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Algorithm Knowledge Graph Ontology

This version:
https://mardi4nfdi.de/mathalgodb/0.1
Revision:
0.1
Authors:
Christian Himpe (https://orcid.org/0000-0003-2194-6754)
Frank Wübbeling (https://orcid.org/0000-0002-2375-2008)
Hendrik Kleikamp (https://orcid.org/0000-0003-1264-5941)
René Fritze (https://orcid.org/0000-0002-9548-2238)
Stephan Rave (https://orcid.org/0000-0003-0439-7212)
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License:
https://creativecommons.org/licenses/by/4.0
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Cite as:
MaRDI Task Area 2 - Scientific Computing @ University of Münster. MathAlgoDB - Algorithm Knowledge Graph - Ontology (Version 0.1). MaRDI (Mathematical Research Data Initiative), 2022. https://mardi4nfdi.de/mathalgodb/0.1
Provenance of this page
Draft

Abstract

This vocabulary and grammar defines which types of objects are admissible to the MathAlgoDB - the algorithm knowledge graph - and by which properties they can relate. All in all five classes, "problem", "algorithm", "benchmark", "software", "publication", are defined, as well as a minimal but intuitively intelligible number of properties. As opposed to the more liberal WikiData, MathAlgoDB relies on the strict adherence to the ontology to provide a reliable machine-readable database of (numerical) algorithm knowledge.

Introduction back to ToC

This is a place holder text for the introduction. The introduction should briefly describe the ontology, its motivation, state of the art and goals.

Namespace declarations

Table 1: Namespaces used in the document
mathalgodb<https://mardi4nfdi.de/mathalgodb/0.1#>
owl<http://www.w3.org/2002/07/owl>
rdf<http://www.w3.org/1999/02/22-rdf-syntax-ns>
xml<http://www.w3.org/XML/1998/namespace>
xsd<http://www.w3.org/2001/XMLSchema>
skos<http://www.w3.org/2004/02/skos/core>
dcterms<http://purl.org/dc/terms>
bibo<http://purl.org/ontology/bibo>
rdfs<http://www.w3.org/2000/01/rdf-schema>
vann<http://purl.org/vocab/vann>
foaf<http://xmlns.com/foaf/0.1>
dc<http://purl.org/spar/datacite>

Algorithm Knowledge Graph Ontology: Overview back to ToC

This ontology has the following classes and properties.

Classes

Object Properties

Data Properties

Algorithm Knowledge Graph Ontology: Description back to ToC

This is a placeholder text for the description of your ontology. The description should include an explanation and a diagram explaining how the classes are related, examples of usage, etc.

Cross-reference for Algorithm Knowledge Graph Ontology classes, object properties and data properties back to ToC

This section provides details for each class and property defined by Algorithm Knowledge Graph Ontology.

Classes

Algorithmc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#algorithm

The main building blocks of the graph are algorithms. Here you can take a look at all algorithms documented in the graph.
is in domain of
has component op, has subclass op, is analyzed in op, is applied in op, is component of op, is implemented by op, is invented in op, is related to op, is studied in op, is subclass of op, is surveyed in op, solves op
is in range of
analyzes op, applies op, has component op, has subclass op, implements op, invents op, is component of op, is related to op, is solved by op, is subclass of op, studies op, surveys op

All allgodata objectsc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#all_objects

is equivalent to
Algorithm c or Benchmark c or Problem c or Publication c or Software c
is in domain of
has category dp

Benchmarkc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#benchmark

For testing, evaluating and comparing numerical algorithms, so called benchmark problems are often useful.
is in domain of
is instance of op, is tested by op
is in range of
instantiates op, tests op

Identifiablec back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#identifiable

is equivalent to
Benchmark c or Publication c or Software c
is in domain of
has identifier dp

Problemc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#problem

When interested in algorithms solving a certain problem at hand, we here provide an overview of all problems defined in the graph.
An engineering challenge that includes a mathematical part
is in domain of
instantiates op, is solved by op, specializedBy op, specializes op
is in range of
is instance of op, solves op, specializedBy op, specializes op

Publicationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#publication

To find theoretical or numerical results on the performance of algorithms, take a look at the related publications in this list.
is in domain of
analyzes op, applies op, documents op, invents op, studies op, surveys op, uses op
is in range of
is analyzed in op, is applied in op, is documented in op, is invented in op, is studied in op, is surveyed in op, is used in op

Realizationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#realization

Union of all MathAlgoDB-Classes that *may* have a unique identifier.
is equivalent to
Benchmark c or Software c
is in domain of
is documented in op, is used in op
is in range of
documents op, uses op

Softwarec back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#software

This table contains software packages that implement some of the algorithms from the graph.
is in domain of
implements op, tests op
is in range of
is implemented by op, is tested by op

Object Properties

analyzesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#analyzes

has domain
Publication c
has range
Algorithm c
is inverse of
is analyzed in op

appliesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#applies

has domain
Publication c
has range
Algorithm c
is inverse of
is applied in op

documentsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#documents

has domain
Publication c
has range
Realization c
is inverse of
is documented in op

has componentop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#hasComponent

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
is component of op

has subclassop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#hasSubclass

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
is subclass of op

implementsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#implements

has domain
Software c
has range
Algorithm c
is inverse of
is implemented by op

instantiatesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#instantiates

has domain
Problem c
has range
Benchmark c
is inverse of
is instance of op

inventsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#invents

has domain
Publication c
has range
Algorithm c
is inverse of
is invented in op

is analyzed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#analyzedIn

has domain
Algorithm c
has range
Publication c
is inverse of
analyzes op

is applied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#appliedIn

has domain
Algorithm c
has range
Publication c
is inverse of
applies op

is component ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#componentOf

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
has component op

is documented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#documentedIn

has domain
Realization c
has range
Publication c
is inverse of
documents op

is implemented byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#implementedBy

has domain
Algorithm c
has range
Software c
is inverse of
implements op

is instance ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#instanceOf

has domain
Benchmark c
has range
Problem c
is inverse of
instantiates op

is invented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#inventedIn

has domain
Algorithm c
has range
Publication c
is inverse of
invents op

is related toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#relatedTo

has characteristics: symmetric, transitive

has domain
Algorithm c
has range
Algorithm c

is solved byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#solvedBy

has domain
Problem c
has range
Algorithm c
is inverse of
solves op

is studied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#studiedIn

has domain
Algorithm c
has range
Publication c
is inverse of
studies op

is subclass ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#subclassOf

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
has subclass op

is surveyed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#reviewedIn

has domain
Algorithm c
has range
Publication c
is inverse of
surveys op

is tested byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#testedBy

has domain
Benchmark c
has range
Software c
is inverse of
tests op

is used inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#usedIn

has domain
Realization c
has range
Publication c
is inverse of
uses op

solvesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#solves

has domain
Algorithm c
has range
Problem c
is inverse of
is solved by op

specializedByop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#specializedBy

has characteristics: transitive

has domain
Problem c
has range
Problem c
is inverse of
specializes op

specializesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#specializes

has characteristics: transitive

has domain
Problem c
has range
Problem c
is inverse of
specializedBy op

studiesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#studies

has domain
Publication c
has range
Algorithm c
is inverse of
is studied in op

surveysop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#reviews

has domain
Publication c
has range
Algorithm c
is inverse of
is surveyed in op

testsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#tests

has domain
Software c
has range
Benchmark c
is inverse of
is tested by op

usesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#uses

has domain
Publication c
has range
Realization c
is inverse of
is used in op

Data Properties

has categorydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#category

has domain
All allgodata objects c
has range
string

has identifierdp back to ToC or Data Property ToC

IRI: http://purl.org/spar/datacite/hasIdentifier

has domain
Identifiable c
has range
string

Legend back to ToC

c: Classes
op: Object Properties
dp: Data Properties

References back to ToC

Add your references here. It is recommended to have them as a list.

Acknowledgments back to ToC

The authors would like to thank Silvio Peroni for developing LODE, a Live OWL Documentation Environment, which is used for representing the Cross Referencing Section of this document and Daniel Garijo for developing Widoco, the program used to create the template used in this documentation.