Bridging the gap between modal temporal logics and constraint-based QSR as an ALC(D) spatio-temporalisation with weakly cyclic TBoxes

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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 domainan. In particular, the concrete domain Dₓ is generated by a qualitative spatial Relation Algebra (RA) x. We show the important result that satisfiability of an MTALC(Dₓ) concept with respect to a weakly cyclic TBox is decidable in nondeterministic exponential time, by reducing it to the emptiness problem of a weak alternating automaton augmented with spatial constraints, which we show to remain decidable, although the accepting condition of a run involves, additionally to the standard case, consistency of a CSP (Constraint Satisfaction Problem) potentially infinite. The result provides an effective tableaux-like satisfiability procedure which is discussed.