E Pluribus Unum - Computational Creativity Research: Towards Creative Machines - page 169

Fig. 9.3 The basic
integration network for
blending: concepts in the base
ontology are first refined to
concepts in the input
ontologies and then
selectively blended into the
blendoid

Blendoid

B

Input 1

blendoid morphisms

Input 2

O1 O2

base morphisms

Base Ontology

base ontologies , and where a second distinguished set of nodes I ={ I j | j ∈ J }ↂ

| D | are called input ontologies , and where the theory morphisms μ ij : B i ₒ I j

from base ontologies to input ontologies are called the base morphisms .
If there are exactly two inputs I 1 , I 2 , and precisely one base B ∈ B and two base

μ k : ₒ = ,

morphisms B I k , k 1 2, the diagram D is called classical and has the

B

shape of a 'V'. In this case, is also called the tertium comparationis .

Figure 9.3 illustrates the basic, classical case of an ontological blending diagram.
The lower part of the diagram shows the base space (tertium), i.e. the common
generalisation of the two input spaces, which is connected to these via total (theory)
morphisms, the base morphisms. The newly invented concept is at the top of this
diagram, and is computed from the base diagram via a colimit. More precisely, any
consistent subset of the colimit of the base diagram may be seen as a newly invented
concept, a blendoid . 5 Note that, in general, ontological blending can deal with more
than one base and two input ontologies, and in particular, the sets of input and base
nodes need not exhaust the nodes participating in a base diagram. We will further
discuss this and give some examples in Sect. 9.4.2 .

9.3.1 Computing the Tertium Comparationis

To find candidates for base ontologies that could serve for the generation of onto-
logical blendoids, much more shared semantic structure is required than the sur-
face similarities that statistical term alignment approaches rely on (e.g., [ 11 ]). The
common structural properties of the input ontologies that are encoded in the base
ontology are typically of a more abstract nature. The standard example here relies

5 A technically more precise definition of this notion is given in Kutz et al. [ 42 ]. Note also that our
usage of the term 'blendoid' does not coincide with the (non-primary) blendoids defined in Goguen
and Harrell [ 23 ].