Parsing is quite possibly not required. Assuming that the variables can be assumed to contain a true value why not just leverage perl.
$str =~ s/\*/&&/g;
$str =~ s/\+/||/g;
# $str =~ s/'/!/g;
$str =~ s/(\w+)'/!$1/g;
$str =~ s/\(([^\)]+)\)'/!($1)/g;
$str =~ s/\w+/1/g;
my $truth = eval $str;
If the a/b/A/B vars have associated values all that is required is to substitute them in. Perl does the parsing and calculates the truth.
Modified to deal with ' postfix syntax
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