An Inductive Formalization of Self Reproduction in Dynamical Hierarchies
  Formalizing self reproduction in dynamical hierarchies is one of the
important problems in Artificial Life (AL) studies. We study, in this paper, an
inductively defined algebraic framework for self reproduction on macroscopic
organizational levels under dynamical system setting for simulated AL models
and explore some existential results. Starting with defining self reproduction
for atomic entities we define self reproduction with possible mutations on
higher organizational levels in terms of hierarchical sets and the
corresponding inductively defined `meta' - reactions. We introduce constraints
to distinguish a collection of entities from genuine cases of emergent
organizational structures.
