has identifier
type: DatatypeProperty
domain: Identifiable
range: string
cardinality: 0

Algorithm Knowledge Graph Ontology
type: Ontology
bibliographic citation: 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
creator: Aurela Shehu (https://orcid.org/0000-0002-1994-0612), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
creator: Björn Schembera (https://orcid.org/0000-0003-2860-6621), Universität Stuttgart (https://ror.org/04vnq7t77, https://isni.org/isni/0000000419369713)
creator: Burkhard Schmidt (https://orcid.org/0000-0002-9658-499X), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
creator: Christian Himpe (https://orcid.org/0000-0003-2194-6754)
creator: Christine Biedinger (https://orcid.org/0009-0002-5082-8386), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
creator: Frank Wübbeling (https://orcid.org/0000-0002-2375-2008)
creator: Hendrik Kleikamp (https://orcid.org/0000-0003-1264-5941)
creator: Jochen Fiedler (https://orcid.org/0000-0002-9176-780X), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
creator: Marco Reidelbach (https://orcid.org/0000-0002-1919-1834), Zuse Institute Berlin (https://ror.org/02eva5865, https://isni.org/isni/000000011010926X)
creator: René Fritze (https://orcid.org/0000-0002-9548-2238)
creator: Stephan Rave (https://orcid.org/0000-0003-0439-7212)
creator: Thomas Koprucki (https://orcid.org/0000-0001-6235-9412), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
description: 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.
license: https://creativecommons.org/licenses/by/4.0
status: Draft
preferred namespace prefix: mathalgodb
preferred namespace uri: https://mardi4nfdi.de/mathalgodb/0.1#
comment: This is the MathModDB Ontology for documenting mathematical models.
label: MathModDB Ontology
version info: 0.1

Algorithm
type: Class
comment: The main building blocks of the graph are algorithms. Here you can take a look at all algorithms documented in the graph.
cardinality: 10

All MathAlgoDB objects
type: Class
label: All allgodata objects
equivalent class: Class
  union of: Algorithm
  union of: Benchmark
  union of: Algorithmic Task
  union of: Publication
  union of: Software
equivalent class: Class
  union of: Algorithm
  union of: Benchmark
  union of: Algorithmic Task
  union of: Publication
  union of: Software
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
  union of: Quantity
  union of: Quantity Kind
  union of: Research Field
  union of: Research Problem
  union of: Task

is analyzed in
type: ObjectProperty
domain: Algorithm
range: Publication
cardinality: 60

analyzes
type: ObjectProperty
domain: Publication
range: Algorithm
cardinality: 60
inverse of: is analyzed in

is applied in
type: ObjectProperty
domain: Algorithm
range: Publication
cardinality: 80

applies
type: ObjectProperty
domain: Publication
range: Algorithm
cardinality: 80
inverse of: is applied in

Benchmark
type: Class
comment: For testing, evaluating and comparing numerical algorithms, so called benchmark problems are often useful.
cardinality: 40

has category
type: DatatypeProperty
domain: All MathAlgoDB objects
range: string

is component of
type: ObjectProperty
type: TransitiveProperty
domain: Algorithm
range: Algorithm
cardinality: 40
inverse of: has component

contains formulation
type: ObjectProperty
domain: Algorithmic Task
range: Mathematical Formulation
cardinality: 200

is documented in
type: ObjectProperty
domain: Realization
range: Publication
cardinality: 120

documents
type: ObjectProperty
domain: Publication
range: Realization
cardinality: 120
inverse of: is documented in

equivalent to
type: ObjectProperty
domain: Algorithmic Task
range: Computational Task
cardinality: 200
inverse of: equivalent to

has component
type: ObjectProperty
type: TransitiveProperty
domain: Algorithm
range: Algorithm
cardinality: 40

has subclass
type: ObjectProperty
type: TransitiveProperty
domain: Algorithm
range: Algorithm
cardinality: 20
inverse of: is subclass of

