# model (abstract)

## Information about model (abstract)

An abstract model (or conceptual model) is a theoretical construct that represents something, with a set of variables and a set of logical and quantitative relationships between them. Models in this sense are constructed to enable reasoning within an idealized logical framework about these processes and are an important component of scientific theories. Idealized here means that the model may make explicit assumptions that are known to be false (or incomplete) in some detail. Such assumptions may be justified on the grounds that they simplify the model while, at the same time, allowing the production of acceptably accurate solutions, as is illustrated below.

## Examples

### Mathematical models

Main article: Mathematical model
• Model of a particle in a potential field. In this model we consider a particle as being a point of mass m that describes a trajectory modelled by a function x: RR3 given its coordinates in space as a function of time. The potential field is given by a function V:R3R and the trajectory is a solution of the differential equation
:
Note this model assumes that the particle is a point mass, which is certainly known to be false in many cases where we use the model, e.g. when we use it as a model of planetary motion.
• Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labelled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which she uses to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes one of constrained maximization, that is maximize
:
subject to
:
This model has been used in models of general equilibrium theory, particularly to show existence and Pareto optimality of economic equilibria. However, the fact that this particular formulation assigns numerical values to levels of satisfaction is a source of criticism. But this is not an essential ingredient of the theory and again, the model is an idealization.

### Other types of models

These two models are examples of mathematical models; following are examples of models that are not mathematical (or at least not numerical).
• Myers-Briggs personality type. Myers-Briggs Type Indicator® is a technique that claims to produce a representation of a person's preferences, using four scales. These scales can be combined in various ways to produce 16 personality types. Types are typically denoted by four letters — for example, INTJ (introverted intuition with extroverted thinking) — to represent a person's preferences. This model is claimed by CPP (formerly known as Consulting Psychologists Press, Inc.) to produce a good predictor of a person's career and marriage partner preference. It should be pointed out, see http://skepdic.com/myersb.html, that there is considerable disagreement among psychologists on whether this assessment technique (and the implied idealized personality model) is of any value.
• Model of political contagion. Some versions of this model are sometimes referred to as the domino theory. In the broadest possible terms, according to this model, political movements that take hold in one country are likely to spread to geographically neighboring ones. This model is surprisingly popular, although as it stands, it is extremely impoverished conceptually, saying nothing about the type of political movement, the degree of geographical proximity, the time scale at which these events take place, etc.

## Use of models

The purpose of a model is to provide an argumentative framework for applying logic and mathematics that can be independently evaluated (for example by testing) and that can be applied for reasoning in a range of situations. Models are used throughout the natural and social sciences, psychology and the philosophy of science. Some models are predominantly statistical (for example portfolio models used in finance); others use calculus, linear algebra or convexity, see mathematical model. Of particular political significance are models used in economics, since they are used to justify decisions regarding taxation and government spending. This often leads to hotly contested debates in the academic world as well as in the political arena; see for instance supply side economics.

Abstract models are used primarily as a reusable tool for discovering new facts, for providing systematic logical arguments as explicatory or pedagogical aids, for evaluating hypotheses theoretically, and for devising experimental procedures to test them. Reasoning within models is determined by a set of logical principles, although rarely is the reasoning used completely mathematical.

In some cases, abstract models can be used to implement computer simulations that illustrate the behavior of a system over time. Simulations are used everywhere in science, especially in economics, engineering, biology, ecology etc., to discover the effects of changing a variable. The validity of different simulation methodologies is a subject of debate in the philosophy and methodology of science.

The automated use of modeling has been identified as a significant issue in the creation of artificial intelligence. Some researchers argue a system without a model cannot achieve understanding, while others argue that running full, consistent models is too computationally costly for either machines or animals, and that much intelligent behavior is reactive or instinctive.

## Structure of models

''Main article: Conceptual schema
A conceptual model is a representation of some phenomenon, data or theory by logical and mathematical objects such as functions, relations, tables, stochastic processes, formulas, axiom systems, rules of inference etc. A conceptual model has an ontology, that is the set of expressions in the model which are intended to denote some aspect of the modeled object. Here we are deliberately vague as to how expressions are constructed in a model and particularly what the logical structure of formulas in a model actually is. In fact, we have made no assumption that models are encoded in any formal logical system at all, although we briefly address this issue below. Moreover, the definition given here is oblivious about whether two expressions really should denote the same thing. Note that this notion of ontology is different from (and weaker than) ontology as is sometimes understood in philosophy; in our sense there is no claim that the expressions actually denote anything which exists physically or spatio-temporally (to use W. Quine's formulation).

