In this paper, we propose a model named Logical Markov Decision Processes with Negation for Relational Reinforcement Learning for applying Reinforcement Learning algorithms on the relational domains with the states and actions in relational form. In the model, the logical negation sented explicitly, so that the abstract state space can be constructed from the goal state(s) of a given task simply by applying a generating method and an expanding method, and each ground state can be represented by one and only ract state. Prototype action is also introduced into l, so that the applicable abstract actions can be obtained automatically. Based on the model, a model-free ()-learning algorithm is implemented to evaluate the state-action-substitution value function. We also propose a state refinement method guided by two formal definitions loop degree and common characteristic of abstract o construct the abstract state space automatically by the agent itself rather than manually. The experiment...