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The aim of this work is to provide a family of qualitative theories forspatial change in general, and for motion of spatial scenes in particular. Toachieve this, we consider a spatio-temporalisation MTALC(Dx), of the well-knownALC(D) family of Description Logics (DLs) with a concrete domain: the MTALC(Dx)concepts are interpreted over infinite k-ary Sigma-trees, with the nodesstanding for time points, and Sigma including, additionally to its uses inclassical k-ary Sigma-trees, the description of the snapshot of an n-objectspatial scene of interest; the roles split into m+n immediate-successor(accessibility) relations, which are serial, irreflexive and antisymmetric, andof which m are general, not necessarily functional, the other n functional; theconcrete 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 objectsof the "followed" spatial scene, eventually at different time points of theinput trees. In order to capture the expressiveness of most modal temporallogics encountered in the literature, we introduce weakly cyclic TerminologicalBoxes (TBoxes) of MTALC(Dx), whose axioms capture the decreasing property ofmodal temporal operators. We show the important result that satisfiability ofan MTALC(Dx) concept with respect to a weakly cyclic TBox can be reduced to theemptiness problem of a Buchi weak alternating automaton augmented with spatialconstraints. In another work, complementary to this one, also submitted to thisconference, we thoroughly investigate Buchi automata augmented with spatialconstraints, and provide, in particular, a translation of an alternating into anondeterministic, and an effective decision procedure for the emptiness problemof the latter.

A spatio-temporalisation of ALC(D) and its translation into alternating automata augmented with spatial constraints