E Pluribus Unum - Computational Creativity Research: Towards Creative Machines - page 170

on image schemata , such as the notion of a container (see e.g. [ 36 ]). Thus, in partic-
ular, foundational ontologies can support such selections. In analogical reasoning,
'structure' is (partially) mapped from a source domain to a target domain [ 16 , 65 ].
Therefore, intuitively the operation of computing a base ontology can be seen as
a bi-directional search for analogy or generalisation into a base ontology together
with the corresponding mappings. Providing efficient means for finding a number of
suitable candidate generalisations is essential to making the entire blending process
computationally feasible. Consider the example of blending 'house' with 'boat' dis-
cussed in detail in Sect. 9.4.1 : even after fixing the base ontology itself, guessing the
right mappings into the input ontologies means guessing within a space of approx-
imately 1.4 billion signature morphisms. Three promising candidates for finding
generalisations are:
(1) Ontology intersection: Normann [ 57 ] has studied the automatisation of theory
interpretation search for formalised mathematics, implemented as part of the Hetero-
geneous Tool Set ( , see below). Kutz and Normann [ 45 ] applied these ideas to

ontologies by using the ontologies' axiomatisations for finding their shared structure.
Accidental naming of concept and role names is deliberately ignored and such names
are treated as arbitrary symbols (i.e., any concept may be matched with any other). By
computing mutual theory interpretations between the inputs, the method allows the
computation of a base ontology as an intersection of the input ontologies together with
corresponding theory morphisms. While this approach can be efficiently applied to
ontologies with non-trivial axiomatisations, lightweight ontologies are less applica-
ble, e.g., 'intersecting' a smaller taxonomy with a larger one clearly results in a huge
number of possible taxonomy matches [ 45 ]. In this case, the following techniques
are more appropriate.
(2) Structure-based ontology matching: matching and alignment approaches
are often restricted to find simple correspondences between atomic entities of the
ontology vocabulary. In contrast, work such as [ 63 , 73 ] focuses on defining a num-
ber of complex correspondence patterns that can be used together with standard
alignments in order to relate complex expressions between two input ontologies.
For instance, the 'Class by Attribute Type Pattern' may be employed to claim the
equivalence of the atomic concept PositiveReviewedPaper in ontology O 1 with
the complex concept

Hets

Positive of O 2 . Such an equivalence can be
taken as an axiom of the base ontology; note, however, that it could typically not be
found by intersecting the input ontologies. Giving such a library of design patterns
may be seen as a variation of the idea of using a library of image schemata.
(3) Analogical Reasoning: Heuristic-driven theory projection is a logic-based
technique for analogical reasoning that can be employed for the task of comput-
ing a common generalisation of input theories. Schwering et al. [ 65 ] establish an
analogical relation between a source theory and a target theory (both first-order) by
computing a common generalisation (called 'structural description'). They imple-
ment this by using anti-unification [ 62 ]. A typical example is to find a generalisation
(base ontology) formalising the structural commonalities between the Rutherford
atomic model and a model of the solar system. This process may be assisted by a
background knowledge base (in the ontological setting, a related domain or foun-

∃ hasEvaluation .