Artificial Intelligence frameworks should allow for ever more autonomous and general systems in contrast to very narrow and restricted (human pre-defined) domain systems, in analogy to how the brain works. Self-constructive Artificial Intelligence ($SCAI$) is one such possible framework. We herein propose that $SCAI$ is based on three principles of organization: self-growing, self-experimental and self-repairing. Self-growing: the ability to autonomously and incrementally construct structures and functionality as needed to solve encountered (sub)problems. Self-experimental: the ability to internally simulate, anticipate and take decisions based on these expectations. Self-repairing: the ability to autonomously re-construct a previously successful functionality or pattern of interaction lost from a possible sub-component failure (damage). To implement these principles of organization, a constructive architecture capable of evolving adaptive autonomous agents is required. We present Schema-based learning as one such architecture capable of incrementally constructing a myriad of internal models of three kinds: predictive schemas, dual (inverse models) schemas and goal schemas as they are necessary to autonomously develop increasing functionality. We claim that artificial systems, whether in the digital or in the physical world, can benefit very much form this constructive architecture and should be organized around these principles of organization. To illustrate the generality of the proposed framework, we include several test cases in structural adaptive navigation in artificial intelligence systems in Paper II of this series, and resilient robot motor control in Paper III of this series. Paper IV of this series will also include $SCAI$ for problem structural discovery in predictive Business Intelligence.