# 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.