Development of Unit Calculation Algebra as an Application Function of the Cellular Data System

Cyberworlds are information worlds where data and its dependencies are always changing and may evolve unpredictably, just like living things. Thus far, it has been difficult to model cyberworlds with higher freedom using the existing model because of its complexity. We believe that Incrementally Modular Abstraction Hierarchy (IMAH), which has an abstraction hierarchy preserving invariants from the abstract to the concrete level, and which was invented by one of the authors (T. L. Kunii), makes it possible. We have developed a data processing system called Cellular Data System (CDS) based on IMAH. With CDS, you can express any space, with forms or not, and attach or divide spaces by an equivalence relation to output information like you do in your head. In this paper we have designed and implemented wide-use algebra called unit calculation algebra on the presentation level in IMAH as an application function of CDS, and we have shown its effectiveness through examples.