As a novel type of semi-discrete dynamical systems, Boolean delay equations (BDEs) are models with Boolean-valued variables that evolve in continuous time. Since at the present time, most phenomena are too complex to be modeled by partial differential equations (as continuous infinite-dimensional systems), BDEs are intended as a (heuristic) first step on the challenging road to further understanding and modeling them. For instance, one can mention complex problems in fluid dynamics, climate dynamics, solid-earth geophysics, and many problems elsewhere in natural sciences where much of the discourse is still conceptual.
Hopes and promises
Although in recent centuries, differential equations (both ordinary and partial) have extensively served as quantitative models of vast categories of problems, by the recent greedy and rapid burst of complexities everywhere, the gap between quantitative and qualitative modeling and reasoning techniques is widening. BDEs offer a formal mathematical language that is promising to help bridge that gap.