Data
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In this article, the data notion is mathematically conceptualized as typed information based on the two concepts of information and computable functionality. A data type is defined as a pair of a set of distinguishable characters (an alphabet) and a set of operations (surjective, computable functions) that operate on this alphabet as domain and capture the intent of a parameterizable concept. Two different ways to construct new data types from existing ones are described: restriction and extension. They lead to two different partial orders on types in the sense of subtyping as formulated by Liskov and Wing. It is argued that the proposed data concept matches the concept of characteristics (Merkmale) of the automation industry.
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