Minimal Property Sets

Those expressions of a defined properties language $ L_{PROP}$ which really have to be applied for a problem description $ L_{P}$ are usually only a subset of the set of all possible expressions.


$\displaystyle L_{P}$ $\displaystyle \subseteq$ $\displaystyle 2^{L_{PROP}}$ (4.5)

In the above case we can possibly assume the following static properties: $ \{ 'Door', 'Open', 'A', 'B', 'C', 'Pressed'\}$ assuming that the 'usual' state of the keys is 'not pressed' and the usual state of the door 'closed' as 'not open'. As static relations we could assume $ \{'=', '\ne' \}$. With these assumptions we can have the following possible situations $ S_{1}, S_{2},...$ with $ S_{i} \in 2^{L_{PROP}}$:


$\displaystyle S_{1}$ $\displaystyle =$ $\displaystyle \{ 'Door\ne Open', 'A\ne Pressed', 'B\ne Pressed', 'C\ne Pressed'\}$ (4.6)
$\displaystyle S_{2}$ $\displaystyle =$ $\displaystyle \{ 'Door\ne Open', 'A= Pressed', 'B\ne Pressed', 'C\ne Pressed'\}$ (4.7)
$\displaystyle S_{3}$ $\displaystyle =$ $\displaystyle \{ 'Door\ne Open', 'A\ne Pressed', 'B=Pressed', 'C\ne Pressed'\}$ (4.8)
$\displaystyle S_{4}$ $\displaystyle =$ $\displaystyle \{ 'Door\ne Open', 'A\ne Pressed', 'B\ne Pressed', 'C=Pressed'\}$ (4.9)
$\displaystyle S_{5}$ $\displaystyle =$ $\displaystyle \{ 'Door=Open', 'A\ne Pressed', 'B\ne Pressed', 'C\ne Pressed'\}$ (4.10)

How does this help for the consctruction of a transition diagram?

Gerd Doeben-Henisch 2010-03-03