32
3 Marketplace-Level Domain Ontologies
names, A c is a function representing conceptual assertions, such that an individual
name I ∈ I is mapped to a set of concepts A c (I ) and A r ⊆ I × R × I is a set of
relational assertions. The function H maps individuals I ∈ I to sets of elementary
datatype property assertions H (I ) = {η 1 , . . . , η n } where
1 each elementary datatype
property assertion η i = (k i , v i ) consists of a textual key k i ∈
and a textual or
numerical value v i ∈ R ∪
, with representing the employed alphabet and
the free monoid over .
On the semantic web, using the Web Ontology Language (OWL), elementary
names correspond to Internationalized Resource Identifiers (IRIs), and anything
referred to by an IRI, including concepts, relations and individuals, is accordingly
also called a “resource”. An IRI consists of a prefix and a suffix, where the alphabet
is the Unicode/ISO10646 universal coded character set. For the prefix, the same
well-known syntax applies as for a URL, and indeed, resolvable locators can be used
as IRIs; however, it is equally allowed to use non-resolvable identifiers, which cannot
be directly looked up on the web. Most notations permit an abbreviation of the prefix
so that osmo:workflow_graph can be written instead of the full IRI
https://purl.vimmp.eu/semantics/osmo/osmo.ttl#workflow_graph
for the concept name with the suffix workflow_graph from the ontology OSMO,
cf. Sect. 3.3. Conceptual and relational assertions are of the type
I : C
I a C,
(I, J ) : R
I R J ,
(3.1)
respectively, where I, J ∈ I are individuals, C is a concept and R is a relation
(in OWL, an owl:ObjectProperty)
2 ; the assertions above state that C ∈ A c (I ) and
(I, R, J ) ∈ A r . DL notation [1] is given on the left side and Terse Triple Language
(TTL) notation [4] on the right side; “triple” here refers to the sequence of a subject
(e.g. I ), a predicate (e.g. C) and an object (e.g. J ). The predicate “a” in TTL notation is an abbreviation for rdf:type, referring to the Resource Description Framework
(RDF), so that I a C indicates that C is the type of I , i.e. that I is an individual that
instantiates the concept C.
Examples for triples corresponding to conceptual and relational assertions, using
OSMO (Sect. 3.3) and VOV (Chap. 4), would be the following rendering of “ex:D
is a dipole moment vector and its value is zero:”
ex:D
a
vov:electric_dipole_moment;
vov:shares_value_with
osmo:ZERO_VECTOR_3D.
(3.2)
1 Dedicated description logics that were developed to formalize elementary datatype properties
(owl:DatatypeProperty) include DAML+OIL [5–7] and SHOQ(D) [8].
2 Elementary datatype properties (k, v) ∈ H (I ) are asserted as I kv in TTL, where the key k is an
owl:DatatypeProperty.
3 Marketplace-Level Domain Ontologies
names, A c is a function representing conceptual assertions, such that an individual
name I ∈ I is mapped to a set of concepts A c (I ) and A r ⊆ I × R × I is a set of
relational assertions. The function H maps individuals I ∈ I to sets of elementary
datatype property assertions H (I ) = {η 1 , . . . , η n } where
1 each elementary datatype
property assertion η i = (k i , v i ) consists of a textual key k i ∈
and a textual or
numerical value v i ∈ R ∪
, with representing the employed alphabet and
the free monoid over .
On the semantic web, using the Web Ontology Language (OWL), elementary
names correspond to Internationalized Resource Identifiers (IRIs), and anything
referred to by an IRI, including concepts, relations and individuals, is accordingly
also called a “resource”. An IRI consists of a prefix and a suffix, where the alphabet
is the Unicode/ISO10646 universal coded character set. For the prefix, the same
well-known syntax applies as for a URL, and indeed, resolvable locators can be used
as IRIs; however, it is equally allowed to use non-resolvable identifiers, which cannot
be directly looked up on the web. Most notations permit an abbreviation of the prefix
so that osmo:workflow_graph can be written instead of the full IRI
https://purl.vimmp.eu/semantics/osmo/osmo.ttl#workflow_graph
for the concept name with the suffix workflow_graph from the ontology OSMO,
cf. Sect. 3.3. Conceptual and relational assertions are of the type
I : C
I a C,
(I, J ) : R
I R J ,
(3.1)
respectively, where I, J ∈ I are individuals, C is a concept and R is a relation
(in OWL, an owl:ObjectProperty)
2 ; the assertions above state that C ∈ A c (I ) and
(I, R, J ) ∈ A r . DL notation [1] is given on the left side and Terse Triple Language
(TTL) notation [4] on the right side; “triple” here refers to the sequence of a subject
(e.g. I ), a predicate (e.g. C) and an object (e.g. J ). The predicate “a” in TTL notation is an abbreviation for rdf:type, referring to the Resource Description Framework
(RDF), so that I a C indicates that C is the type of I , i.e. that I is an individual that
instantiates the concept C.
Examples for triples corresponding to conceptual and relational assertions, using
OSMO (Sect. 3.3) and VOV (Chap. 4), would be the following rendering of “ex:D
is a dipole moment vector and its value is zero:”
ex:D
a
vov:electric_dipole_moment;
vov:shares_value_with
osmo:ZERO_VECTOR_3D.
(3.2)
1 Dedicated description logics that were developed to formalize elementary datatype properties
(owl:DatatypeProperty) include DAML+OIL [5–7] and SHOQ(D) [8].
2 Elementary datatype properties (k, v) ∈ H (I ) are asserted as I kv in TTL, where the key k is an
owl:DatatypeProperty.