As stated by the accepted answer in Which HTTP method should Login and Logout Actions use in a "RESTful" setup it is recommendable to use HTTP POST (= create) for a login in a RESTful webservice (e.g.
Generally your webserver should neither have a session or a logout feature. A REST service should be stateless and authentication information sent along with every request.
However, if you are authenticating the user with some token, and you want to explicitly tell the server to expire the token, and you want to express this in a RESTful manner, it would make sense to me that:
DELETEon that url
It does not make sense to me that you have a url like
/webservice/logout/ that you delete.
Issuing a POST request with some information to issue a 'logout' action is a sensible HTTP API design approach, but it's not REST.