Conceptual model
Encyclopedia
In the most general sense, a model is anything used in any way to represent anything else. Some models are physical objects, for instance, a toy model which may be assembled, and may even be made to work like the object it represents. They are used to help us know
and understand
the subject matter they represent. The term conceptual model may be used to refer to models which are represented by concepts or related concepts which are formed after a conceptualization process in the mind. Conceptual models represent human intentions or semantics. Conceptualization from observation of physical existence and conceptual modeling are the necessary means human employ to think and solve problems. Concepts are used to convey semantics during various natural languages based communication. Since that a concept might map to multiple semantics by itself, an explicit formalization is usually required for identifying and locating the intended semantic from several candidates to avoid misunderstandings and confusions in conceptual models.
, most models are concepts. But they are, mostly, intended to be models of real world states of affairs. The value of a model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A model of a concept is quite different because in order to be a good model it need not have this real world correspondence.
Models of concepts are usually built by analysts who are not primarily concerned about the truth or falsity of the concepts being modeled. For example, in management problem structuring, Conceptual Models of human activity systems are used in Soft systems methodology to explore the viewpoints of stakeholders in the client organization. In artificial intelligence conceptual models and conceptual graphs are used for building expert systems and knowledge-based systems
, here the analysts are concerned to represent expert opinion on what is true not their own ideas on what is true.
of a familiar physical object, to the formal generality and abstractness of mathematical model
s which do not appear to the mind as an image. Conceptual models also range in terms of the scope of the subject matter that they are taken to represent. A model may, for instance, represent a single thing (e.g. the Statue of Liberty), whole classes of things (e.g. the electron), and even very vast domains of subject matter such as the physical universe. The variety and scope of conceptual models is due to the variety of purposes had by the people using them.
may also refer to a nonphysical external model of the mind itself.
the answers to fundamental questions such as whether matter
and mind
are one or two substances; or whether or not humans have free will
.
and the knowable.
, a model is a type of interpretation
under which a particular statement is true. Logical models can be broadly divided into ones which only attempt to represent concepts, such as mathematical models; and ones which attempt to represent physical objects, and factual relationships, among which are scientific models.
Model theory
is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra.
A more comprehensive type of mathematical model uses a linguistic version of category theory
to model a given situation. Akin to entity-relationship models, custom categories
or sketches
can be directly translated into database schemas
. The difference is that logic is replaced by category theory, which brings powerful theorems to bear on the subject of modeling, especially useful for translating between disparate models (as functors between categories).
objects, phenomena, and physical processes in a logic
al way. Attempts to formalize
the principles of the empirical sciences, use an interpretation
to model reality, in the same way logicians axiomatize
the principle
s of logic
. The aim of these attempts is to construct a formal system
for which reality
is the only interpretation. The world is an interpretation (or model) of these sciences, only insofar as these sciences are true.
proposed as generating data. In a parametric model
, the probability distribution function has variable parameters, such as the mean
and variance
in a normal distribution, or the coefficients for the various exponents of the independent variable
in linear regression
. A nonparametric model has a distribution function without parameters, such as in bootstrapping
, and is only loosely confined by assumptions. Model selection
is a statistical method for selecting a distribution function within a class of them, e.g., in linear regression where the dependent variable is a polynomial of the independent variable with parametric coefficients, model selection is selecting the highest exponent, and may be done with nonparametric means, such as with cross validation.
In statistics there can be models of mental events as well as models of physical events. For example, a statistical model of customer behavior is a model that is conceptual, (because behavior is physical) but a statistical model of customer satisfaction is a model of a concept (because satisfaction is a mental not a physical event).
, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using mathematical techniques. Frequently, economic models use structural parameters. Structural parameters are underlying parameters in a model or class of models. A model may have various parameters and those parameters may change to create various properties.
of a system
. A system model can represent multiple views
of a system by using two different approaches. The first one is the non-architectural approach and the second one is the architectural approach. The non-architectural approach respectively picks a model for each view. The architectural approach, also known as system architecture, instead of picking many heterogeneous and unrelated models, will use only one integrated architectural model.
