Andrew Assad and Norman Packard - Emergence (1992)
This chapter marks a watershed as the first from the perspective of computational modelling and artificial life. It's very brief, with its prime contributions being an outline of a couple of key characteristics of (epistemic-computational) emergence plus a useful bibliography from the field: Bergson, Langton, Kauffman, Pattee, Cariani (who, I would argue, is by far the most glaring omission as an author in this book).
Assad and Packard offer a yardstick scale of emergence, based on mechanical deducibility of behaviours:
Non-emergent: Behavior is immediately deducible upon inspection of the specification or rules generating it
Weakly emergent: Behavior is deducible in hindsight from the specification after observing the behavior
Strongly emergent: Behavior is deducible in theory, but its elucidation is prohibitively difficult
Maximally emergent: Behavior is impossible to deduce from the specification.
It strikes me that, if we are to maintain an axiom of fundamental reducibility, the "maximally emergent" pole must be approached asymptotically (ie, cannot be attained) as "impossible to deduce" implies that the base-level laws are insufficient to explain the properties - so we have smuggled in (in Bedau's terminology) strong emergence.
More interestingly, they suggest a hierarchy of subsets of the types of thing that emerge from a substrate: structure (in space-time or symbolic space); from which arises computation (information-processing capabilities); from which then arises functionality (towards beneficial objectives). This seems like an elegant and useful formulation which can clearly be see when looking back at the emergence of complexity described in the previous chapter.