The multiple valued logic of inexactness and approximation we proposed in the past as framework for scientific thought in general is in this paper considered as logic for quantum theory in particular. In this logic truth-values are viewed as degrees of error and a deduction is considered valid if the error in the conclusion can be minimized whenever the error in the premise is brought under control. Applications of this logic to quantum mechanics encompass notions from earlier (non-classical) formal-logical approaches (modal, intuitionistic and multi-valued) and enable rigorous formulations of ideas relating to uncertainty, to states of quantum mechanical systems and to the familiar Hilbert space presentation of quantum physics.