## Ontologies for Plane, Polygonal Mereotopology (1997)

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Citations: | 31 - 3 self |

### BibTeX

@MISC{Pratt97ontologiesfor,

author = {Ian Pratt and Oliver Lemon},

title = {Ontologies for Plane, Polygonal Mereotopology},

year = {1997}

}

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### Abstract

Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in 2-dimensional space. Our strategy is to define a mereotopological language together with a familiar, point-based interpretation. It is proposed that, to be practically useful, any alternative region-based spatial ontology must support the same sentences in our language as this familiar interpretation. This proposal has the merit of transforming a vague, open-ended question about ontologies for "practical" mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace.

### Citations

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(Show Context)
Citation Context ...old. A model A is said to be atomic if any n-tuple �� a in A satisfies a formula OE(��x) in A such that OE(��x) is complete in Th(A). Then we have the following standard result from Chang =-=and Keisler [10]-=-: Theorem 5.1 (Chang and Keisler: 2.3.4) A model is countable atomic if and only if it is prime. Our task, then, is to show that Q is atomic. The following results will also feature in the sequel. The... |

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(Show Context)
Citation Context ...reotopology has received attention from several research groups in AI, working with the loosely defined area of qualitative spatial reasoning, for example, Gotts, Gooday and Cohn [17], Asher and Vieu =-=[2]-=-, and Borgo, Guarino, and Masolo [6]. For a treatment of region-based topology in a general setting, see Roeper [31]. Motivations for these developments vary, and we do not intend to provide a compreh... |

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Citation Context .... If regions are first class entities and points are logical constructions based on them, then who knows what interesting new ways of considering spatial entities and relations there might be? Clarke =-=[11]-=-, [12], following an idea of Whitehead [39], sought to reconstruct mereotopology in terms of a primitive relation of connection holding between regions. Following this work, Biacino and Gerla [5] have... |

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Citation Context ...ork, Biacino and Gerla [5] have studied models of Clarke's theory. More recently, and partially as a response to debates concerning temporal reasoning and knowledge representation (for example, Allen =-=[1]-=-), Clarke's mereotopology has received attention from several research groups in AI, working with the loosely defined area of qualitative spatial reasoning, for example, Gotts, Gooday and Cohn [17], A... |

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Citation Context ...rom several research groups in AI, working with the loosely defined area of qualitative spatial reasoning, for example, Gotts, Gooday and Cohn [17], Asher and Vieu [2], and Borgo, Guarino, and Masolo =-=[6]-=-. For a treatment of region-based topology in a general setting, see Roeper [31]. Motivations for these developments vary, and we do not intend to provide a comprehensive account of them here. However... |

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Citation Context ...egions are first class entities and points are logical constructions based on them, then who knows what interesting new ways of considering spatial entities and relations there might be? Clarke [11], =-=[12]-=-, following an idea of Whitehead [39], sought to reconstruct mereotopology in terms of a primitive relation of connection holding between regions. Following this work, Biacino and Gerla [5] have studi... |

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Citation Context ...he statement of theorem 5.6). Moreover, T is countable, so by theorem 5.6, Q ' T. 7 Related work The results presented here not only have ramifications for mereotopological theories (Casati and Varzi =-=[8, 9]-=-, Varzi [36] and references in section 1), but they have connections with more practical disciplines. Various logicians have sought to give deductive theories of space and space-time (Basri [4], Carna... |

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Citation Context ...r more practical area in which ontological issues about the plane are raised is in the construction of computational spatial representations for robots, and in Geographical Information Systems (Davis =-=[13]-=-, Vieu [37]). As we have mentioned, GISs use planar polygonal regions to represent geographic objects. In mobile robotics too, it is common to represent a robot's information about its environment as ... |

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Citation Context ...he statement of theorem 5.6). Moreover, T is countable, so by theorem 5.6, Q ' T. 7 Related work The results presented here not only have ramifications for mereotopological theories (Casati and Varzi =-=[8, 9]-=-, Varzi [36] and references in section 1), but they have connections with more practical disciplines. Various logicians have sought to give deductive theories of space and space-time (Basri [4], Carna... |

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Citation Context ...rzi [8, 9], Varzi [36] and references in section 1), but they have connections with more practical disciplines. Various logicians have sought to give deductive theories of space and space-time (Basri =-=[4]-=-, Carnap [7], Goldblatt [16], Henkin, Suppes and Tarski [19]), many in terms of modal logics (Balbiani et al. [3], Rescher and Garson [29], Rescher and Urquhart [30], Segerberg [32], Shehtman [34], vo... |

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4 |
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Citation Context ...arious logicians have sought to give deductive theories of space and space-time (Basri [4], Carnap [7], Goldblatt [16], Henkin, Suppes and Tarski [19]), many in terms of modal logics (Balbiani et al. =-=[3]-=-, Rescher and Garson [29], Rescher and Urquhart [30], Segerberg [32], Shehtman [34], von Wright [38]). Recent interest in the analysis of visual languages, such as maps and diagrams (Haarslev [18], Le... |

2 |
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(Show Context)
Citation Context ...Varzi [36] and references in section 1), but they have connections with more practical disciplines. Various logicians have sought to give deductive theories of space and space-time (Basri [4], Carnap =-=[7]-=-, Goldblatt [16], Henkin, Suppes and Tarski [19]), many in terms of modal logics (Balbiani et al. [3], Rescher and Garson [29], Rescher and Urquhart [30], Segerberg [32], Shehtman [34], von Wright [38... |

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2 | Review of "Logic and Visual Information" by - Lemon - 1997 |

2 | Incomplete spatial logics: On the foundations of computational geography - Lemon, Pratt - 1996 |

2 | Putting Channels on the Map: imperfect information flow in a formal semantics of (geo)graphical information systems - Lemon, Pratt - 1996 |