  The aim of this work is to provide a family of qualitative theories for
spatial change in general, and for motion of spatial scenes in particular. To
achieve this, we consider a spatio-temporalisation MTALC(Dx), of the well-known
ALC(D) family of Description Logics (DLs) with a concrete domain: the MTALC(Dx)
concepts are interpreted over infinite k-ary Sigma-trees, with the nodes
standing for time points, and Sigma including, additionally to its uses in
classical k-ary Sigma-trees, the description of the snapshot of an n-object
spatial scene of interest; the roles split into m+n immediate-successor
(accessibility) relations, which are serial, irreflexive and antisymmetric, and
of which m are general, not necessarily functional, the other n functional; the
concrete domain Dx is generated by an RCC8-like spatial Relation Algebra (RA)
x, and is used to guide the change by imposing spatial constraints on objects
of the "followed" spatial scene, eventually at different time points of the
input trees. In order to capture the expressiveness of most modal temporal
logics encountered in the literature, we introduce weakly cyclic Terminological
Boxes (TBoxes) of MTALC(Dx), whose axioms capture the decreasing property of
modal temporal operators. We show the important result that satisfiability of
an MTALC(Dx) concept with respect to a weakly cyclic TBox can be reduced to the
emptiness problem of a Buchi weak alternating automaton augmented with spatial
constraints. In another work, complementary to this one, also submitted to this
conference, we thoroughly investigate Buchi automata augmented with spatial
constraints, and provide, in particular, a translation of an alternating into a
nondeterministic, and an effective decision procedure for the emptiness problem
of the latter.
