# 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
- Information Systems Design
- Formalization of Information Systems Design
- Component Problems of Information Systems

- The Function of an Information System
- The Function of an Information System
- Two Tasks of an Information System
- Operative Information Requirments. An Example.
- The value of Directive Information
- Effect of time for Decomposing. Executive Decisions.
- Transient Decision Situation. Satisficing.
- Information Needed in a Simplified Model of a Manufacturing Shop

- The Economic Quantity of Information and Processing
- The Economic Quantity of Information and Processing
- Information Value as an Information Systems Design Parameter
- Information and System Control
- The Meaning of Information within a System
- The Value of Information in a System
- Data Representation aof Information in a System. Volume of Data
- The Information System for a Simple Inventory
- Operative vs. Directive Information
- An Example of Optimum Reduction. Information Processing for a Simple Inventory
- Information System for a Simple Work Station

- Some Problems of Information Systems Design
- Complexity of an Information System

- Precedence Relations between Information Sets in and Information System
- Data Structure of an Information System
- On the Definition of Elementary Files (e-files)
- Inference Problem in Information Systems Design
- A Further Illustration [of] Information Precedence and Elementary File Definition; Computation of Weekly Wage
- Cost Distribution of Job Costs as Another Illustration of Discussing Elementary Files
- Identification of Precedence Information
- Use of the Information Precedence Matrix P
^{00}for Compatibility Checking - Some Other Uses of the Precedence Matrix P
- The Precedence Structure and the Dynamic Flow of Processing
- Completeness Theorem of Information Precedence
- Systematic Design of a Directive 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

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

This TOC, as reproduced here, is the normative designation by which I reference the text of the original document, not the original section numbering. A small number of copies of the work appear to be available online. The reader may safely take this TOC as a surrogate for the work under the presumption that its use as noted below will make its content clear and I have provided synoptic pages here for the critical sections.

## Import

TAIS is significant for several obvious 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. Since Langefors actually developed his system during the even earlier period and thus to some extent its time and space complexity concerns seem archaic. 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.

The work would probably not be acceptable in the computer science community of today as it exposits a mathematical treatment of systems analysis without actually providing details of that math. This doesn't detract from its intrinsic value and is even an advantage as it doesn't offer anything to undo in basing on operational elements now existing which can provide same.

## 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