  Relational concept analysis (RCA) is an extension of formal concept analysis
allowing to deal with several related contexts simultaneously. It has been
designed for learning description logic theories from data and used within
various applications. A puzzling observation about RCA is that it returns a
single family of concept lattices although, when the data feature circular
dependencies, other solutions may be considered acceptable. The semantics of
RCA, provided in an operational way, does not shed light on this issue. In this
report, we define these acceptable solutions as those families of concept
lattices which belong to the space determined by the initial contexts
(well-formed), cannot scale new attributes (saturated), and refer only to
concepts of the family (self-supported). We adopt a functional view on the RCA
process by defining the space of well-formed solutions and two functions on
that space: one expansive and the other contractive. We show that the
acceptable solutions are the common fixed points of both functions. This is
achieved step-by-step by starting from a minimal version of RCA that considers
only one single context defined on a space of contexts and a space of lattices.
These spaces are then joined into a single space of context-lattice pairs,
which is further extended to a space of indexed families of context-lattice
pairs representing the objects manippulated by RCA. We show that RCA returns
the least element of the set of acceptable solutions. In addition, it is
possible to build dually an operation that generates its greatest element. The
set of acceptable solutions is a complete sublattice of the interval between
these two elements. Its structure and how the defined functions traverse it are
studied in detail.
