  Managing inputs that are novel, unknown, or out-of-distribution is critical
as an agent moves from the lab to the open world. Novelty-related problems
include being tolerant to novel perturbations of the normal input, detecting
when the input includes novel items, and adapting to novel inputs. While
significant research has been undertaken in these areas, a noticeable gap
exists in the lack of a formalized definition of novelty that transcends
problem domains. As a team of researchers spanning multiple research groups and
different domains, we have seen, first hand, the difficulties that arise from
ill-specified novelty problems, as well as inconsistent definitions and
terminology. Therefore, we present the first unified framework for formal
theories of novelty and use the framework to formally define a family of
novelty types. Our framework can be applied across a wide range of domains,
from symbolic AI to reinforcement learning, and beyond to open world image
recognition. Thus, it can be used to help kick-start new research efforts and
accelerate ongoing work on these important novelty-related problems. This
extended version of our AAAI 2021 paper included more details and examples in
multiple domains.
