E Pluribus Unum - Computational Creativity Research: Towards Creative Machines - page 163

is important in order to generate meaningful blends. 2 The use that we might typically
make of ontological blending is situated somewhere in the middle: re-arrangement
and new combination of basic categories can be quite interesting, but has to be finely
controlled through corresponding interfaces, often regulated by or related to choices
found in foundational or upper ontologies so that basic categorial relationships are
maintained.
For all such cases, however, we can consider the formal mechanisms that support
specific blends that we explore with respect to their potential relevance and value
for understanding 'blending' phenomena in general. This will be the main purpose
of the current chapter. We will summarise some of the progress that has been made
in recent years towards adopting the fruitful idea of conceptual blending in a theo-
retically well-understood and computationally supported formal model for concept
invention, focusing in particular on ontology languages. Here we elaborate on ideas
first introduced in Hois et al. [ 32 ], with detailed technical definitions given in Kutz
et al. [ 42 ]. More specifically, we:

• briefly characterise the kinds of creativity that have been considered hitherto in

the areas of blends, metaphors and related operations where structured mappings
or analogies are relied upon;

• sketch the logical analysis of conceptual blending in terms of blending diagrams

and colimits, as originally proposed by Joseph Goguen, and give an abstract defin-
ition of ontological blendoids capturing the basic intuitions of conceptual blending
in the ontological setting;

•

sketch a formal meta-language, namely the distributed ontology language DOL ,
that is capable of declaratively specifying blending diagrams in a variety of ontol-
ogy languages. This provides a structured approach to ontology languages and
blending and combines the simplicity and good tool support for languages such
as

3 with the more complex blending facilities of OBJ3 [ 24 ]orHaskell[ 36 ];
DOL also facilitates the specification of a range of variations of the basic blending
technique;

OWL

• discuss the capabilities of the Ontohub/ ecosystem with regard to collabora-

tively managing, creating, and displaying blended concepts, ontological theories,
and entire blending diagrams; this includes an investigation of the evaluation prob-
lem in blending, together with a discussion of structural optimality principles and
current automated reasoning support.

Hets

We close with a discussion of open problems and future work.

2 For instance when creating the theory of transfinite cardinals by blending the perfective aspect of
counting up to any fixed finite number with the imperfective aspect of 'endless counting' [ 58 ].
3 With '

OWL ' we refer to OWL 2 DL, see http://www.w3.org/TR/owl2-overview/ .