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A Decidable Spatial Generalization of Metric Interval Temporal Logic

By Davide Bresolin, Dario Della Monica, Angelo Montanari, Pietro Sala and Guido Sciavicco

Abstract

Temporal reasoning plays an important role in\ud artificial intelligence. Temporal logics provide a natural framework\ud for its formalization and implementation. A standard\ud way of enhancing the expressive power of temporal logics is\ud to replace their unidimensional domain by a multidimensional\ud one. In particular, such a dimensional increase can be exploited\ud to obtain spatial counterparts of temporal logics. Unfortunately,\ud it often involves a blow up in complexity, possibly losing\ud decidability. In this paper, we propose a spatial generalization\ud of the decidable metric interval temporal logic RPNL+INT,\ud called Directional Area Calculus (DAC). DAC features two\ud modalities, that respectively capture (possibly empty) rectangles\ud to the north and to the east of the current one, and\ud metric operators, to constrain the size of the current rectangle.\ud We prove the decidability of the satisfiability problem for\ud DAC, when interpreted over frames built on natural numbers,\ud and we analyze its complexity. In addition, we consider a\ud weakened version of DAC, called WDAC, which is expressive\ud enough to capture meaningful qualitative and quantitative\ud spatial properties and computationally better

Publisher: IEEE Computer Society
Year: 2010
DOI identifier: 10.1109/TIME.2010.22
OAI identifier: oai:iris.unife.it:11392/2326768
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