A computational account of conceptual blending in basic mathematics

ASP, Amalgamation, and the Conceptual Blending Workflow

“…On top of the ASP-based implementation, we propose metrics to evaluate the quality of blends, based on the cognitive optimality principles by Fauconnier and Turner [4]. A number of researchers in the field of computational creativity have recognised the value of conceptual blending for building creative systems, and particular implementations of this cognitive theory have been proposed [18,15,16,6,8,3]. They are, however, mostly limited in the expressiveness of their representation language, and it is in most cases unclear how they deal with inconsistencies and how the generic space is computed.…”

On Cognitive Aspects of Human-Level Artificial Intelligence

“…The selection of formulae is again based on a heuristic component: Mappings in which substitutions can be reused get assigned a lower cost than isolated substitutions, leading to a preference for coherent over incoherent mappings. 2 Concerning applications of HDTP, for instance Guhe et al (2010) apply the framework in modeling a potential inductive analogy-based process for establishing the fundamental concepts of arithmetics, Guhe et al (2011) describe an account of a process blending different conceptualizations of number into new conceptualizations recognizing common features and combining distinct ones, and use HDTP for solving geometric analogies. Further successful and completely worked out application examples, among others, also can be found as part of this thesis in Chap.…”

Modeling semantic knowledge structures for creative problem solving: Studies on expressing concepts, categories, associations, goals and context

“…As opposed to other domains, like architecture, where abstractions relate to the current closure, abstractions in analytical problem solving relates to the problem goal. Analogies for similar problems are a powerful solving strategy as entire feature association sequences are revealed (Guhe et al, 2011). Analogies are used to find structural similarities between precedents and the current problem and then the unmatched parts represent the subrequirements to be solved.…”