E Pluribus Unum - Computational Creativity Research: Towards Creative Machines - page 171

dational ontology). Indeed, this idea has been further developed in Martinez et al.
[ 49 ].

9.3.2 Selecting the Blendoids: Optimality Principles

Assuming a common base ontology (computed or given) with appropriate base mor-
phism, there is typically still a large number of possible blendoids whenever some
kind of partiality is allowed. For example, even in the rather simple case of combining
House and Boat , allowing for blendoids which only partially maintain structure
(called non-primary blendoids in [ 23 ]), i.e., where any subset of the axioms may be
propagated to the resulting blendoid, the number of possible blendoids is of the order
of 1,000. Clearly, from an ontological viewpoint, the overwhelming majority of these
candidates will be rather meaningless. A ranking therefore needs to be applied on
the basis of specific ontological principles. In conceptual blending theory, a number
of optimality principles are given in an informal and heuristic style [ 14 ]. While
these provide useful guidelines for evaluating natural language blends, they do not
suggest a direct algorithmic implementation, as also analysed in Goguen and Harrell
[ 23 ], who in their prototype implementation only covered certain structural, logical
criteria. However, the importance of designing computational versions of optimality
principles was realised early on, and one such attempt may be found in the work of
Pereira and Cardoso [ 61 ], who proposed an implementation of the eight optimality
principles presented in Fauconnier and Turner [ 13 ] based on quantitative metrics
for their more lightweight logical formalisation of blending. Such metrics, though,
are not directly applicable to more expressive languages such as OWL or first-order
logic.
Moreover, the standard blending theory of Fauconnier and Turner [ 14 ] does not
assign types, which might make sense in the case of linguistic blends where type
information is often ignored. A typical example of a type mismatch in language
is the operation of personification , e.g., turning a boat into an 'inhabitant' of the
'boathouse'. However, in the case of blending in mathematics or ontology, this loss
of information is often rather unacceptable: on the contrary, a fine-grained control
of type or sort information may be of the utmost importance.

Optimality principles for ontological blending will be of two kinds:
(1) purely structural/logical principles : these will extend and refine the criteria as
given in Goguen and Harrell [ 23 ], namely degree of commutativity of the blend dia-
gram, type casting (preservation of taxonomical structure), degree of partiality (of
signature morphisms), and degree of axiom preservation . In the context of

,
typing needs to be replaced with preservation of specific axioms encoding the tax-
onomy.
(2) heuristic principles : these include introducing preference orders on morphisms
(an idea that Goguen [ 21 ] labelled 3

OWL

2 pushouts) reflecting their 'quality', e.g. mea-
sured in terms of degree of type violation; specific ontological principles, e.g. adher-

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