  This paper presents a high-level conceptual framework to help orient the
discussion and implementation of open-endedness in evolutionary systems.
Drawing upon earlier work by Banzhaf et al., three different kinds of
open-endedness are identified: exploratory, expansive, and transformational.
These are characterised in terms of their relationship to the search space of
phenotypic behaviours. A formalism is introduced to describe three key
processes required for an evolutionary process: the generation of a phenotype
from a genetic description, the evaluation of that phenotype, and the
reproduction with variation of individuals according to their evaluation. The
distinction is made between intrinsic and extrinsic implementations of these
processes. A discussion then investigates how various interactions between
these processes, and their modes of implementation, can lead to open-endedness.
However, an important contribution of the paper is the demonstration that these
considerations relate to exploratory open-endedness only. Conditions for the
implementation of the more interesting kinds of open-endedness - expansive and
transformational - are also discussed, emphasizing factors such as multiple
domains of behaviour, transdomain bridges, and non-additive compositional
systems. These factors relate not to the generic evolutionary properties of
individuals and populations, but rather to the nature of the building blocks
out of which individual organisms are constructed, and the laws and properties
of the environment in which they exist. The paper ends with suggestions of how
the framework can be used to categorise and compare the open-ended evolutionary
potential of different systems, how it might guide the design of systems with
greater capacity for open-ended evolution, and how it might be further
improved.
