Completeness Theorem of Information Precedence
Preface
Wiki transcription of original with editing of grammar up to the Analysis §.
Overview
The method of information precedence analysis had a fundamental property which makes it a very efficient tool: it is complete in a certain sense. An information system for management control has the purpose of making integrated management possible.
Theorem
Propostion 1
Integrated management as as its purpose the obtaining of both "local efficiency" at each operating station in the organization and efficient coordination of the activities of all stations.
Corollary
Each management activity must have an influence, direct or indirect, upon at least one operating station.
Proposition 2
A management activity exercises influence by means of information.
Theorem 1
Each information set in a management information system must be a precedent (of some order) of at least one operation station.[1]
Theorem 2
Completeness theorem. Each and all relevant information sets in a management information system can be determined, and defined, by an information precedence analysis which starts at every operating station.
Discussion
Notice that the theorem states only that each relevant information [element] can be determined by precedence analysis starting at some operating station. There is no guarantee that it will be determined because the individual precedence analysis steps are intuitive procedures, or search procedures, which cannot be guaranteed to be complete. In other words the method has been prove[n] to be complete in the weak sense that any information that can be found by some means can also be found by the precedence analysis as described. Whether it actually will be found depends on how the precedence analysis is performed. Nevertheless, the likelihood that an information [element] which is relevant will actually be found seems higher when precedence analysis is used because it allows a concentrated effort on one [element] and its precedents at a time. It also allows a more systematic documentation, which can also be processed on a computer.
Analysis
In a modern context, current technology as well as the advancement of experience and perspective with info sytems allows us to fill in the gaps and give a solid foundation to the above with technology such as Haskell, Prolog, RDF, etc.
Notes
- ↑ We are talking here of operations management. Strategic[al] planning systems, for instance, do not satisfy Proposition 1. Hence the theorems 1 and 2 do not hold for such systems.
