  Previous research into the relation between ASP and classical logic has
identified at least two different ways in which the former extends the latter.
First, ASP program typically contain sets of rules that can be naturally
interpreted as inductive definitions, and the language FO(ID) has shown that
such inductive definitions can elegantly be added to classical logic in a
modular way. Second, there is of course also the well-known epistemic component
of ASP, which was mainly emphasized in the early papers on stable model
semantics. To investigate whether this kind of knowledge can also, and in a
similarly modular way, be added to classical logic, the language of Ordered
Epistemic Logic was presented in recent work. However, this logic views the
epistemic component as entirely separate from the inductive definition
component, thus ignoring any possible interplay between the two. In this paper,
we present a language that extends the inductive definition construct found in
FO(ID) with an epistemic component, making such interplay possible. The
eventual goal of this work is to discover whether it is really appropriate to
view the epistemic component and the inductive definition component of ASP as
two separate extensions of classical logic, or whether there is also something
of importance in the combination of the two.