Identifiable
type: Class
equivalent class: Class
  union of: Benchmark
  union of: Publication
  union of: Software

is implemented by
type: ObjectProperty
domain: Algorithm
range: Software
cardinality: 100
inverse of: implements

implements
type: ObjectProperty
domain: Software
range: Algorithm
cardinality: 100

is instance of
type: ObjectProperty
domain: Benchmark
range: Algorithmic Task
cardinality: 100

instantiates
type: ObjectProperty
domain: Algorithmic Task
range: Benchmark
cardinality: 100
inverse of: is instance of

is invented in
type: ObjectProperty
domain: Algorithm
range: Publication
cardinality: 50

invents
type: ObjectProperty
domain: Publication
range: Algorithm
cardinality: 50
inverse of: is invented in

precludes
type: ObjectProperty
domain: Algorithm
range: Mathematical Formulation
cardinality: 200

Algorithmic Task
type: Class
comment: When interested in algorithms solving a certain problem at hand, we here provide an overview of all problems defined in the graph.
cardinality: 30
definition: An engineering challenge that includes a mathematical part

Publication
type: Class
comment: To find theoretical or numerical results on the performance of algorithms, take a look at the related publications in this list.
cardinality: 100

Realization
type: Class
equivalent class: Class
  union of: Benchmark
  union of: Software
definition: Union of all MathAlgoDB-Classes that *may* have a unique identifier.

recommends
type: ObjectProperty
domain: Algorithm
range: Mathematical Formulation
cardinality: 200

is related to
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Algorithm
range: Algorithm
cardinality: 30

requires
type: ObjectProperty
domain: Algorithm
range: Mathematical Formulation
cardinality: 200

is surveyed in
type: ObjectProperty
domain: Algorithm
range: Publication
cardinality: 90

surveys
type: ObjectProperty
domain: Publication
range: Algorithm
cardinality: 90
inverse of: is surveyed in

Software
type: Class
comment: This table contains software packages that implement some of the algorithms from the graph.
cardinality: 20

is solved by
type: ObjectProperty
domain: Algorithmic Task
range: Algorithm
cardinality: 10
inverse of: solves

solves
type: ObjectProperty
domain: Algorithm
range: Algorithmic Task
cardinality: 10

specializedBy
type: ObjectProperty
type: TransitiveProperty
domain: Algorithmic Task
range: Algorithmic Task
cardinality: 5
inverse of: specializes

specializes
type: ObjectProperty
type: TransitiveProperty
domain: Algorithmic Task
range: Algorithmic Task
cardinality: 5

is studied in
type: ObjectProperty
domain: Algorithm
range: Publication
cardinality: 70

studies
type: ObjectProperty
domain: Publication
range: Algorithm
cardinality: 70
inverse of: is studied in

is subclass of
type: ObjectProperty
type: TransitiveProperty
domain: Algorithm
range: Algorithm
cardinality: 20

is tested by
type: ObjectProperty
domain: Benchmark
range: Software
cardinality: 110
inverse of: tests

tests
type: ObjectProperty
domain: Software
range: Benchmark
cardinality: 110

is used in
type: ObjectProperty
domain: Realization
range: Publication
cardinality: 130

uses
type: ObjectProperty
domain: Publication
range: Realization
inverse of: is used in

Computational Task
type: Class
comment: A specific computational tasks associated with a mathematical model. Typically, various tasks differ from each other by the choice of given quantities (input), unknown quantities (output), parameters or constants as well as boundary conditions, inital conditions and/or final conditions.
label: Berechnungsaufgabe @de
subclass of: Task
cardinality: 200
disjoint with: Mathematical Formulation
disjoint with: Mathematical Model
disjoint with: Publication
disjoint with: Quantity
disjoint with: Quantity Kind
disjoint with: Research Field
disjoint with: Research Problem

