Bridging the gap between modal temporal logics and constraint-based QSR as an ALC(D) spatio-temporalisation with weakly cyclic TBoxes
<|reference_start|>Bridging the gap between modal temporal logics and constraint-based QSR as an ALC(D) spatio-temporalisation with weakly cyclic TBoxes: 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(D_x), of the well-known ALC(D) family of Description Logics (DLs) with a concrete domainan. In particular, the concrete domain D_x is generated by a qualitative spatial Relation Algebra (RA) x. We show the important result that satisfiability of an MTALC(D_x) 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.<|reference_end|>
@article{isli2003bridging,
    title={Bridging the gap between modal temporal logics and constraint-based QSR
  as an ALC(D) spatio-temporalisation with weakly cyclic TBoxes},
    author={Amar Isli},
    journal={arXiv preprint arXiv:cs/0307040},
    year={2003},
    number={Technical Report FBI-HH-M-311/02, Fachbereich Informatik,
  Universitaet Hamburg},
    archivePrefix={arXiv},
    eprint={cs/0307040},
    primaryClass={cs.AI cs.LO}
}