Many reinforcement learning domains are highly relational.Whiletraditional temporal-difference methods can be applied to these domains, they are limited in their capacity to exploit the relational nature of the domain. Our algorithm, AMBIL, constructs relational world models in the form of relational Markov decision processes (MDPs). AMBIL works backwards from collections of high-reward states, utilizing inductive logic programming to learn their preimage, logical definitions of the region of state space that leads to the high-reward states via some action. These learned preimages are chained together to form an MDP that abstractly represents the domain. AMBIL estimates the reward and transition probabilities of this MDP from past experience. Since our MDPs are small, AMBIL uses value-iteration to quickly estimate the Q-values of each action in the induced states and determine a policy. AMBIL is able to employ complex background knowledge and supports relational representations. Empirical evaluation on both synthetic domains and a sub-task of the RoboCup soccer domain shows significant performance gains compared to standard Q-learning.