of RCC-8 formulas is consistent there exists a realization in any dimension, even when the regions are constrained to be (sets of) polytopes. For three- and higher dimensional space this is also true for internally connected regions. Using the canonical model we give algorithms for generating

preserves satisfiability. As a consequence, the known algorithms for reasoning in modal logics can be applied to qualitative spatial reasoning. Our results lay a formal foundation to previous work by Bennett, Nebel, Renz, and others on spatial reasoning in the RCC8 formalism. 1 Introduction An approach

hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 atomic binary relations and 13 feasible as well as jointly exhaustive relations

System through the DyKnow framework. The temporal reasoning is done in the Metric Temporal Logic and the spatial reasoning in the Region Connection Calculus RCC-8. Progression is used to evaluate spatio-temporal formulas over incrementally available streams of states. To handle incomplete information

Abstract—Causal processing of a signal’s samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problems of predict-ing future samples and causally interpolating deterministic sig-nals. We treat a rich variety of sampling mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an anti-aliasing filter and magnetic resonance imaging (MRI), which correspond respectively to the translation and modulation operators. From an abstract Hilbert-space viewpoint, such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, although our problems are deterministic by nature. In particular, we provide necessary and sufficient conditions on the sampling mechanism such that perfect prediction is possible. For cases where perfect prediction is impossible, we derive the predictor minimizing the prediction error. We also derive a causal interpo-lation method that best approximates the commonly used non-causal solution. Finally, we study when causal processing of the samples of a signal can be performed in a stable manner.

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