Quantum logic (QL) has been developed using various methods. Among them, orthomodular lattices and binary relational models have been discussed as models that concisely express the logic of quantum mechanics. Although these models are compatible with mathematical logic, some elements are still missing. In this study, a new binary relational model that introduces the concept of inner product in a Hilbert space is proposed. We also propose dynamic extended quantum logic (DEQL), which is the logic based on the new model, and prove some of the usefulness of the model and logic.