"Three value logic" is of little use when you only have binary control mechanisms.

To be of value, you'd have to have a control structures that had three branches:

if( <condition> ) {
    ...
}
else {
    ...
}
otherwise {

}

my $var = <COND> ? $a :: $b :: $c;
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Given that about 90% of programmers seem unable to handle the idea of:

unless( <cond> ) {
    ...
}
else {
    ...
}
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It seems unlikely that they'd go for trinary control mechanisms any time soon.

Without them, you'd just end up coding the direct equivalent of:

if( $loginAttempted ) {
    if( $loginSuccessful ) {
        ...
    }
    else {
        ...
    }
}
else {
    ...
}
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But in a far more obscure way.