In this paper, two proposals for modification of two logical systems, namely Dynamic Predicate Calculus and Dynamic Semantics with Choice Functions, are introduced. These two systems do not grasp adequately the anaphoric bond in so-called donkey sentences. The aim of the proposal is to eliminate this limitation. First, the phenomenon of anaphor is introduced. Then, the author articulates the presuppositions for adequate grasping of this phenomenon for any semantic system. After that, the paper aims at particular problem of analysis of anaphor in donkey sentences. The analysis using two systems is demonstrated. The paper contains presentation of those parts of the two systems, which are relevant to this problem. After this, the author sheds light on problems connected with the weak reading and some limits of two systems in the issue. Conditions for adequate analysis of the weak reading are articulated. Then, the author demonstrates an analysis of the weak reading using the modified systems. The paper ends in discussion about the relation between the original and modified systems.