E Pluribus Unum - Computational Creativity Research: Towards Creative Machines - page 175

with the ingredients as above. The simplest (and still fully general) form is just
combine D
where D is a diagram. The semantics of combinations is the colimit of the generated
diagram. A colimit involves both pasting together (technically: disjoint union) and
identification of shared parts (technically: a quotient).
In our example, houseboat can be defined by the colimit based on the interpreta-
tions. To make the result easier to read, some of the classes are renamed:
ontology house_boat =
combine boat_habitable, house_floating
with Object ₒ HouseBoat , Site ₒ BodyOfWater
This captures formally the informal description of the house boat blend as often

given in examples of blending diagrams. Our specification then allows us to go
further and derive both consequences of this and other blends. Here Ontohub is
able to compute the colimit, which combines both the

+

ontologies
along the morphism. The colimit inherits the axioms of the input ontologies and the
base with appropriate identifications of symbols. Here we just show the generated
declaration of the blended class Houseboat :
Class : HouseBoat
SubClassOf :Artifact
and has_function some MeansOfTransportation
and has_function some Floating
and is_navigated_by some Agent
SubClassOf :Artifact
and is_located_on some BodyOfWater
and has_function some ServeAsResidence
In the case of blending

boat and house

, the crucial part in this
blend is to view a boat as a kind of “person” that lives in a house. The two ontologies
House and Boat presented above can be blended by selecting a base, which here
provides (among others) a class Agent , and two interpretations, mapping Agent to
Boat and Person , respectively. Therefore, the second base ontology only differs
from the first by replacing the class Agent by Person and two additional classes,
namely Object and Site .
ontology base1 =
Class :Artifact

boat and house to boathouse

[...] Class : Agent

end
In this way, we let a boat play the role of a person (that inhabits a house). 10

interpretation boat_personification :
base1 to Boat =
Agent

ₒ

Boat

10 Compared to [ 23 ], the advantage of our formulation is that no projections (“retracts”) from a
supersort to a subsort are needed. Instead, we can carefully select which parts of the theory of houses
and their inhabitants are instantiated with boats.