LaTeX
type: Datatype
cardinality: 200

MathML
type: Datatype
cardinality: 200

Mathematical Formulation
type: Class
comment: Typically, a mathematical formulation is based on equations (general construct indicating equality of quantities) or on inequalities (non-equal relations between quantities), or a logic quantifier
label: Mathematische Formulierung @de
cardinality: 200
disjoint with: Mathematical Model
disjoint with: Publication
disjoint with: Quantity
disjoint with: Quantity Kind
disjoint with: Research Field
disjoint with: Research Problem
disjoint with: Task
wikidata ID: Q11345
wikidata ID: Q28113351
wikidata ID: Q592911
wikidata ID: Q976981

Mathematical Model
type: Class
comment: A mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions. The aim of modeling is to make a particular part or feature of the world easier to simulate, interpret and/or optimize based on existing knowledge.
label: Mathematisches Modell @de
cardinality: 200
disjoint with: Publication
disjoint with: Quantity
disjoint with: Quantity Kind
disjoint with: Research Field
disjoint with: Research Problem
disjoint with: Task
wikidata ID: Q486902

Matrix Properties
type: DatatypeProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Datatype
  one of: NegativeDefinite
  one of: NegativeSemiDefinite
  one of: PositiveDefinite
  one of: PositiveSemiDefinite
cardinality: 200

Matrix Structure
type: DatatypeProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Datatype
  one of: Block
  one of: CentroSymmetric
  one of: Circulant
  one of: Diagonal
  one of: Hessenberg
  one of: SkewSymmetric
  one of: Symmetric
  one of: Toeplitz
  one of: TriDiagonal
cardinality: 200

Publication
type: Class
comment: A scientific publication
label: Publikation @de
cardinality: 200
disjoint with: Quantity
disjoint with: Quantity Kind
disjoint with: Research Field
disjoint with: Research Problem
disjoint with: Task

Quantity
type: Class
comment: A quantity is a property of a system that can be measured or obtained from calculation/simulation. Can be a scalar, a vector, a matrix or a higher-order tensor. The overarching, abstract quantity in the QuantityKind class should be referenced if possible/applicable.
label: Quantität @de
cardinality: 200
disjoint with: Quantity Kind
disjoint with: Research Field
disjoint with: Research Problem
disjoint with: Task
wikidata ID: Q309314

Quantity Kind
type: Class
comment: The kind of quantity, e.g. the abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, .... Note that the kind of a quantity cannot be generalized by another (kind of a) quantity.
label: Basisquantität @de
cardinality: 200
disjoint with: Research Field
disjoint with: Research Problem
disjoint with: Task

Research Field
type: Class
comment: A field of research (or academic discipline), e.g. Arts & Humanities, Life Sciences & Biomedicine, Physical & Natural Sciences or Engineering.
label: Forschungsgebiet @de
cardinality: 200
disjoint with: Research Problem
disjoint with: Task
wikidata ID: Q11862829

Research Problem
type: Class
comment: A research problem (or research question) to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research.
label: Forschungsthema @de
cardinality: 200
disjoint with: Task
wikidata ID: Q123578571

Task
type: Class
comment: A specific task associated with a mathematical model. The subclasses of this superclass should reflect their differences, e.g. a computational task or a task of doing a mathematical analysis (the latter is not yet implemented).
label: Aufgabe @de
cardinality: 200

applied by
type: ObjectProperty
cardinality: 200

applied by task
type: ObjectProperty
domain: Mathematical Model
range: Computational Task
sub property of: applied by
cardinality: 200
inverse of: applies model

applies
type: ObjectProperty
cardinality: 200

applies model
type: ObjectProperty
domain: Computational Task
range: Mathematical Model
sub property of: applies
cardinality: 200

approximated by
type: ObjectProperty
type: TransitiveProperty
cardinality: 200
inverse of: approximates

approximated by formulation
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: approximated by
cardinality: 200
inverse of: approximates formulation

