TaskDependent Qualitative Model Abstraction

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Task-Dependent Qualitative Model Abstraction

• Martin Sachenbacher
• September 2003

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On-board, Real-time Environments
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Qualitative Model Abstraction

• Map real-valued constraints to finite domains
• Problem Find adequate distinctions
• avoid unnecessary details

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Interchangeability Freuder 91

• Domain values val1, val2 are interchangeable, iff
  exchanging val1, val2 preserves solutions
• Task-independent form of abstraction

v2
R
val1
val'
val2
v1
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Task-Dependent Abstraction

• Idea Relaxed version of interchangeability
  that keeps only distinctions essential for a
  given task
• Granularity of observations and solutions

Ç


R Ç Robs
Robs
R
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Task-Dependent Abstraction

• Observable Distinctions
• Partition defining granularity of observations

tobs
Ç


R Ç Robs
Robs
R
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Task-Dependent Abstraction

• Target Distinctions
• Partition defining granularity of solutions

tobs
ttarg
Ç


Rext(v)
R(v) Ç Rext(v)
R
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Task-Dependent Abstraction

• Induced Abstraction
• (Maximal) partition preserving solutions

tobs
ttarg
Ç


Rext(v)
tobs (Robs)
R(v) Ç Rext(v)
R
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Qualitative Abstraction Problem

• Find domain abstraction tind for R such that "
  Robs
• Adequacy ttarg(R Ç tobs(Robs)) ttarg(tind(R) Ç
  tind(tobs(Robs)))
• Simplicity any abstraction of tind is not
  adequate
• Definition of Properties
• Obs-complete, iff each possible Robs can occur
• Sol-complete, iff each possible solution can
  occur

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Determining Induced Abstractions
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Determining Induced Abstractions
tobs
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Determining Induced Abstractions
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Determining Induced Abstractions
Partition S
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Theorem

• Induced abstraction tind formed by intersection
  of interchangeable values for each element of S

Partition S
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Results Sachenbacher et al. 01

• On-board Vehicle Diagnosis Application
• Observable distinctions sensor values
• Target distinction threshold for air/fuel ratio
  ?

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Discussion

• Conclusions
• Generalizes notion of interchangeability
• Increases efficiency and/or fidelity of models
• Facilitates re-usability of model for several
  tasks
• Current Work
• Extend to probabilistic models
• Extend to quantitative constraints
• Extend to dynamic models (transitions)
• Frame as (pareto-) optimization problem

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Material

• Pedal Position Sensor Example

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Example Pedal Position Sensor
Potentiometer
Switch
Pedal
vleft
vright
vleft
vright
On-board Diagnosis requires distinction
corresponding to switching point
Battery
vpot
vswitch
Control Unit