Entity-relationship models have had wide application in the building of information systems intended to support activities involving objects and events in the real world. In these cases they are models that are conceptual. However, this modeling method can be used to build computer games or a family tree of the Greek Gods, in these cases it would be used to model concepts.
). A domain model includes the various entities, their attributes and relationships, plus the constraints governing the conceptual integrity of the structural model elements comprising that problem domain. A domain model may also include a number of conceptual views, where each view is pertinent to a particular subject area of the domain or to a particular subset of the domain model which is of interest to a stakeholder of the domain model.
Like entity-relationship models, domain models can be used to model concepts or to model real world objects and events.
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
and understand
Understanding
Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object....
the subject matter they represent. The term conceptual model may be used to refer to models which are represented by concepts or related concepts which are formed after a conceptualization process in the mind. Conceptual models represent human intentions or semantics. Conceptualization from observation of physical existence and conceptual modeling are the necessary means human employ to think and solve problems. Concepts are used to convey semantics during various natural languages based communication. Since that a concept might map to multiple semantics by itself, an explicit formalization is usually required for identifying and locating the intended semantic from several candidates to avoid misunderstandings and confusions in conceptual models.
Models of concepts and models that are conceptual
The term "conceptual model" is ambiguous. It could mean a model of concept or it could mean a model that is conceptual. A distinction can be made between what models are and what models are models of. With the exception of iconic models, such as a scale model of Winchester CathedralWinchester Cathedral
Winchester Cathedral at Winchester in Hampshire is one of the largest cathedrals in England, with the longest nave and overall length of any Gothic cathedral in Europe...
, most models are concepts. But they are, mostly, intended to be models of real world states of affairs. The value of a model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A model of a concept is quite different because in order to be a good model it need not have this real world correspondence.
Models of concepts are usually built by analysts who are not primarily concerned about the truth or falsity of the concepts being modeled. For example, in management problem structuring, Conceptual Models of human activity systems are used in Soft systems methodology to explore the viewpoints of stakeholders in the client organization. In artificial intelligence conceptual models and conceptual graphs are used for building expert systems and knowledge-based systems
Knowledge-based systems
Knowledge based systems are artificial intelligent tools working in a narrow domain to provide intelligent decisions with justification. Knowledge is acquired and represented using various knowledge representation techniques rules, frames and scripts...
, here the analysts are concerned to represent expert opinion on what is true not their own ideas on what is true.
Type and scope of conceptual models
Conceptual models (models that are conceptual) range in type from the more concrete, such as the mental imageMental image
A mental image is an experience that, on most occasions, significantly resembles the experience of perceiving some object, event, or scene, but occurs when the relevant object, event, or scene is not actually present to the senses...
of a familiar physical object, to the formal generality and abstractness of mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
s which do not appear to the mind as an image. Conceptual models also range in terms of the scope of the subject matter that they are taken to represent. A model may, for instance, represent a single thing (e.g. the Statue of Liberty), whole classes of things (e.g. the electron), and even very vast domains of subject matter such as the physical universe. The variety and scope of conceptual models is due to the variety of purposes had by the people using them.
Mental model
In cognitive psychology and philosophy of mind, a mental model is a representation of something in the mind, but a mental modelMental model
A mental model is an explanation of someone's thought process about how something works in the real world. It is a representation of the surrounding world, the relationships between its various parts and a person's intuitive perception about his or her own acts and their consequences...
may also refer to a nonphysical external model of the mind itself.
Metaphysical models
A metaphysical model is a type of conceptual model which is distinguished from other conceptual models by its proposed scope. A metaphysical model intends to represent reality in the broadest possible way. This is to say that it explainsExplanation
An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....
the answers to fundamental questions such as whether matter
Matter (philosophy)
Matter is the substrate from which physical existence is derived, remaining more or less constant amid changes. anything that occupies space and has mass and weight...
and mind
Mind
The concept of mind is understood in many different ways by many different traditions, ranging from panpsychism and animism to traditional and organized religious views, as well as secular and materialist philosophies. Most agree that minds are constituted by conscious experience and intelligent...
are one or two substances; or whether or not humans have free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
.
