Theory - Related Work

In this section we describe selected issues from different areas of ontology engineering, that we consider important for a theory about ontologies. We will return to some of these issues in the Theory - Results. Guarino discusses in [Guar1998] “A Minimal Ontology of Universals". We will propose our own ontology of universals and compare it to Guarino‘s. Suchanek et al. present in [SuKa2007] with YAGO “a large ontology with high coverage and precision. ... YAGO is based on a clean logical model with a decidable consistency”. To this end, they provide a rewriting system with a small set of rules. The rules are based on the relations type, subClassOf, domain, range and subRelationOf, and the classes entity, class, and relation.

Guizzardi et al. discuss in [GuBe2021] a large set of axioms for formalizing UFO in first-order modal logic. In comparison, we will investigate how properties of universals can be used to define additional axioms for the subsumption of classes and relationship types. Herre et al. ([HeHe2006a], page 12) discuss axioms for their Abstract Top Level (ATO) of GFO. We will use these axioms implicitly to define our axioms for sets of elements (items) of universals and particulars of ontologies. The early paper by Noy and McGuiness [NoMG2000], page 18, raises the question “An instance or a class?”. We want to find an answer to this question by looking at the abstraction levels of ontologies and through modeling guidelines. The book by Arp, Smith and Spear on [ArSm2015], page 145 ff, contains “Some Examples of Axioms”. For example, they state that “Something is a universal if it is instantiated by something”. On page 13 they explain that universals are “repeatable” while particulars are not. We think it would be worthwhile to provide an extended formal definition of what instantiation is. Also, the WonderWeb deliverable [MaBo2003] by Masolo et al. contains many ontology definitions and an extensive axiom system. We use the basic formalisms of Formal Concept Analysis (FCA) described by Uta Priss [Pris1998], by Bernhard Ganter [Gant2000], and by Lübbert and Zeh [LuZe2021] to specify axioms for subsumption. We think that none of the references discusses subsumption to the extent that we think it is necessary to capture order relations of universals.

Guarino in [Guar1998] introduces the notion of an Identity Criterion (IC), which allows to identify the identity or non-identity of two knowledge entities based on their properties and he states that “ICs for classes corresponding to natural language words are difficult or impossible to express". It seems important to us to investigate how the IC criterion can be extended to classes in general.