Belongs to pivot table in Laravel 5

Let's say I'm having the following database schema:

dogs and owners are connected with classic belongsToMany. How about the walks table? I'd like to be able to use Eloquent goodies in such kind of relationship:

$dogs = Dog::with('walks')->get();
$walks = Walk::with('dogs')->get();

In theory, I could replace dog_owner_id with two separate columns: dog_id and owner_id. That would make it easy to use Eloquent, but I'd lose some data integrity, because unrelated Dog and Owner could potentially go for a walk (and that's not safe for neither!).

In Walk.php, how should the relations be defined?

public function dog() {
    // return ???;
}

How about Dog.php and Owner.php?

public function walks() {
    // return ???;
}

via Chebli Mohamed