This paper discusses picture logic, a visual language for the specification of diagrams and diagram transformations. Formal specification techniques for diagrammatic or visual languages have previously mainly been targeted towards static diagrammatic languages. For reasoning about certain types of diagrams, however, formalizing a notion of change is inevitable. This is particularly true of visual mathematical notations whose evaluation rules or consequence relations correspond to visual or graphical transformations. The paper presents constraint-based extensions of picture logic which render it suitable for the specification of such diagram notations and the required transformations.