approximated by model
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Model
range: Mathematical Model
sub property of: approximated by
cardinality: 200
inverse of: approximates model

approximated by quantity
type: ObjectProperty
type: TransitiveProperty
domain: Quantity
range: Quantity
sub property of: approximated by
cardinality: 200
inverse of: approximates quantity

approximated by task
type: ObjectProperty
type: TransitiveProperty
domain: Computational Task
range: Computational Task
sub property of: approximated by
cardinality: 200
inverse of: approximates task

approximates
type: ObjectProperty
type: TransitiveProperty
cardinality: 200

approximates formulation
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: approximates
cardinality: 200

approximates model
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Model
range: Mathematical Model
sub property of: approximates
cardinality: 200

approximates quantity
type: ObjectProperty
type: TransitiveProperty
domain: Quantity
range: Quantity
sub property of: approximates
cardinality: 200

approximates task
type: ObjectProperty
type: TransitiveProperty
domain: Computational Task
range: Computational Task
sub property of: approximates
cardinality: 200

arxivID
type: AnnotationProperty
cardinality: 200

contained as assumption in
type: ObjectProperty
type: TransitiveProperty
comment: Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains assumption

contained as boundary condition in
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains boundary condition

contained as constant in
type: ObjectProperty
comment: This property serves to indicate that a certain quantity is considered as a constant in a computational task.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
sub property of: contained in
cardinality: 200
inverse of: contains constant

contained as constraint condition in
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains constraint condition

contained as coupling condition in
type: ObjectProperty
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains coupling condition

contained as final condition in
type: ObjectProperty
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains final condition

contained as formulation in
type: ObjectProperty
type: TransitiveProperty
comment: use this property to denote that a formulation is contained in a (single or coupled) model or formulation or task, e.g., a Darcy formulation is contained in a Darcy-Stokes model or formulation or a related task
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains formulation

contained as formulation in task
type: ObjectProperty
domain: Mathematical Formulation
range: Algorithmic Task
cardinality: 200
inverse of: contains formulation

contained as initial condition in
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains initial condition

contained as input in
type: ObjectProperty
comment: Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Computational Task
sub property of: contained in
cardinality: 200
inverse of: contains input

contained as objective in
type: ObjectProperty
comment: This property serves to indicate that a certain quantity is to be minimized or maximized in a mathematical optimization task.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Computational Task
sub property of: contained in
cardinality: 200
inverse of: contains objective
wikidata ID: Q984063

contained as output in
type: ObjectProperty
comment: Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Computational Task
sub property of: contained in
cardinality: 200
inverse of: contains output

contained as parameter in
type: ObjectProperty
comment: Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Computational Task
sub property of: contained in
cardinality: 200
inverse of: contains parameter

contained in
type: ObjectProperty
cardinality: 200
inverse of: contains

contained in field
type: ObjectProperty
domain: Research Problem
range: Research Field
sub property of: contained in
cardinality: 200
inverse of: contains problem

contained in formulation
type: ObjectProperty
comment: use this property to denote that a quantity is contained in a formulation e.g. masses are contained in a Newton Equation
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Mathematical Formulation
sub property of: contained in
cardinality: 200
inverse of: contains quantity

contained in model
type: ObjectProperty
type: TransitiveProperty
comment: use this property to denote that a single model is included in a coupled model, e.g. a Darcy model and a Stokes model are included in a Darcy Stokes model
domain: Mathematical Model
range: Mathematical Model
sub property of: contained in
cardinality: 200
inverse of: contains model

contained in task
type: ObjectProperty
comment: This indicates that a computational sub-task is contained in a higher task.
domain: Computational Task
range: Computational Task
sub property of: contained in
cardinality: 200
inverse of: contains task

contains
type: ObjectProperty
cardinality: 200

contains assumption
type: ObjectProperty
type: TransitiveProperty
comment: Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200
wikidata ID: Q29463760

