In this paper, we propose Tunsr, a unified neural symbolic inference framework that combines the advantages of neural network and symbolic logic approaches in knowledge graph inference. Tunsr uses a consistent inference graph structure that starts from a query entity and iteratively explores its neighbors. It updates the propositional representation and attention of each node, as well as the first-order logic (FOL) representation and attention, through a forward-logic message-passing mechanism. It integrates multiple rules by merging possible relations at each stage, and derives FOL rules by performing attention computation on the inference graph via the FARI algorithm. Experimental results on 19 datasets with four inference scenarios (transition, induction, interpolation, and extrapolation) demonstrate the effectiveness of Tunsr.