Chapter 3
Marketplace-Level Domain Ontologies
3.1 Ontologies and Formal Notation
This chapter and the subsequent two chapters present ontologies from the VIMMP
project, their relation to other work (including other ontologies) and examples for
their use in practice. While this is not a theoretical work, we begin with a brief introduction to the usual formal notation, on the one hand to support certain arguments,
e.g. concerning ontology alignment, and on the other hand to make related literature,
where such notation is employed, more accessible. For a dedicated presentation of
Description Logic (DL), the logical formalism is employed for ontologies from the
point of view of theoretical computer science, which exists in a great variety of versions, the reader is referred to Baader et al. [1] as well as Schneider and Šimkus [2];
the present work partly adheres to the notation used by the DL community, but deviates from it on occasion. Formal ontology also has philosophical aspects—which
is natural given its origin in that discipline—that we do not address here; for this
purpose, the reader is pointed to Berto and Plebani [3], whereas an easily accessible
introduction to semantic technology from the point of view of ontology engineering
is provided by Allemang and Hendler [4].
The formal representation of what is known in any given context is called a
knowledge base; it is defined as a pair K = (T , A), where T is the ontology and
A is the scenario. In the DL community, T is called the TBox (terminological box)
and A is called the ABox (assertional box)—hence the notation—while in model
theory, A is referred to as a model. The ontology describes how we formalize a
domain of knowledge, in general, irrespective of the circumstances, whereas the
scenario contains statements that are contingent; depending on context this may
be the meaning of the content of a database or a file. The ontology is given by
a tuple T = (C, R, ,), where C is a set of elementary concept (also “class” or
“universal”) names, R is a set of elementary relation (also “role”) names, and
is a set of rules (also “general inclusions” or “axioms”). The scenario, in turn, is a
tuple A = (I, A c , A r , H ), where I is a set of individual (also “object” or “particular”)
© The Author(s) 2021
M. Horsch et al., Data Technology in Materials Modelling,
SpringerBriefs in Applied Sciences and Technology,
https://doi.org/10.1007/978-3-030-68597-3_3
31
Marketplace-Level Domain Ontologies
3.1 Ontologies and Formal Notation
This chapter and the subsequent two chapters present ontologies from the VIMMP
project, their relation to other work (including other ontologies) and examples for
their use in practice. While this is not a theoretical work, we begin with a brief introduction to the usual formal notation, on the one hand to support certain arguments,
e.g. concerning ontology alignment, and on the other hand to make related literature,
where such notation is employed, more accessible. For a dedicated presentation of
Description Logic (DL), the logical formalism is employed for ontologies from the
point of view of theoretical computer science, which exists in a great variety of versions, the reader is referred to Baader et al. [1] as well as Schneider and Šimkus [2];
the present work partly adheres to the notation used by the DL community, but deviates from it on occasion. Formal ontology also has philosophical aspects—which
is natural given its origin in that discipline—that we do not address here; for this
purpose, the reader is pointed to Berto and Plebani [3], whereas an easily accessible
introduction to semantic technology from the point of view of ontology engineering
is provided by Allemang and Hendler [4].
The formal representation of what is known in any given context is called a
knowledge base; it is defined as a pair K = (T , A), where T is the ontology and
A is the scenario. In the DL community, T is called the TBox (terminological box)
and A is called the ABox (assertional box)—hence the notation—while in model
theory, A is referred to as a model. The ontology describes how we formalize a
domain of knowledge, in general, irrespective of the circumstances, whereas the
scenario contains statements that are contingent; depending on context this may
be the meaning of the content of a database or a file. The ontology is given by
a tuple T = (C, R, ,), where C is a set of elementary concept (also “class” or
“universal”) names, R is a set of elementary relation (also “role”) names, and
is a set of rules (also “general inclusions” or “axioms”). The scenario, in turn, is a
tuple A = (I, A c , A r , H ), where I is a set of individual (also “object” or “particular”)
© The Author(s) 2021
M. Horsch et al., Data Technology in Materials Modelling,
SpringerBriefs in Applied Sciences and Technology,
https://doi.org/10.1007/978-3-030-68597-3_3
31