# TAIS

**Theoretical Analysis of Information Systems**¹ is a published approach to mathematical modeling of a general enterprise information system based on systems theory and algebra. Its results are basic and startling only to the degree in which something like what the book does has not become an element of common IS practice.

## Studentenliiteratur

The TOC as reproduced below does not capture the incidence string style of the Auerbach original text, for example "Boundary Operator for Generalized Systems" the is marked § "12.31".

- Systems Theory
- Basic Problems of Systems Theory
- Needs for a Formal Systems Theory
- Common Faults in Systems Design Analysis
- Different Kinds of Systems Study
- Systems Engineering
- Structural Systems Theory, Electric Networks and Elastic Systems
- Mathematical Systems Theory as a System
- Other Kinds of System Study
- Elements of a Systems Theory
- Usefulness of our Concise Definition of Systems
- The Systems Analysis Approach
- The Fundamental Principle of Systems Work
- General and Special Properties of System Problems
- Systems, Subsystems, Parts, and Boundaries
- Structure Types of a System
- System Partitioning
- Systems Partitioning of Outer Boundary
- A Sketch of a Basic Theory of Systems Analysis
- The Suitable Number of Subsystems in a System

- Systems Algebra
- Algebraic Tools for Describing Systems
- Precedemce Operator of a System (or Graph)
- The Precdence Matrix of a System
- The Precendents of s set of Parts
- Use of the Precedence Matrix P to Determine the Precedents of a Set of parts
- Connections with a Linked Data Structure
- Matrix by Matrix Composition p
^{n}, n-th Precedents and Paths - Succedence Matrix P
_{T} - Generalization of the Precendence Concept
- A generalized Matrix by Vector Operation
- Generalized Matrices
- Matrix Operations as Processing of Data Structures
- Other Kinds of Algorithms for Processing Data Structures
- P
^{11}, the 1-dimensional Precendence Matrix - P
^{01}and P^{10}, Precendence Matrices for Mixed 0-1 and 1-0 Dimension Respectively - Relations between P
^{01}, P^{10}, P^{11}, and P^{00}Respectively - Definition of E
^{10}, the Incidence Matrix - Boundary Operations on a System and the Incidence Matrix
- Co-boundary Operation and Incidence Matrix
- The Coincidence Matrix M
^{10} - Data Structure Representations of Incidence and Coincidence Matrices
- Illustrations of Boundary Operations in Accounting
- Built-up Systems and Gross Systems
- System Connections, Boundary Operation and Cycles
- Positional Operator for the System Graph
- Simple Paths and Closed Paths in a System Graph
- Transposed Positional Operator, Forward Positioning
- General Positioning
- Requirements Computation and Scheduling
- Determining the Boundary Operator from M
^{10}and the Part Boundary Operator R^{T} - Boundary Operator for Generalized Systems

- Basic Problems of Systems Theory
- Information Systems Theory
- Information Systems
- The Function of an Information System
- The Economic Quantity of Information and Processing
- Some Problems of Information Systems Design
- Precedence Relations between Information Sets in and Information System
- Data and Information Files
- Files, Computations, and Processes
- Effect of a Process Grouping
- File Consolidation
- System Design Computation Using Matrix Algebra
- File Storage Considerations
- File Organizations
- System Reliability

- Some Data Processing Problems
- Relation between a Process and its Files
- Influence of Word Structure

The approach was developed over some time before the mid-1970s and so reflects a relatively low-level focus that seems quaint in a modern context. However the material culminating in the chapter on System Design Computation is of enduring value. I believe Langefors died a few years before the turn of the century and there was both a final work by him, related work by colleagues in *Regnecentralen* and other organizations, and related work from unrelated sources.

## Import

TAIS is significant for several reasons. One is historical. The work was published shortly after the introduction of the concept of Software Engineering and before the emergence of OOP, Design Patterns, and other currents which came to represent the mainstream of of systems analysis and design practice.

## Role in **ai-integration.biz**

TAIS is the theoretical foundation of the general approach to information systems development in ai-integration.biz.

## Further Reading

¹ Lagefors, B. Fourth Edition, AUERBACH. 1973 ISBN 0-87769-151-7