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Algebraic Databases
[article]

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*. ...

##
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Plan Databases: Model and Algebra
[chapter]

2004
*
Lecture Notes in Computer Science
*

We then propose a set of operators similar to the relational

doi:10.1007/978-3-540-24627-5_20
fatcat:ansvhrva5feyreihljc4z5g27u
*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*. ...##
###
Cylindric Algebras and Relational Databases
[chapter]

2013
*
Bolyai Society Mathematical Studies
*

An interpretation of the relational data model and various dependencies is given within the framework of cylindric

doi:10.1007/978-3-642-35025-2_15
fatcat:xj3jtcrjyzd7bjebhf2u6j7uya
*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. ...##
###
Probabilistic temporal databases, I: algebra

2001
*
ACM Transactions on Database Systems
*

Next, we present a Temporal Probabilistic

doi:10.1145/383734.383736
fatcat:xqswmh2frbgpznbrg6sekyhlhm
*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 ...##
###
An algebra of database preferences

2015
*
Journal of Logical and Algebraic Methods in Programming
*

Preferences allow more flexible and personalised queries in

doi:10.1016/j.jlamp.2015.01.001
fatcat:ofsy4n7jvnhu7iyzxxx7jcmuum
*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. ...##
###
An algebra for probabilistic databases

1994
*
IEEE Transactions on Knowledge and Data Engineering
*

The probabilistic

doi:10.1109/69.277772
fatcat:3x7mo6roq5dg5fnybaoy4lefjq
*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*...##
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An extended algebra for constraint databases

1998
*
IEEE Transactions on Knowledge and Data Engineering
*

The de nition of an

doi:10.1109/69.729722
fatcat:ilma452c45dslfyht2j7yobg6i
*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. ...##
###
On Query Algebras for Probabilistic Databases

2009
*
SIGMOD record
*

This article proposes a core query

doi:10.1145/1519103.1519116
fatcat:ex2el4xphvdzdo6hjxvqgmgnne
*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*. ...##
###
An Algebraic Calculus of Database Preferences
[chapter]

2012
*
Lecture Notes in Computer Science
*

Preference

doi:10.1007/978-3-642-31113-0_13
fatcat:3l2xx4updfb4joryne4owgzcmu
*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*. ...##
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A parallel algebra for object databases

1999
*
Proceedings. Tenth International Workshop on Database and Expert Systems Applications. DEXA 99
*

This paper describes an

doi:10.1109/dexa.1999.795145
dblp:conf/dexaw/SampaioPWS99
fatcat:omnotkaytre3jczmdx2hgc42u4
*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. ...##
###
Algebraic aspects of relational database decomposition

1983
*
Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems - PODS '83
*

An

doi:10.1145/588058.588106
dblp:conf/pods/Hegner83
fatcat:xdy5af2fqzeihalnyzyv3y2goy
*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. ...##
###
SWITCHING-ALGEBRAIC ANALYSIS OF RELATIONAL DATABASES

2014
*
Journal of Mathematics and Statistics
*

This equivalence pertains to both concepts and procedures of the FD relational

doi:10.3844/jmssp.2014.231.243
fatcat:7cghlexgf5hobimtbxks444mnu
*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*...##
###
Real Algebraic Geometry and Constraint Databases
[chapter]

2007
*
Handbook of Spatial Logics
*

A relational

doi:10.1007/978-1-4020-5587-4_13
fatcat:5oemzcnwe5egnkkrjxquwsl5ve
*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. ...##
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Reduction of Database Independence to Dividing in Atomless Boolean Algebras
[article]

2017
*
arXiv
*
pre-print

We prove that the form of conditional independence at play in

arXiv:1409.1839v5
fatcat:njkndkc62jbppkvhfh4blqcrbm
*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*. ...##
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Relational Algebra for In-Database Process Mining
[article]

2017
*
arXiv
*
pre-print

We define the operator using the well-known relational

arXiv:1706.08259v1
fatcat:4aufflc62bc55okkhbobjtis4y
*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. ...
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