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Algebraic Databases
[article]
2016
arXiv
pre-print
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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]
2004
Lecture Notes in Computer Science
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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]
2013
Bolyai Society Mathematical Studies
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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
2001
ACM Transactions on Database Systems
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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
2015
Journal of Logical and Algebraic Methods in Programming
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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
1994
IEEE Transactions on Knowledge and Data Engineering
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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
1998
IEEE Transactions on Knowledge and Data Engineering
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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
2009
SIGMOD record
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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]
2012
Lecture Notes in Computer Science
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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
1999
Proceedings. Tenth International Workshop on Database and Expert Systems Applications. DEXA 99
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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
1983
Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems - PODS '83
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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
SWITCHING-ALGEBRAIC ANALYSIS OF RELATIONAL DATABASES
2014
Journal of Mathematics and Statistics
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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]
2007
Handbook of Spatial Logics
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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]
2017
arXiv
pre-print
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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]
2017
arXiv
pre-print
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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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