## Logical Representations for Automated Reasoning about Spatial Relationships (1997)

Citations: | 33 - 5 self |

### BibTeX

@TECHREPORT{Bennett97logicalrepresentations,

author = {Brandon Bennett},

title = {Logical Representations for Automated Reasoning about Spatial Relationships},

institution = {},

year = {1997}

}

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### Abstract

This thesis investigates logical representations for describing and reasoning about spatial situations. Previously proposed theories of spatial regions are investigated in some detail --- especially the 1st-order theory of Randell, Cui and Cohn (1992). The difficulty of achieving effective automated reasoning with these systems is observed. A new approach is presented, based on encoding spatial relations in formulae of 0-order (`propositional ') logics. It is proved that entailment, which is valid according to the standard semantics for these logics, is also valid with respect to the spatial interpretation. Consequently, well-known mechanisms for propositional reasoning can be applied to spatial reasoning. Specific encodings of topological relations into both the modal logic S4 and the intuitionistic propositional calculus are given. The complexity of reasoning using the intuitionistic representation is examined and a procedure is presented which is shown to be of O(n 3 ) complexity ...