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quasi-mv-algebra [2011/07/14 09:10]
jipsen
quasi-mv-algebra [2011/07/17 13:32] (current)
jipsen
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====Examples==== ====Examples====
The standard qMV-algebra is $\mathbf S=\langle [0,1]^2,\oplus, ', \mathbf 0, \mathbf 1\rangle$ where The standard qMV-algebra is $\mathbf S=\langle [0,1]^2,\oplus, ', \mathbf 0, \mathbf 1\rangle$ where
-$\langle a,b\rangle\oplus \langle c,d\rangle=\langle \min(1,a+c), \frac12\rangle$, $\langle a,b\rangle'=\langle 1-b,1-a\rangle$,+$\langle a,b\rangle\oplus \langle c,d\rangle=\langle \min(1,a+c), \frac12\rangle$, $\langle a,b\rangle'=\langle 1-a,1-b\rangle$,
$\mathbf 0=\langle 0,\frac12\rangle$ and $\mathbf 1=\langle 1,\frac12\rangle$. $\mathbf 0=\langle 0,\frac12\rangle$ and $\mathbf 1=\langle 1,\frac12\rangle$.