COINVENT: Towards a Computational Concept Invention Theory Marco Schorlemmer, 1 Alan Smaill, 2 Kai-Uwe K ¨ uhnberger, 3 Oliver Kutz, 4 and Simon Colton, 5 Emilios Cambouropoulos 6 and Alison Pease 7 1 Artificial Intelligence Research Institute, IIIA-CSIC, Spain 2 School of Informatics, The University of Edinburgh, UK 3 Institute of Cognitive Science, University of Osnabr¨ uck, Germany 4 Institute of Knowledge and Language Engineering, Otto-von-Guericke University Magdeburg, Germany 5 Department of Computing, Goldsmiths, University of London, UK 6 School of Music Studies, Aristotle University of Thessaloniki, Greece 7 School of Computing, University of Dundee, UK Abstract We aim to develop a computationally feasible, cognitively- inspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to de- scribing combinational creativity in a varied number of fields, has barely been used at all for implementing creative compu- tational systems, mainly due to the lack of sufficiently precise mathematical characterisations thereof. The model we will define will be based on Goguen’s proposal of a Unified Con- cept Theory, and will draw from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity. To validate our model, we will implement a proof of concept of an autonomous computational creative system that will be evaluated in two testbed scenarios: mathematical reasoning and melodic har- monisation. We envisage that the results of this project will be significant for gaining a deeper scientific understanding of creativity, for fostering the synergy between understand- ing and enhancing human creativity, and for developing new technologies for autonomous creative systems. Introduction Of the three forms of creativity put forward in (Boden 1990)—combinational, exploratory, and transformational— the most difficult to capture computationally turned out to be the combinational type (Boden 2009), i.e., when novel ideas (concepts, theories, solutions, works of art) are pro- duced through unfamiliar combinations of familiar ideas. Although generating novel ideas, or concepts, by combining old ones is not complicated in principle, the difficulty lies in doing this in a computationally tractable way, and in being able to recognise the value of newly invented concepts for better understanding a certain domain; even without it being specifically sought—i.e., by ‘serendipity’ (Boden 1990, p. 234), (Pease et al. 2013). To address this problem, we will concentrate on an im- portant development that has significantly influenced the current understanding of the general cognitive principles operating during creative thinking, namely Fauconnier and Turner’s theory of conceptual blending, also known as con- ceptual integration (Fauconnier and Turner 1998). Faucon- nier and Turner proposed conceptual blending as the fun- damental cognitive operation underlying much of every- Figure 1: ‘Houseboat’ blend, adapted from (Goguen and Harrell 2010) day thought and language, and modelled it as a process by which people subconsciously combine particular elements and their relations, of originally separate mental spaces, into a unified space, in which new elements and relations emerge, and new inferences can be drawn. For instance, a ‘house- boat’ or a ‘boathouse’ are not simply the intersection of the concepts of ‘house’ and ‘boat’. Instead, the concepts ‘house- boat’ and ‘boathouse’ selectively integrate different aspects of the source concepts in order to produce two new concepts, each with its own distinct internal structure (see Figure 1 for the ‘houseboat’ blend). The cognitive, psychological and neural basis of concep- tual blending has been extensively studied (Fauconnier and Turner 2003; Gibbs, Jr. 2000; Baron and Osherson 2011). Moreover, Fauconnier and Turner’s theory has been success- fully applied for describing existing blends of ideas and con- cepts in a varied number of fields, such as linguistics, mu-