It works for me. Which version of Perl are you using?

sub my_sub
{
    my $arg1 = shift;
    my $arg2 = shift;
    my $arg3 = shift;
    my $arg4 = shift;

    print defined $arg1 ? "$arg1\n" : "undefined\n";
    print defined $arg2 ? "$arg2\n" : "undefined\n";
    print defined $arg3 ? "$arg3\n" : "undefined\n";
    print         $arg4 ? "$arg4\n" : "false/null\n";
}

my_sub( 'string', undef, 123, '' );
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