34
3 Marketplace-Level Domain Ontologies
C C
Crdfs:subClassOf C’,
R R
Rrdfs:subPropertyOf R’,
C ≡ C
Cowl:equivalentClass C’,
R ≡ R
Rowl:equivalentProperty R’,
(3.5)
such as
osmo:simulation_workflow
osmo:workflow_graph ∃S.evmpo:simulation,
(3.6)
where S is an abbreviation for the relation “is sign for” (viprs:is_sign_for, cf. Sect.
5.2). Accordingly, Expression (3.6) states that “every simulation workflow is a workflow graph that is a sign for a simulation”, relating the concept of a simulation workflow to those of a workflow graph and a simulation.
Similarly,
osmo:is_governing_equation_in
P osmo:governing_equation
•
• osmo:materials_model,
(3.7)
where P denotes “is proper part of” (viprs:is_proper_part_of) states that “if I is a
governing equation in J , then I is a governing equation, J is a materials model and
I is a proper part of J .” In TTL notation, this is expressed as
osmo:is_governing_equation_in rdfs:domain
osmo:governing_equation;
rdfs:range
osmo:materials_model;
rdfs:subPropertyOf viprs:is_proper_part_of.
Other types of rules concern the disjointness of concepts and algebraic properties of
relations such as symmetry, transitivity and reflexivity.
Different types and fragments of DL restrict composites and rules that can be
included in a knowledge base in various ways to avoid computational undecidability,
and beyond this, to limit the complexity of reasoning tasks [1]. This is also the case
for OWL DL, the description logic associated with OWL as well as the DL language
profile of OWL2, which is the main standard for ontology engineering [11]. Adherence to the expressivity restrictions of this logic is prescribed by reasoners such as
FaCT++ and other widespread tools such as protégé. Relational composites (R R
,
etc.) cannot be included as such
5 in OWL DL; however, indirect constructions can
often be devised. Chain relations of the type R 1 ◦ R 2 , with the usual meaning
(I, J ) : (R 1 ◦ R 2 ) ⇐⇒ ∃I
∈ I : (I, I
) : R 1 ∧ (I
, J ) : R 2
(3.8)
5 We will use such notational constructions here nonetheless, where appropriate, with the intuitive
meaning, e.g. (I, J ) : (R R ) ⇔ (I, J ) : R ∧ (I, J ) : R .
3 Marketplace-Level Domain Ontologies
C C
Crdfs:subClassOf C’,
R R
Rrdfs:subPropertyOf R’,
C ≡ C
Cowl:equivalentClass C’,
R ≡ R
Rowl:equivalentProperty R’,
(3.5)
such as
osmo:simulation_workflow
osmo:workflow_graph ∃S.evmpo:simulation,
(3.6)
where S is an abbreviation for the relation “is sign for” (viprs:is_sign_for, cf. Sect.
5.2). Accordingly, Expression (3.6) states that “every simulation workflow is a workflow graph that is a sign for a simulation”, relating the concept of a simulation workflow to those of a workflow graph and a simulation.
Similarly,
osmo:is_governing_equation_in
P osmo:governing_equation
•
• osmo:materials_model,
(3.7)
where P denotes “is proper part of” (viprs:is_proper_part_of) states that “if I is a
governing equation in J , then I is a governing equation, J is a materials model and
I is a proper part of J .” In TTL notation, this is expressed as
osmo:is_governing_equation_in rdfs:domain
osmo:governing_equation;
rdfs:range
osmo:materials_model;
rdfs:subPropertyOf viprs:is_proper_part_of.
Other types of rules concern the disjointness of concepts and algebraic properties of
relations such as symmetry, transitivity and reflexivity.
Different types and fragments of DL restrict composites and rules that can be
included in a knowledge base in various ways to avoid computational undecidability,
and beyond this, to limit the complexity of reasoning tasks [1]. This is also the case
for OWL DL, the description logic associated with OWL as well as the DL language
profile of OWL2, which is the main standard for ontology engineering [11]. Adherence to the expressivity restrictions of this logic is prescribed by reasoners such as
FaCT++ and other widespread tools such as protégé. Relational composites (R R
,
etc.) cannot be included as such
5 in OWL DL; however, indirect constructions can
often be devised. Chain relations of the type R 1 ◦ R 2 , with the usual meaning
(I, J ) : (R 1 ◦ R 2 ) ⇐⇒ ∃I
∈ I : (I, I
) : R 1 ∧ (I
, J ) : R 2
(3.8)
5 We will use such notational constructions here nonetheless, where appropriate, with the intuitive
meaning, e.g. (I, J ) : (R R ) ⇔ (I, J ) : R ∧ (I, J ) : R .