tag.tag is likely not what you want:

$_= $_->id() for @with, @without;
my @articles= $schema->r­esultset('­articles')­->search(
    {­}, 
    {   join => { 'articleli­nks' => 'tag' },
        'tag.tag' => { '-not_in' => \@without, '-in' => \@with },
    },
);
[download]