For example, a stochastic model of stock prices includes in its ontology a sample space, random variables, the mean and variance of stock prices, various regression coefficients etc. Models of quantum mechanics in which pure states are represented as unit vectors in a Hilbert space include in their ontologies observables, dynamics, measurement operators etc. It is possible that observables and states of quantum mechanics are as physically real as the electrons they model, but by adopting this purely formal notion of ontology we avoid altogether this question.

## Modeling

Modeling, especially scientific modeling refers to the process of generating a model as a conceptual representation of some phenomenon as discussed above. Typically a model will refer only to some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different, that is in which the difference is more than just a simple renaming. This may be due to differing requirements of the model's end users or to conceptual or esthetic differences by the modellers and decisions made during the modeling process. Esthetic considerations that may influence the structure of a model might be the modeller's preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic ones, discrete vs continuous time etc. For this reason users of a model need to understand the model's original purpose and the assumptions of its validity. Having found a model for some desired aspect of reality, it can serve as the basis for simulation, the only way for non-invasive examination of physical reality besides real-world experiments.

## References

• I. Briggs Myers with P. Myers, Gifts Differing. Understanding Personality Type, CPP Books, 1993.
• R. Frigg and S. Hartmann, Models in Science. Entry in the Stanford Encyclopedia of Philosophy.
• K. Lancaster, Mathematical Economics, Dover Publications, 1968.
• W. Quine, From a Logical Point of View, Harper Torchbooks, 1961.

## External links

A model is a pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept. And also it is a study of a miniature of the actual.
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Reasoning is the mental (cognitive) process of looking for reasons for beliefs, conclusions, actions or feelings.[1] Humans have the ability to engage in reasoning about their own reasoning using introspection.
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The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.

In common usage, people often use the word theory to signify a conjecture, an opinion, or a speculation.
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mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social
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Pareto efficiency, or Pareto optimality, is an important notion in economics with broad applications in game theory, engineering and the social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency
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The Myers-Briggs Type Indicator (MBTI) is a personality questionnaire designed to identify certain psychological differences according to the typological theories of Carl Gustav Jung as published in his 1921 book Psychological Types (English edition, 1923).
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The Myers-Briggs Type Indicator (MBTI) is a personality questionnaire designed to identify certain psychological differences according to the typological theories of Carl Gustav Jung as published in his 1921 book Psychological Types (English edition, 1923).
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The domino theory was a mid-20th century foreign policy theory, promoted by the government of the United States, that speculated that if one land in a region came under the influence of communism, then the surrounding countries would follow in a domino effect.
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Only a valid argument with true premises must have a true conclusion.
The validity of an argument depends on its form, not on the truth or falsity of its premises and conclusions. Logic seeks to discover the forms of valid arguments.
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A statistical model is used in applied statistics. Three basic notions are sufficient to describe all statistical models.
1. We choose a statistical unit which we will observe directly. Multiple observations of the same unit over time is called longitudinal research.

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mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social
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In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and quantitative relationships between them.
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Academia is a collective term for the scientific and cultural community engaged in higher education and research, taken as a whole.

The word comes from the akademeia just outside ancient Athens, where the gymnasium was made famous by Plato as a center of learning.
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Supply-side economics is a school of macroeconomic thought that argues that economic growth can be most effectively created using incentives for people to produce (supply) goods and services, such as adjusting income tax and capital gains tax rates.
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Only a valid argument with true premises must have a true conclusion.
The validity of an argument depends on its form, not on the truth or falsity of its premises and conclusions. Logic seeks to discover the forms of valid arguments.
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computer simulation, a computer model or a computational model is a computer program that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of mathematical modelling of many natural systems in physics
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Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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Biology (from Greek: βίος, bio, "life"; and λόγος, logos, "knowledge"), also referred to as the biological sciences, is the scientific study of life.
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Ecology (also known as Oekologie, Okology, or Oekology[1],from Greek: οίκος, oikos, "household"; and λόγος, logos
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artificial intelligence (or AI) is "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions which maximizes its chances of success.
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As a branch of the theory of computation in computer science, computational complexity theory investigates the problems related to the amounts of resources required for the execution of algorithms (e.g.
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reactive planning denotes a group of techniques for action selection by autonomous agents. These techniques differ from classical planning in two aspects. First, they operate in a timely fashion and hence can cope with highly dynamic and unpredictable environments.
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Instinct is the inherent disposition of a living organism toward a particular behavior. Instincts are unlearned, inherited fixed action patterns of responses or reactions to certain kinds of stimuli.
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A conceptual schema, or conceptual data model is a map of concepts and their relationships. This describes the semantics of an organization and represents a series of assertions about its nature.
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function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
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relation or relationship is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order,
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A stochastic process, or sometimes random process, is the opposite of a deterministic process (or deterministic system) in probability theory. Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for
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Ontology is a study of conceptions of reality and the nature of being. In philosophy, ontology (from the Greek ὤν, genitive ὄντος: of being (part.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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