contains boundary condition
type: ObjectProperty
type: TransitiveProperty
comment: In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.[1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200
wikidata ID: Q18382796

contains constant
type: ObjectProperty
comment: This property serves to indicate that a certain quantity is considered as a constant in a computational task.
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200

contains constraint condition
type: ObjectProperty
type: TransitiveProperty
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200
wikidata ID: Q1193699

contains coupling condition
type: ObjectProperty
comment: Conditions needed to model the interaction of two or more systems that are interacting with each other
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200

contains final condition
type: ObjectProperty
comment: Similar to initial conditions. Sometimes used in the context of optimal control.
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200

contains formulation
type: ObjectProperty
type: TransitiveProperty
comment: use this property to denote that a (single or coupled) model or formulation includes a mathematical formulation, e.g. a Darcy Stokes model/formulation includes a Darcy formulation and a Stokes formulation
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200

contains initial condition
type: ObjectProperty
type: TransitiveProperty
comment: In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
range: Mathematical Formulation
sub property of: contains
cardinality: 200
wikidata ID: Q18351510

contains input
type: ObjectProperty
comment: Indicates that a (base) quantity is considered as input in the context of a (specific!) computational task.
domain: Computational Task
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200

contains model
type: ObjectProperty
type: TransitiveProperty
comment: use this property to denote that a coupled model includes single models, e.g. a Darcy Stokes model includes a Darcy model and a Stokes model
domain: Mathematical Model
range: Mathematical Model
sub property of: contains
cardinality: 200

contains objective
type: ObjectProperty
comment: This property serves to indicate that a certain quantity is to be minimized or maximized in a computational optimization task. An objective function, a target function, a loss function or cost function (minimization), a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.
domain: Computational Task
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200
wikidata ID: Q984063

contains output
type: ObjectProperty
comment: Indicates that a (base) quantity is considered as output in the context of a (specific!) computational task.
domain: Computational Task
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200

contains parameter
type: ObjectProperty
comment: Auxiliary variable or arbitrary constant that characterizes a system or specifies a mathematical function among a family of functions. This property serves to indicate that a certain quantity is considered as a parameter in a computational task.
domain: Computational Task
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200

contains problem
type: ObjectProperty
domain: Research Field
range: Research Problem
sub property of: contains
cardinality: 200

contains quantity
type: ObjectProperty
comment: use this property to denote that a mathematical formulation contains a quantity, e.g., a Newton Equation contains masses
domain: Mathematical Formulation
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: contains
cardinality: 200

contains task
type: ObjectProperty
type: TransitiveProperty
comment: This indicates that a computational task contains a subtask.
domain: Computational Task
range: Computational Task
sub property of: contains
cardinality: 200

dbpediaID
type: AnnotationProperty
cardinality: 200

defined by
type: ObjectProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Mathematical Formulation
cardinality: 200
inverse of: defines

defines
type: ObjectProperty
domain: Mathematical Formulation
range: Class
  union of: Quantity
  union of: Quantity Kind
cardinality: 200

defining formulation
type: DatatypeProperty
comment: Equations, inequalities, expressions, logic quantifiers, ... in Latex or MathML, e.g. $F = ma$, $v \llt c$, $\forall n \in N$, ...
domain: Mathematical Formulation
range: Datatype
  union of: LaTeX
  union of: MathML
sub property of: Formulation Property
cardinality: 200

discretized by
type: ObjectProperty
comment: Discrete models are the discrete analogues of continuous models. In discrete modelling, processes are described by discrete data, i.e., data that could potentially take on only a countable set of values, such as the integers, and which are not infinitely divisible. Thus, discrete modeling yields a computer representable and computable versions of continuous mathematical models,
cardinality: 200
inverse of: discretizes

discretized by formulation
type: ObjectProperty
comment: Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: discretized by
cardinality: 200
inverse of: discretizes formulation

discretized by model
type: ObjectProperty
comment: Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
domain: Mathematical Model
range: Mathematical Model
sub property of: discretized by
cardinality: 200
inverse of: discretizes model

