Abstract
Image schemas are vital for embodied cognition. In addition to image schemas considering one object or the interplay between two objects, there are also some having a ternary nature and allowing for the definition of some form of betweenness, such as for instance the introduction of a goal in between a start- and endpoint of a path. Betweenness is a central notion both in cognitive and formal aspects of modeling concepts. For example, in conceptual spaces, an object in between two other objects belonging to some concept again belongs to that same concept, according to the convexity assumption. This kind of betweenness understood as a path-searching procedure allows for increasing the comprehensibility of the resulting in-between objects because of a better understanding of the creation and origin of those objects. This view can also be applied to the task of finding new, creative objects based on given ones, thus finding paths that are not the straightforward solution, that is, not within a given convex conceptual space. This offers a direct connection to the framework of conceptual blending which allows for a structured creation of a blend of two input objects. We show that blending can be interpreted as a betweenness relation and that this path-based view is helpful to allow for a different viewpoint on conceptual blending. We argue that conceptual blending defined in this way as betweenness fulfills basic betweenness axioms and is thus a viable betweenness relation. As a proof of concept, these considerations are applied to visual blending.