## Quantum Mereotopology (2000)

### Cached

### Download Links

- [wings.buffalo.edu]
- [wings.buffalo.edu]
- [ontology.buffalo.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | Annals of Mathematics and Artificial Intelligence |

Citations: | 17 - 8 self |

### BibTeX

@ARTICLE{Smith00quantummereotopology,

author = {Barry Smith and Berit Brogaard},

title = {Quantum Mereotopology},

journal = {Annals of Mathematics and Artificial Intelligence},

year = {2000},

volume = {35},

pages = {153--175}

}

### OpenURL

### Abstract

While mereotopology -- the theory of boundaries, contact and separation built up on a mereological foundation -- has found fruitful applications in the realm of qualitative spatial reasoning, it faces problems when its methods are extended to deal with those kinds of spatial and non-spatial reasoning which involve a factor of granularity. This is because granularity cannot easily be represented within a mereology-based framework. We sketch how this problem can be solved by means of a theory of coarse-grained partitions, drawing on methods developed for the manipulation of partitions in the spatial realm and applying these to a range of partitions of non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of partitions evolving over time, or to what we shall call coarse- and fine-grained histories. Keywords: mereotopology, granularity, ontology, partitions, histories 1. Introduction As a result of a series of important contribut...

### Citations

804 | Word and Object - Quine - 1961 |

522 |
Graphs and Hypergraphs
- Berge
- 1973
(Show Context)
Citation Context ...e tree will exist only where the tree has exactly two vertices on that level. We can go back and forth between trees and partitions of the given sort in virtue of a standard graph-theoretical result (=-=Berge 1973-=-, Mark 1978) to the effect that there is a one-to-one correspondence between families of non-intersecting, possibly nested rings in the plain and trees in which each vertex represents a ring in the ar... |

388 | On the Plurality of Worlds - Lewis - 1986 |

346 |
Parts: A Study in Ontology
- Simons
(Show Context)
Citation Context ... if and only if x is a maximal occupant of z. (Here and in what follows ‘≤’ abbreviates: ‘is a proper or improper part of’ understood according to the usual axioms of classical extensional m=-=ereology (Simons 1987-=-).) Intuitively, all boundaries of x then coincide with those of z. Given the presence of empty cells, it is necessary to distinguish in our theory between cell-intersection in the general sense discu... |

241 | The Interpretation of Quantum Mechanics - Omnés - 1994 |

159 | Supporting Ontological Analysis of Taxonomic Relationships - Welty, Guarino - 2001 |

134 | The ‘egg-yolk’ representation of regions with indeterminate boundaries
- Cohn, Gotts
- 1996
(Show Context)
Citation Context ...e fact that mereological topology is region based, and thus it yields a more realistic representation of the qualitative space of common sense than does standard point-set topology. Recent work (e.g. =-=Cohn and Gotts 1997-=-) has concentrated on adding the factors of vagueness, imprecision and uncertainy to standard mereotopological approaches, and on finding ways to bridge the qualitative-quantitative divide, so that al... |

114 | Quantum Mechanics in the Light of Quantum Cosmology - Gell-Mann, Hartle - 1990 |

96 | Consistent Histories and the Interpretation of Quantum Mechanics - Griffiths - 1984 |

94 | Mereotopology: A Theory of Parts and Boundaries - Smith |

91 | Parts of classes - Lewis - 1991 |

75 | Beiträge zur Begründung der transfiniten Mengenlehre - Cantor |

68 | Classical equations for quantum systems - Gell-Mann, Hartle - 1993 |

54 | Papers on Time and Tense - Prior - 1968 |

52 | An introduction to population ecology - HUTCHINSON - 1978 |

51 | Qualitative spatial change - Galton - 2000 |

50 |
Parts and Places
- Casati, Varzi
- 1999
(Show Context)
Citation Context ...can be an element of a set (or singleton) in only one way, an object can be in a cell within a partition in any number of ways. Certainly some objects are exactly located in the corresponding cells. (=-=Casati and Varzi 1999-=-) Exact location is illustrated for example by the relation between a concrete parcel of land and the corresponding cell in a cadastre, or (again), in set theory, by the relation of an element to its ... |

43 | A general framework for time granularity and its application to temporal reasoning - Bettini, Wang, et al. - 1998 |

32 | A common structure for concepts of individuals, stuffs and real kinds: More Mama, more milk, and more mouse. Behavioral and Brain Sciences 21:55–100 - Millikan - 1998 |

29 | A boundary-sensitive approach to qualitative location - Bittner, Stell - 1998 |

27 |
The mereology of discrete space
- Galton
- 1999
(Show Context)
Citation Context ...ve divide, so that algorithms can be found for moving back and forth between the qualitativate spatial representations ofscommon sense and the discrete, digital representations used in applications. (=-=Galton 1999-=-, Stell 1999, 2000) Mereotopology resists a similarly realistic extension to a theory of granularity however. This is because such a theory would presuppose a means of talking about objects (at differ... |

25 | Boundaries: An Essay in Mereotopology - Smith - 1997 |

12 | Relevance, Relatedness and Restricted Set Theory - Smith - 1991 |

11 | A qualitative coordinate language of location of figures within the ground, in: Spatial Information Theory – A Theoretical Basis for
- Bittner
- 1997
(Show Context)
Citation Context ...lso for ignoring things – for placing certain parts and moments of reality into the foreground of our attentions in such a way that other parts and moments are traced over in the background. (Compar=-=e Bittner 1997) A -=-partition is a labeled system of cells demarcated by fiat boundaries (comparable to the familiar types of fiat boundaries – of census tracts and postal districts – which are introduced into geospa... |

11 | Parts as Essential to Their Wholes - Chisholm - 1973 |

6 | Quantum Philosophy: Understanding and Interpreting Contemporary Science - Omnès - 1999 |

5 |
Topological properties of geographic surfaces
- Mark
- 1977
(Show Context)
Citation Context ...exist only where the tree has exactly two vertices on that level. We can go back and forth between trees and partitions of the given sort in virtue of a standard graph-theoretical result (Berge 1973, =-=Mark 1978-=-) to the effect that there is a one-to-one correspondence between families of non-intersecting, possibly nested rings in the plain and trees in which each vertex represents a ring in the array and eac... |

3 | Presentist Four-dimensionalism”, forthcoming in The Monist - Brogaard - 2000 |

3 | The Consistency of Consistent Histories - Griffiths - 1993 |

2 | The Honeycomb Model of - Erwig, Schneider - 1999 |