To facilitate the top-level ontology alignment of the VIMMP ontologies, a module with a scaled-down EMMO in TTL format is included,
EMMO version 1 simplified (EMMO1s), which at the present stage (version 1.0.4) is based on EMMO version 1.0.0 alpha 2 (April 2020). EMMO1s provides user-friendly IRIs for EMMO concepts,
2 retaining the labels, e.g. the IRI of the EMMO concept with
rdfs:label “Semiosis” is given in the original EMMO as
emmo-semiotics:EMMO_008fd3b2_ 4013_451f_8827_52bceab11841. For these entities, EMMO1s specifies aliases that can be accessed directly through the label, such as
emmo1s:Semiosis. In the interest of notational clarity, to indicate the origin of the concept definitions and the respective EMMO modules, these entities will here be denoted by the EMMO prefix followed by the EMMO1s suffix, e.g. by
emmo-semiotics:Semiosis, even though internally, for VIMMP, it is actually
emmo1s:Semiosis.
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 (
\( \Box \)) and possibility (
\( \Diamond \)), 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
, “
: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”
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
with
\( K _ I \,\mathsf {C}\, I \) 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”
Relations from the EMMO are mereological (or, more properly, mereotopological [
10,
18,
19]), represented here at the highest level by proper parthood
$$\begin{aligned} \mathsf {P}~ \equiv ~ \textsf {{viprs:is\_proper\_part\_of}} ~ \equiv ~ {\textsf {{emmo-mereotopology:hasProperPart}}}^ - , \end{aligned}$$
(5.7)
and semiotic, represented at the highest level by the sign-to-object reference relation
6
cf. Expressions (
3.6) and (
3.7). To facilitate ontology alignment, which is discussed in Sects.
5.3 and
5.4, VIPRS also contains
mereosemiotic chain products of these fundamental relations, i.e. elements of the free semigroup
\(\mathbf {R}_\mathrm {ms}^+\) over
\(\mathbf {R}_\mathrm {ms}= \{\mathsf {P}, \mathsf {S}, {\mathsf {P}}^ - , {\mathsf {S}}^ - \}\), with the product defined by concatenation. The mereosemiotic relations for which there is an explicit definition in VIPRS are limited to
\(\mathbf {R}_\mathrm {ms}\, \cup \, \mathbf {R}_\mathrm {ms}^2 \, \cup \, \mathbf {R}_\mathrm {ms}^3\), i.e. relations generated by a sequence of up to three fundamental relations which are not redundant (
\(\mathsf {P}\circ \,\mathsf {P}\) and its inverse),
7 complete (or almost complete), i.e. relating everything to everything, except possibly for a single “universe” entity,
8 as it is the case for
\(\mathsf {P}\circ {\mathsf {P}}^ - \), or consist of three elements from the same category, e.g.
\({\mathsf {S}}^ - \circ \,\mathsf {S}\,\circ \,{\mathsf {S}}^ - \) is excluded, because all three constituent elements are semiotic. In the nomenclature employed by VIPRS, the IRI elements
ip,
hp,
is and
hs stand for “is proper part,” “has proper part,” “is sign” and “has sign,” respectively. Accordingly, the binary chain relations include
while the ternary chain relations include
With minor exceptions, datatype properties (
owl:DatatypeProperty) are absent from the EMMO [
9]; by the domain ontologies, however, datatype properties are amply employed to associate objects with textual (
xs:string), numerical (
xs:decimal) attributes and
xs:boolean flags. Figure
5.4 visualizes the hierarchy of
top-level datatype properties introduced in VIPRS. At the highest level, VIPRS categorizes datatype properties according to their role:
-
Identification of an object is positioned below viprs:has_identifier; examples include otras:has_topic_code, which maps a materials modelling topic (otras:mm_topic) from OTRAS to a four-digit code. Each topic code uniquely corresponds to one topic, and its purpose is identification.
-
Where an elementary-datatype entry is the content (or part of the content) of an object, datatype properties below
viprs:has_content are used, e.g. this applies to textual or numerical content of MODA from entries (in OSMO, aspects), corresponding to
osmo:has_aspect_text_content and
osmo:has_aspect_text_content [
20,
21], cf. Section
3.3.
-
Elementary descriptors, specifiers and similar metadata that provide additional, contingent information on objects, viprs:has_specifier is used, e.g. otras:has_cited_video_duration_seconds points to a metadata item on the length of a video. This contributes to our knowledge about the video by specification, while it does not permit its identification; moreover, the video duration is information about the video content, but it is not itself the content. Therefore, otras:has_cited_video_duration_seconds \( \sqsubseteq \) viprs:has_specifier.