discretized by task
type: ObjectProperty
domain: Computational Task
range: Computational Task
sub property of: discretized by
cardinality: 200
inverse of: discretizes task

discretizes
type: ObjectProperty
comment: Discretizing is the process of obtaining discrete models/formulations that are the analogues of continuous models/formulations. Thus, discretization yields a computer representable and computable versions.
cardinality: 200

discretizes formulation
type: ObjectProperty
comment: Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: discretizes
cardinality: 200

discretizes model
type: ObjectProperty
comment: Discretizing is the process of obtaining discrete models that are the analogues of continuous models, thus making them computer representable and hopefully(!) computer solvable. Note, however, that certain models are already discretized from the outset.
domain: Mathematical Model
range: Mathematical Model
sub property of: discretizes
cardinality: 200

discretizes task
type: ObjectProperty
domain: Computational Task
range: Computational Task
sub property of: discretizes
cardinality: 200

documented in
type: ObjectProperty
comment: A property to express that an entity (problem, model, ...) is documented in a specific Publication
range: Publication
cardinality: 200
inverse of: documents

documents
type: ObjectProperty
comment: A property that expresses a Publication is documenting some entity (problem, model, ...)
domain: Publication
cardinality: 200

doiID
type: AnnotationProperty
cardinality: 200

equivalent to
type: ObjectProperty
domain: Computational Task
range: Algorithmic Task
cardinality: 200

Formulation Property
type: DatatypeProperty
domain: Mathematical Formulation
cardinality: 200

generalized by
type: ObjectProperty
type: TransitiveProperty
cardinality: 200
inverse of: generalizes

generalized by field
type: ObjectProperty
type: TransitiveProperty
domain: Research Field
range: Research Field
sub property of: generalized by
cardinality: 200
inverse of: generalizes field

generalized by formulation
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: generalized by
cardinality: 200
inverse of: generalizes formulation

generalized by model
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Model
range: Mathematical Model
sub property of: generalized by
cardinality: 200
inverse of: generalizes model

generalized by problem
type: ObjectProperty
type: TransitiveProperty
domain: Research Problem
range: Research Problem
sub property of: generalized by
cardinality: 200
inverse of: generalizes problem

generalized by quantity
type: ObjectProperty
type: TransitiveProperty
domain: Quantity
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: generalized by
cardinality: 200
inverse of: generalizes quantity

generalized by task
type: ObjectProperty
type: TransitiveProperty
domain: Computational Task
range: Computational Task
sub property of: generalized by
cardinality: 200
inverse of: generalizes task

generalizes
type: ObjectProperty
type: TransitiveProperty
cardinality: 200

generalizes field
type: ObjectProperty
type: TransitiveProperty
domain: Research Field
range: Research Field
sub property of: generalizes
cardinality: 200

generalizes formulation
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: generalizes
cardinality: 200

generalizes model
type: ObjectProperty
type: TransitiveProperty
domain: Mathematical Model
range: Mathematical Model
sub property of: generalizes
cardinality: 200

generalizes problem
type: ObjectProperty
type: TransitiveProperty
domain: Research Problem
range: Research Problem
sub property of: generalizes
cardinality: 200

generalizes quantity
type: ObjectProperty
type: TransitiveProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Quantity
sub property of: generalizes
cardinality: 200

generalizes task
type: ObjectProperty
type: TransitiveProperty
domain: Computational Task
range: Computational Task
sub property of: generalizes
cardinality: 200

has Formulation Order
type: DatatypeProperty
comment: The Order of a mathematical formulation
domain: Mathematical Formulation
range: integer
sub property of: Formulation Property
cardinality: 200

has Formulation Property
type: DatatypeProperty
domain: Mathematical Formulation
range: string
sub property of: Formulation Property
cardinality: 200

