Object Theories over List Superstructures

In this paper the potential of semantic programming methods based on the theory of hereditarily finite list superstructures (GES) for the logical simulation of the object-oriented approach is considered and estimated. Based on GES, we develop a formal system, which is analogous to the description logic $\mathcal{OODL}$, but in contrast with $\mathcal{OODL}$, it allows the natural simulation of ordered data structures (e.g. lists and arrays). The formal system, which is introduced and investigated in this paper, can help for the development of the logical semantics of programming languages, in particular, the object-oriented programming language Libretto.