In: A.M. Olteteanu, Z. Falomir (eds.): Proceedings of ProSocrates 2017: Symposium on Problem-solving, Creativity and Spatial Reasoning in Cognitive Systems, at Delmenhorst, Germany, July 2017, published at http://ceur-ws.org
Cognitive scientists of the embodied cognition tradition have been providing evidence that a large part of our creative reasoning and problemsolving processes are carried out by means of conceptual metaphor and blending, grounded on our bodily experience with the world. In this talk I shall aim at eshing out a mathematical model that has been proposed in the last decades for expressing and exploring conceptual metaphor and blending with greater precision than has previously been done. In particular, I shall focus on the notion of aptness of a metaphor or blend and on the validity of metaphorical entailment. Towards this end, I shall use a generalisation of the category-theoretic notion of colimit for modelling conceptual metaphor and blending in combination with the idea of reasoning at a distance as modelled in the BarwiseSeligman theory of information ow. I shall illustrate the adequacy of the proposed model with an example of creative reasoning about space and time for solving a classical brain-teaser. Furthermore, I shall argue for the potential applicability of such mathematical model for ontology engineering, computational creativity, and problem-solving in general. Copyright c by the paper's authors. Copying permitted for private and academic purposes.