We present our use of Aristotle's square and its extensions (see [Beziau03], [Moretti04]) to formalize a pragmatic logic of scientific discovery. We provide an interpretation of the resulting hypercubic structure to frame the paraconsistent and paracomplete representation of the computation of a theoretical predictive model corroborated by experimentation. This activity of producing a predictive and explicative model is at the core of the scientific interactive process of publication, refutation, and model confrontation that occurs during the construction of a consensual theory by a community. Finally, we describe in a constructive way how this logic can be achieved by a hierarchical and modular community of auto-epistemic and adaptive agents, as in [Sallantin06].