SIGMOD record  
This article proposes a core query algebra for probabilistic databases.  ...  As a core algebra, we present probabilistic world-set algebra (WSA), origi-  ...  Ideally, a similar core algebra for probabilistic databases could help us replicate our previous success with relational databases.  ... 
doi:10.1145/1519103.1519116 fatcat:ex2el4xphvdzdo6hjxvqgmgnne

An Algebraic Calculus of Database Preferences [chapter]

Bernhard Möller, Patrick Roocks, Markus Endres
2012 Lecture Notes in Computer Science  
Preference algebra, an extension of the algebra of database relations, is a well-studied field in the area of personalized databases.  ...  We enrich the standard theory of relational databases to an algebraic framework that allows completely point-free reasoning about complex preferences.  ...  algebra.  ... 
doi:10.1007/978-3-642-31113-0_13 fatcat:3l2xx4updfb4joryne4owgzcmu

A parallel algebra for object databases

S.deF. Mendes Sampaio, N.W. Paton, P. Watson, J. Smith
1999 Proceedings. Tenth International Workshop on Database and Expert Systems Applications. DEXA 99  
This paper describes an algebra for use with parallel object databases, and in particular ODMG compliant databases with OQL.  ...  The paper presents not only the algebra, but also its role in the architecture of a parallel database.  ...  An algebraic query plan is represented as a tree, in which the internal nodes represent operators, and the leaf nodes represent database extents.  ... 
doi:10.1109/dexa.1999.795145 dblp:conf/dexaw/SampaioPWS99 fatcat:omnotkaytre3jczmdx2hgc42u4

Algebraic aspects of relational database decomposition

Stephen J. Hegner
1983 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems - PODS '83  
An algebraic framework for investigating the problem of decomposing a relational database schema into components is developed.  ...  It is argued that the views of a relational schema which are to be the components of a decomposition should form a finite atomic Boolean algebra. The unit of the  ...  This is crucial in guaranteeing closure of algebraic operations. Algebra is used as the tool to model interactions of database schemata and mappings.  ... 
doi:10.1145/588058.588106 dblp:conf/pods/Hegner83 fatcat:xdy5af2fqzeihalnyzyv3y2goy


2014 Journal of Mathematics and Statistics  
This equivalence pertains to both concepts and procedures of the FD relational database domain and the switching algebraic domain.  ...  There is an established equivalence between relational database Functional Dependencies (FDs) and a fragment of switching algebra that is built typically of Horn clauses.  ...  CONCLUSION This study is a serious attempt to transform relational database concepts to the switching-algebraic domain and hence to utilize switching-algebraic procedures and concepts in relational databases  ... 
doi:10.3844/jmssp.2014.231.243 fatcat:7cghlexgf5hobimtbxks444mnu

Real Algebraic Geometry and Constraint Databases [chapter]

Floris Geerts, Bart Kuijpers
2007 Handbook of Spatial Logics  
A relational database is usually modeled following a database schema. A schema contains information on the relation names and on the names of the attributes appearing in relation.  ...  The constraint database model can be seen as a generalization of the classical relational database model that was introduced by Codd in the 1970s to deal with the management of alpha-numerical data, typically  ...  sets), a semi-algebraic set in R k , where D is any database instance of S.  ... 
doi:10.1007/978-1-4020-5587-4_13 fatcat:5oemzcnwe5egnkkrjxquwsl5ve

Reduction of Database Independence to Dividing in Atomless Boolean Algebras [article]

Tapani Hyttinen, Gianluca Paolini
2017 arXiv   pre-print
We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras.  ...  This establishes interesting connections between independence in database theory and stochastic independence.  ...  In Section 2.2 we then use this characterization to establish an abstract reduction of database independence to dividing in atomless Boolean algebras.  ... 
arXiv:1409.1839v5 fatcat:njkndkc62jbppkvhfh4blqcrbm

Relational Algebra for In-Database Process Mining [article]

Remco Dijkman, Juntao Gao, Paul Grefen, Arthur ter Hofstede
2017 arXiv   pre-print
We define the operator using the well-known relational algebra that forms the formal underpinning of relational databases.  ...  To help facilitate this ideal of in-database process mining, this paper formally defines a database operator that extracts the 'directly follows' relation from an operational database.  ...  Relational Algebra for Process Mining This section defines the 'directly follows' relation as a relational algebraic operator.  ... 
arXiv:1706.08259v1 fatcat:4aufflc62bc55okkhbobjtis4y
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