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)