A query Q is monotonically determined over a set of views V if Q can be expressed as a monotonic function of the view image. In the case of relational algebra views and queries, monotonic determinacy coincides with rewritability as a union of conjunctive queries, and it is decidable in important special cases, such as for conjunctive query views and queries. We investigate the situation for views and queries in the recursive query language Datalog. We give both positive and negative results about the ability to decide monotonic determinacy, and also about the co-incidence of monotonic determinacy with Datalog rewritability.