Modeling Through Human-Computer Interactions and Mathematical Discourse

The project ϕ-calculus, or philosophical calculus, concerns the research on a rational framework that, in the context of interactive design, can be source and guarantee of the adequacy of a theory to its application context. The framework focus (i) on the process of theory construction by an Artificial Agent under the supervision of Human Agent(s), (ii) on the knowledge evolving through this process and (iii) on the adequacy of experiments with respect to knowledge represented in a given moment. The project is being developed in three different perspectives, namely, conceptual, formal, and experimental. Conceptual work consists on examining how experiments may point out the need for revising a theory and how to use experiments in order to perform revision. Formal work proposes formalisms to apprehend the dynamics on the process of theory construction, as well as building languages that may, from the one hand, facilitate interaction and, on the other hand, be adapted for computing. Experiments have been carried out in domains like e-commerce and Human Learning. In this paper, we focus on conceptual and formal aspects of the work on ϕ-calculus in its current state.