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 varieties 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 granular partitions, a theory general enough to comprehend not only the familiar sorts of spatial partitions but also a range of coarse-grained partitions of other, non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of granular partitions evolving over time, or to what we shall call coarse- and fine-grained histories.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 153-175 |
| Number of pages | 23 |
| Journal | Annals of Mathematics and Artificial Intelligence |
| Volume | 36 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 2002 |
| Externally published | Yes |
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Keywords
- Consistent histories
- Granularity
- Interpretation of quantum mechanics
- Mereology
- Ontology
ASJC Scopus subject areas
- Artificial Intelligence
- Applied Mathematics
Cite this
Quantum mereotopology. / Smith, Barry; Brogaard, Berit.
In: Annals of Mathematics and Artificial Intelligence, Vol. 36, No. 1-2, 2002, p. 153-175.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Quantum mereotopology
AU - Smith, Barry
AU - Brogaard, Berit
PY - 2002
Y1 - 2002
N2 - 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 varieties 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 granular partitions, a theory general enough to comprehend not only the familiar sorts of spatial partitions but also a range of coarse-grained partitions of other, non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of granular partitions evolving over time, or to what we shall call coarse- and fine-grained histories.
AB - 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 varieties 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 granular partitions, a theory general enough to comprehend not only the familiar sorts of spatial partitions but also a range of coarse-grained partitions of other, non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of granular partitions evolving over time, or to what we shall call coarse- and fine-grained histories.
KW - Consistent histories
KW - Granularity
KW - Interpretation of quantum mechanics
KW - Mereology
KW - Ontology
UR - http://www.scopus.com/inward/record.url?scp=0036083166&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036083166&partnerID=8YFLogxK
U2 - 10.1023/A:1015860121607
DO - 10.1023/A:1015860121607
M3 - Article
VL - 36
SP - 153
EP - 175
JO - Annals of Mathematics and Artificial Intelligence
JF - Annals of Mathematics and Artificial Intelligence
SN - 1012-2443
IS - 1-2
ER -