in defining formulation
type: DatatypeProperty
comment: Symbol / Term of formulation and corresponding quantity in comma-separated list, e.g. ($\mathbf{F}$,qudt:Force) and/or ($m$,dbpedia:Mass) and/or ($\mathbf{a}$,wikidata:Q11376)
domain: Mathematical Formulation
range: Datatype
  union of: string
  union of: LaTeX
  union of: MathML
sub property of: Formulation Property
cardinality: 200

invented in
type: ObjectProperty
comment: A property that states that some entity (problem, model, ...) was invented in a specific Publication
range: Publication
cardinality: 200
inverse of: invents

invents
type: ObjectProperty
comment: A property that states that a Publication invented some entity (problem, model, ...)
domain: Publication
cardinality: 200

is convex
type: DatatypeProperty
comment: Boolean. True if convex, false if not convex
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

is deterministic
type: DatatypeProperty
comment: Boolean. True, if the model is deterministic; false, if the model is probabilistic (stochastic)
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

is dimensionless
type: DatatypeProperty
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
  union of: Quantity
  union of: Quantity Kind
range: boolean
cardinality: 200

is dynamic
type: DatatypeProperty
comment: Boolean. True, if dynamic; false, if static
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

is linear
type: DatatypeProperty
comment: Boolean. True, if linear; false, if non-linear
domain: Class
  union of: Computational Task
  union of: Mathematical Formulation
  union of: Mathematical Model
  union of: Quantity
range: boolean
cardinality: 200

is space-continuous
type: DatatypeProperty
comment: Boolean. True, if continuous in space; false, if discrete in space
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

is stiff
type: DatatypeProperty
comment: Boolean. True, if dynamic; false, if stiff
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

is time-continuous
type: DatatypeProperty
comment: Boolean. True, if continuous in time; false, if discrete in time
domain: Class
  union of: Mathematical Formulation
  union of: Mathematical Model
range: boolean
cardinality: 200

linearized by
type: ObjectProperty
cardinality: 200
inverse of: linearizes

linearized by formulation
type: ObjectProperty
comment: A property that states that a formulation is linearized (exact or approximate) by another formulation.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: linearized by
cardinality: 200
inverse of: linearizes formulation

linearized by model
type: ObjectProperty
comment: A property that states that a model is linearized (exact or approximate) by another model.
domain: Mathematical Model
range: Mathematical Model
sub property of: linearized by
cardinality: 200
inverse of: linearizes model

linearized by quantity
type: ObjectProperty
comment: A property that states that a quantity is linearized (exact or approximate) by another quantity.
domain: Quantity
range: Quantity
sub property of: linearized by
cardinality: 200
inverse of: linearizes quantity

linearized by task
type: ObjectProperty
comment: A property that states that a task is linearized (exact or approximate) by another task.
domain: Computational Task
range: Computational Task
sub property of: linearized by
cardinality: 200
inverse of: linearizes task

linearizes
type: ObjectProperty
comment: Linearization of a formulation, model, quantity or task.
cardinality: 200
wikidata ID: Q1520713

linearizes formulation
type: ObjectProperty
comment: A property that states that a formulation linearizes (exact or approximate) another formulation.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: linearizes
cardinality: 200

linearizes model
type: ObjectProperty
comment: A property that states that a model linearizes (exact or approximate) another model.
domain: Mathematical Model
range: Mathematical Model
sub property of: linearizes
cardinality: 200

linearizes quantity
type: ObjectProperty
comment: A property that states that a quantity linearizes (exact or approximate) another quantity.
domain: Quantity
range: Quantity
sub property of: linearizes
cardinality: 200

linearizes task
type: ObjectProperty
comment: A property that states that a task linearizes (exact or approximate) another task.
domain: Computational Task
range: Computational Task
sub property of: linearizes
cardinality: 200

mardiID
type: AnnotationProperty
cardinality: 200

modeled by
type: ObjectProperty
comment: Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
domain: Research Problem
range: Mathematical Model
cardinality: 200
inverse of: models

