  We introduce a new class of (dynamical) systems that inherently capture
cascading effects (viewed as consequential effects) and are naturally amenable
to combinations. We develop an axiomatic general theory around those systems,
and guide the endeavor towards an understanding of cascading failure. The
theory evolves as an interplay of lattices and fixed points, and its results
may be instantiated to commonly studied models of cascade effects.
  We characterize the systems through their fixed points, and equip them with
two operators. We uncover properties of the operators, and express global
systems through combinations of local systems. We enhance the theory with a
notion of failure, and understand the class of shocks inducing a system to
failure. We develop a notion of mu-rank to capture the energy of a system, and
understand the minimal amount of effort required to fail a system, termed
resilience. We deduce a dual notion of fragility and show that the combination
of systems sets a limit on the amount of fragility inherited.
