Theory - O4Top Ontology

Towards a General Ontology Theory (ONMA)

 Hierarchies:
As a foundation for ontological engineering, we provide the minimal ontology blueprint called O4Top as shown in Figure o4toptl2 as an implementable artifact in the sense of [HeMa2004]. We do not consider O4Top as a top-level ontology, but as a blueprint according to which ontologies should be constructed. For the visualization of knowledge graphs called OntoGraphs we use the symbols and naming conventions which have been introduced by Bense in [Bens2014]. The different colors and shapes for the various ontology elements enable modelers to understand the models more quickly and help him to identify and correct errors, and to reduce developing costs. Compared to other top-level ontologies, the O4Top ontology blueprint contains as a minimal set of ontological elements ^Class, ◊ObjectProperty, .DataProperty, and »^Resource. Having »^Resource as the most generic modeling entity was motivated by Allemang et al. who state in [AlHe2020], page 37: “a resource can be anything that someone might want to talk about”. Classes correspond to formal concepts in Formal Concept Analysis as we will discuss in detail below. Object Properties (OP) represent binary relationship types between classes. A particular is the instantiation (see section Instantiation) of a class and bound to the class with the binary relationship type »pof (particularOf). A relator is the instantiation of a binary relationship type or, in the case of n-ary relations, the binding of one particular to n other particulars.

For completeness, we mention the »^UResource and the additional types of data properties ..MetadataProperty, .ΔTransparentDataProperty, and .^UniversalsDataProperty for streamling conceptual modeling and Meta-Level Modeling (MLM), which are explained in the author‘s article [Bens2023a] and are not relevant to the discussion in this paper.

Fig. O4TopTL: O4Top Ontology Blueprint
For an ontology O, with C we denote its set of classes, with A its set of Data Properties (DP), with R its set of Object Properties (OP), with E (Extension) its set of class particulars, and with EE = E X E its set of object property instances. The OPs ◊subClassOf, ◊subDpOf and ◊subOpOf are acyclic, transitive relationship types and form hierarchies using the order relations ≤◊, ≤∧, and, ≤.:
  • x ≤∧ y ⇔ ∃x, y ∈ C: (x, »subClassOf, y) ∈ KG ∨ (y, »hasSubClass, x) ∈ KG
  • x ≤◊ y ⇔ ∃x, y ∈ R: (x, »subOpOf, y) ∈ KG ∨ (y, »hasOp, x) ∈ KG
  • x ≤. y ⇔ ∃x, y ∈ A: (x, »subDpOf, y) ∈ KG ∨ (y, »hasDp, x) ∈ KG
  • The pair C∴ = (C, ≤∧) is the class hierarchy structure where for each c ∈ C the subclass hierarchy of c is defined as ∴c. Its top element is sup(∴c) = c and sup(C) = ^Class. The set of super classes of c is defined as ∵c.
  • The pair R∴ = (R, ≤◊) is the hierarchy structure of object properties where for each r ∈ R the sub OP hierarchy of r is defined as ∴r. Its top element is sup(∴r) = r and sup(R) = ◊ObjectProperty. The set of super OPs of r is defined as ∵r.
  • For data properties the pair A∴ = (A, ≤.) is the hierarchy structure of data properties where for each a ∈ A the sub DP hierarchy of a is defined as ∴a. Its top element is sup(∴a) = a and sup(A) = .DataProperty. The set of super DPs of a is defined as ∵a. E.g., .GivenName ≤. .PersonName ≤. .Name

Extension: deriver.app

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Source: taoke.de — Theory - O4Top Ontology.