76
5 Applications of the Metadata Standards
While the EMMO can be used to describe materials and models as such, statements
on necessity and possibility anchored in modal logic are metaontological, i.e. beyond
the ontology, from the point of view of the EMMO [9], e.g. within the framework
of the EMMO, an event can be described as a physical process, but the statement
that “this process can possibly occur, but it will not necessarily occur” cannot be
expressed. The present domain ontologies, however, make ample use of relations
that are ultimately modal to specify capabilities (it is possible that :X will be used to
do :Y) or requirements (if is necessary that if :X occurs, :Y also occurs).
To provide a top-level structure for modal relations, VIPRS includes modal
squares of opposition,
4 cf. Fig. 5.3, by which the presence of individuals in a knowledge base can be associated with statements on whether their occurrence is possible,
necessary, factual or fictional [16]. The modal operators can be given a variety of
interpretations, depending on the precise use that is made of the ideas of necessity
() and possibility (♦), respectively [17]; similarly, the definition of “occurrence”
depends on the use that is made of the ontology and may depend on context—VIPRS
accepts this ambiguity in order to be applicable to diverse types of knowledge bases
and infrastructures. The term “to occur” in ♦(occ[:X]), “:X may occur,” and similar,
is employed to refer to the (possible or necessary) appearance of an individual :X in
a certain type of environment, e.g. as an element of a valid simulation workflow. On
this basis, relations concerning the possible or necessary co-occurrence of multiple
individuals are defined, e.g. viprs:n_loc_or_rnoc (and others following the same pattern, cf. Fig. 5.3), where the IRI is to be read as “necessarily, the left occurs or the
right does not occur”
I viprs:n_loc_or_rnoc J ≡ (occ[I ] ∨ ¬occ[J ]) ≡ (occ[J ] → occ[I ]).
(5.4)
cf. Fig. 5.3. Thereby, “occurrence” (by appearing in a certain type of environment)
is not the same as “existence,” i.e. presence in a knowledge base. It is in this sense
that VIPRS can be employed as an implementation of possible-world semantics,
Kripke semantics and/or ontological Meinongianism [16], even though it does not
necessarily presuppose the use of any of these paradigms. The conceptualization
relation
C S viprs:n_loc_or_rnoc,
(5.5)
with K I C I to be read as “K I conceptualizes I ,” relates a more (or equally
5 ) generic
individual to a more (or equally) specific one; it is used to introduce a step of
abstraction into the modal co-occurrence relations, e.g. “necessarily, the left occurs
conceptual-or the right does not occur”
4 A square of opposition, going back to Aristotle, is a diagram containing four related statements,
concepts or predicates labelled A for universal affirmation (“all”), E for universal negation (“no”),
I for existential affirmation (“some”) and O for existential negation (“not all”); cf. Westerståhl [14,
15] for a variety of applications.
5 C is reflexive, ∀K ∈ I : K C K .
5 Applications of the Metadata Standards
While the EMMO can be used to describe materials and models as such, statements
on necessity and possibility anchored in modal logic are metaontological, i.e. beyond
the ontology, from the point of view of the EMMO [9], e.g. within the framework
of the EMMO, an event can be described as a physical process, but the statement
that “this process can possibly occur, but it will not necessarily occur” cannot be
expressed. The present domain ontologies, however, make ample use of relations
that are ultimately modal to specify capabilities (it is possible that :X will be used to
do :Y) or requirements (if is necessary that if :X occurs, :Y also occurs).
To provide a top-level structure for modal relations, VIPRS includes modal
squares of opposition,
4 cf. Fig. 5.3, by which the presence of individuals in a knowledge base can be associated with statements on whether their occurrence is possible,
necessary, factual or fictional [16]. The modal operators can be given a variety of
interpretations, depending on the precise use that is made of the ideas of necessity
() and possibility (♦), respectively [17]; similarly, the definition of “occurrence”
depends on the use that is made of the ontology and may depend on context—VIPRS
accepts this ambiguity in order to be applicable to diverse types of knowledge bases
and infrastructures. The term “to occur” in ♦(occ[:X]), “:X may occur,” and similar,
is employed to refer to the (possible or necessary) appearance of an individual :X in
a certain type of environment, e.g. as an element of a valid simulation workflow. On
this basis, relations concerning the possible or necessary co-occurrence of multiple
individuals are defined, e.g. viprs:n_loc_or_rnoc (and others following the same pattern, cf. Fig. 5.3), where the IRI is to be read as “necessarily, the left occurs or the
right does not occur”
I viprs:n_loc_or_rnoc J ≡ (occ[I ] ∨ ¬occ[J ]) ≡ (occ[J ] → occ[I ]).
(5.4)
cf. Fig. 5.3. Thereby, “occurrence” (by appearing in a certain type of environment)
is not the same as “existence,” i.e. presence in a knowledge base. It is in this sense
that VIPRS can be employed as an implementation of possible-world semantics,
Kripke semantics and/or ontological Meinongianism [16], even though it does not
necessarily presuppose the use of any of these paradigms. The conceptualization
relation
C S viprs:n_loc_or_rnoc,
(5.5)
with K I C I to be read as “K I conceptualizes I ,” relates a more (or equally
5 ) generic
individual to a more (or equally) specific one; it is used to introduce a step of
abstraction into the modal co-occurrence relations, e.g. “necessarily, the left occurs
conceptual-or the right does not occur”
4 A square of opposition, going back to Aristotle, is a diagram containing four related statements,
concepts or predicates labelled A for universal affirmation (“all”), E for universal negation (“no”),
I for existential affirmation (“some”) and O for existential negation (“not all”); cf. Westerståhl [14,
15] for a variety of applications.
5 C is reflexive, ∀K ∈ I : K C K .