change Mike Worboys Department of Spatial Information Science and - - PowerPoint PPT Presentation
The foundations of spatial change Mike Worboys Department of Spatial Information Science and Engineering University of Maine Things that involve change State (part of situation) Absence of change Process (1) Change as it is
Mike Worboys Department of Spatial Information Science and Engineering University of Maine
– Absence of change
– Change as it is actually occurring, something going on
– A chunk of change picked out as an individual from the ongoing flux
– A structured succession of events
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change happens to continuant state change process event
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STATE CHANGE area shape color PROCESS growing in size, changing shape, changing color
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STATE CHANGE area shape color EVENT growing in size, changing shape, changing color ON Christmas Day, 2010 12/25/2010 12/26/2010
– location change – size change – shape change – topological change – dimension change – identity change – posture change – semantic change – viewpoint change
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homeomorphisms
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(McCarthy, Hayes, Kowalski and Sergot, Allen) Time Temporal structure Allen’s interval calculus Time-varying propositions Fluents Event type Predicates
– Occurs (event, time) – HoldsAt (fluent, time) – Initiates (event, fluent, time) – Terminates (event, fluent, time)
Theory examples
– A fluent is true once it has been initiated by an event. – A fluent is false once it has been terminated and before it has been initiated.
Robin Milner 1934 – 2010
– Composition a.P – Disjunction P+Q – Parallelism P|Q – Reaction ((in a)P+Q)|((out a)R+S) P|R – Replication !P – Ambient n[P]
This process is deterministic, as there is at most one transition (q, a, q’), for each pair (q, a). Process notation: Q0 == aR R == bS + cQ0 S == cQ0 q0 r s a c c b
q0 r s a c c b This process is nondeterministic, as there is more than one transition a with start state q0. Process notation: Q0 == aR + aT = a(R+T) R == bS + cQ0 S == cQ0 T == cQ0 t a c
These processes communicate via input action a and
Process notation: Q0 == aR R == bS + cQ0 S == cQ0 T0 == aU U == dT0 q0 r s a c c b t0 u a d Q0 | T0 U | R
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Two continuous functions are called homotopic if one can be "continuously deformed" into the
Such a deformation is called a homotopy between the two functions.
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A homotopy between two continuous functions f and g from a topological space X to a topological space Y is a continuous function H : X × *0,1+ → Y such that, if x ∈ X then H(x,0) = f(x) H(x,1) = g(x).
f g 1 H 1 1
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n0 n1 n2 n4 n3 n'0 n'1 n'2 n'3 node to node
n0 n'0 n'1
T1 T2 n1 n0 n2 n'1 n'0
T1 T2
n0 n1 n'1 n'0 n2
T1 T2 n'0 n0 n1
T1 T2
n'1 n'0 n'2 n1 n0
T1 T2
n'0 n'1 n1 n0 n'2
T1 T2
atomic insert atomic merge I atomic merge II atomic delete atomic split I atomic split II
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– pollution plumes – ocean currents – population movements – ST temperature variations
scalar ar field discretiza retizatio tion approximatio
A basic transition leads to a partition of the spatial domain into different components:
A basic transition A partition
Components that are not adjacent to the transition region are irrelevant to the type of topological changes Hole Self-merge
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Hole Self-merge
Properties of the C-components Type of Transition region: removed
Basic transitions of the same type have the same properties
Different types of basic transitions have different properties
Spatial Fields Using Responsive Geosensor Networks