An Object-Oriented Dynamic Logic with Updates

With the goal of this thesis being to create a dynamic logic for objectoriented languages, ODL is developed along with a sound and relatively complete calculus. The dynamic logic contains only the absolute logical essentials of object-orientation, yet still allows a “natural” representation of all other features of common object-oriented programming languages. ODL is an extension of a dynamic logic for imperative While programs by function modification and dynamic type checks. A generalisation of substitutions, called updates, constitute the central technical device for dealing with object aliasing arising from function modification and for retaining a manageable calculus in practical application scenarios. Further, object enumerators realise object creation in a natural yet powerful way. Finally, completeness is proven relative to first-order arithmetic. Along with the soundness result, this proof constitutes the central part of this thesis and even copes with states containing uncomputable functions.