in scientific literature. Recent research covers its implications, practical applications, and its new developments. In this chapter the most recent formulations and the fundamental principles of the C-K design theory are provided without necessarily giving the details of the formalisms applied in this theory. 1.1.4.1. Origins and intuitive motivation The expectations to the C-K design theory are fivefold: • From the point of view of contemporary innovation challenges: A theory that is able to address design issues that can't be addressed with traditional problem solving and optimization methods, such as "the design of new usages for emerging technologies", "the design of products/services on very open briefs" (e.g. 'smart mobility'), "the design under very strong constraints" (e.g. 'zero energy', 'frugal innovation', etc.). • From the point of view of designing professions: Providing a "unified design theory", similarly useful for all kind of designing professions (e.g. industrial design, engineering design, architectural design,…) • From the point of view of formalisms: A formal model that accounts for "radical creativity", i.e. with strong generativity 1 • From the point of view of methods: A theory that creates and supports methods for the process of so-called 'inventing' or 'discovering' (and actually designing) new functional requirements and the extension of design parameters. • From the cognitive point of view: A theory and related methods for overcoming fixations 2 To give an intuitive motivation of the C-K design theory, one can keep in mind that the theory focuses on the issue of characterizing a design task, its initial point, usually called "brief" or "program" or "specifications": Contrary to "mapping based" design theories (such as programming, problem solving, optimizing, all derived from Simonian theory of design 3), that tend to clarify the initial task to design inside a given mapping, the C-K design theory seeks to preserve the ambiguity, equivocality, incompleteness or fuzziness of the initial brief, precisely because these features will enable to regenerate the mapping itself. The C-K design theory hence models the design of a desirable but partially unknown 'object', which is undecidable whilst applying initially available knowledge. This intuitive motivation raises critical formal issues: How to rigorously reason on a partially unknown object? How to account for the evolutions of the knowledge that needs to be generated and / or has to be extended through the design process? These issues are addressed in the C-K design theory, as it will be shown below. 1.1.4.2. Main definitions and properties The underlying principle of the C-K design theory is to model design as an interaction between two spaces, the space of concepts (C) and the space of knowledge (K), with the following definitions and implications (see also table 1.x): 1 Generativity is the capacity of a design theory to produce 'novel' solutions from a given knowledge background (see academic references in Le Masson et al. 2017). 2 Fixation (in design and creativity cognition) describes the fact that, in a design task, designers tend to explore only a limited set of alternatives. They are cognitively hindered to explore the whole set of imaginable alternatives (see academic references in Le Masson et al. 2017) 3 The Simonian Theory of Design, formulated by H. A. SIMON in the 1960ies, is based on search algorithms in complex combinatorial problem spaces (c.f. e.g [Simo-1997]).