model theory (redirected from Theory of models)

model theory [′mäd·əl ‚thē·ə·rē]

(mathematics)

The general qualitative study of the structure of a mathematical theory.

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Model theory

The body of knowledge that concerns the fundamental nature, function, development, and use of formal models in science and technology. In its most general sense, a model is a proxy. A model is one entity used to represent some other entity for some well-defined purpose. Examples of models include: (1) An idea (mental model), such as the internalized model of a person's relationships with the environment, used to guide behavior. (2) A picture or drawing (iconic model), such as a map used to record geological data, or a solids model used to design a machine component. (3) A verbal or written description (linguistic model), such as the protocol for a biological experiment or the transcript of a medical operation, used to guide and improve procedures. (4) A physical object (scale model, analog model, or prototype), such as a model airfoil used in the wind-tunnel testing of a new aircraft design. (5) A system of equations and logical expressions (mathematical model or computer simulation), such as the mass- and energy-balance equations that predict the end products of a chemical reaction, or a computer program that simulates the flight of a space vehicle. Models are developed and used to help hypothesize, define, explore, understand, simulate, predict, design, or communicate some aspect of the original entity for which the model is a substitute.

Formal models are a mainstay of every scientific and technological discipline. Social and management scientists also make extensive use of models. Indeed, the theory of models and modeling cannot be divorced from broader philosophical issues that concern the origins, nature, methods, and limits of human knowledge (epistemology) and the means of rational inquiry (logic and the scientific method).

Models are usually more accessible to study than the system modeled. Changes in the structure of a model are easier to implement, and changes in the behavior of a model are easier to isolate, understand, and communicate to others. A model can be used to achieve insight when direct experimentation with the actual system is too dangerous, disruptive, or demanding. A model can be used to answer questions about a system that has not yet been observed or built, or even one that cannot be observed or built with present technologies.

Specific models developed in different disciplines may differ in subject, form, and intended use. However, basic concepts such as model description, validation, simplification, and simulation are not unique to any particular discipline. Model theory seeks a formal logical and axiomatic understanding of the underlying concepts that are common to all modeling endeavors.

General and mathematical systems theory have stimulated many of the important developments in model theory. Mathematical models are particularly useful, because of the large body of mathematical theory and technique that exists for the study of logical expressions and the solution of equations. The power and accessibility of digital computers have increased the use and importance of mathematical models and computer simulation in all branches of modern science and technology. A great variety of programming languages and applications software are now available for modeling, computational analysis, and system simulation. See Digital computer, Simulation, Systems analysis, Systems engineering