models
type: ObjectProperty
comment: Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
domain: Mathematical Model
range: Research Problem
cardinality: 200

nondimensionalizes quantity
type: ObjectProperty
comment: A property that states that a quantity nondimensionalizes (partially or complete) another quantity.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: nondimensionalizes
cardinality: 200
inverse of: nondimensionalized by quantity

nondimensionalized by
type: ObjectProperty
type: InverseFunctionalProperty
cardinality: 200
inverse of: nondimensionalizes

nondimensionalized by formulation
type: ObjectProperty
comment: A property that states that a formulation is nondimensionalized (partially or complete) by another formulation.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: nondimensionalized by
cardinality: 200
inverse of: nondimensionalizes formulation

nondimensionalized by quantity
type: ObjectProperty
comment: A property that states that a quantity is nondimensionalized (partially or complete) by another quantity.
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: nondimensionalized by
cardinality: 200

nondimensionalizes
type: ObjectProperty
type: FunctionalProperty
comment: Partial or full removal of physical dimensions from a quantity or a formulation.
cardinality: 200
wikidata ID: Q464133

nondimensionalizes formulation
type: ObjectProperty
comment: A property that states that a formulation nondimensionalizes (partially or complete) another formulation.
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: nondimensionalizes
cardinality: 200

precluded by
type: ObjectProperty
domain: Mathematical Formulation
range: Algorithm
cardinality: 200
inverse of: precludes

Quantity Type
type: DatatypeProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Datatype
  one of: Higher Order Tensor
  one of: Matrix
  one of: Scalar
  one of: Vector
cardinality: 200

qudtID
type: AnnotationProperty
cardinality: 200

recommended by
type: ObjectProperty
domain: Mathematical Formulation
range: Algorithm
cardinality: 200
inverse of: recommends

required by
type: ObjectProperty
domain: Mathematical Formulation
range: Algorithm
cardinality: 200
inverse of: requires

similar to
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
comment: use this property only if the two things are similar but the one is not the generalization of the other one
cardinality: 200

similar to field
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Research Field
range: Research Field
sub property of: similar to
cardinality: 200

similar to formulation
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Mathematical Formulation
range: Mathematical Formulation
sub property of: similar to
cardinality: 200

similar to model
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Mathematical Model
range: Mathematical Model
sub property of: similar to
cardinality: 200

similar to problem
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Research Problem
range: Research Problem
sub property of: similar to
cardinality: 200

similar to quantity
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Class
  union of: Quantity
  union of: Quantity Kind
range: Class
  union of: Quantity
  union of: Quantity Kind
sub property of: similar to
cardinality: 200

similar to task
type: ObjectProperty
type: SymmetricProperty
type: TransitiveProperty
domain: Computational Task
range: Computational Task
sub property of: similar to
cardinality: 200

studied in
type: ObjectProperty
comment: This property states that an entity (problem, model, ...) is studied in a specific Publication
range: Publication
cardinality: 200
inverse of: studies

studies
type: ObjectProperty
comment: This property states that a Publication studies an entity (problem, model, ...)
domain: Publication
cardinality: 200

surveyed in
type: ObjectProperty
comment: This property states that an entity (problem, model, application, ...) is surveyed in a specific Publication. Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
range: Publication
cardinality: 200
inverse of: surveys

surveys
type: ObjectProperty
comment: This property states that a Publication surveys some entity (problem, model, application...). Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
domain: Publication
cardinality: 200

used in
type: ObjectProperty
comment: A property that states that an entity (problem, model, ...) is used in a Publication
range: Publication
cardinality: 200
inverse of: uses

uses
type: ObjectProperty
comment: A property that states that a Publication uses a specific entity (problem, model, ...)
domain: Publication
cardinality: 200

wikidataID
type: AnnotationProperty
cardinality: 200

zbmathID
type: AnnotationProperty
cardinality: 200