Conceptual model vs. semantics model
Semantics are the actually intention when human practice conceptual modeling or use conceptual model after the conceptualization. A cognitive argumentation is that human use languages to think. By languages, human actually use language elements and the relationships which are concepts and concept models. Effort to formalize and clarify the semantics of an expression in languages is closely related to identify and locate the intended semantics which underlie the superficial expression in the form of notations of concepts and concept models.Epistemological models
An epistemological model is a type of conceptual model whose proposed scope is the knownKnowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
and the knowable.
Logical models
In logicLogic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, a model is a type of interpretation
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
under which a particular statement is true. Logical models can be broadly divided into ones which only attempt to represent concepts, such as mathematical models; and ones which attempt to represent physical objects, and factual relationships, among which are scientific models.
Model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra.
Mathematical models
Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.A more comprehensive type of mathematical model uses a linguistic version of category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
to model a given situation. Akin to entity-relationship models, custom categories
Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose...
or sketches
Sketch (mathematics)
A sketch is a category D, together with a set of limit cones and a set of colimit cones. A model of the sketch in a category C is a functorM:D\rightarrow C...
can be directly translated into database schemas
Database schema
A database schema of a database system is its structure described in a formal language supported by the database management system and refers to the organization of data to create a blueprint of how a database will be constructed...
. The difference is that logic is replaced by category theory, which brings powerful theorems to bear on the subject of modeling, especially useful for translating between disparate models (as functors between categories).
Scientific models
A scientific model is a simplified abstract view of the complex reality. A scientific model represents empiricalEmpiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...
objects, phenomena, and physical processes in a logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
al way. Attempts to formalize
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
the principles of the empirical sciences, use an interpretation
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
to model reality, in the same way logicians axiomatize
Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems...
the principle
Rule of inference
In logic, a rule of inference, inference rule, or transformation rule is the act of drawing a conclusion based on the form of premises interpreted as a function which takes premises, analyses their syntax, and returns a conclusion...
s of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
. The aim of these attempts is to construct a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
for which reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
is the only interpretation. The world is an interpretation (or model) of these sciences, only insofar as these sciences are true.
Statistical models
A statistical model is a probability distribution functionProbability distribution function
Depending upon which text is consulted, a probability distribution function is any of:* a probability distribution function,* a cumulative distribution function,* a probability mass function, or* a probability density function....
proposed as generating data. In a parametric model
Parametric model
In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters...
, the probability distribution function has variable parameters, such as the mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
and variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
in a normal distribution, or the coefficients for the various exponents of the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
in linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
. A nonparametric model has a distribution function without parameters, such as in bootstrapping
Bootstrapping (statistics)
In statistics, bootstrapping is a computer-based method for assigning measures of accuracy to sample estimates . This technique allows estimation of the sample distribution of almost any statistic using only very simple methods...
, and is only loosely confined by assumptions. Model selection
Model selection
Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered...
is a statistical method for selecting a distribution function within a class of them, e.g., in linear regression where the dependent variable is a polynomial of the independent variable with parametric coefficients, model selection is selecting the highest exponent, and may be done with nonparametric means, such as with cross validation.
In statistics there can be models of mental events as well as models of physical events. For example, a statistical model of customer behavior is a model that is conceptual, (because behavior is physical) but a statistical model of customer satisfaction is a model of a concept (because satisfaction is a mental not a physical event).
Economic models
In economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using mathematical techniques. Frequently, economic models use structural parameters. Structural parameters are underlying parameters in a model or class of models. A model may have various parameters and those parameters may change to create various properties.
Models in systems architecture
A system model is the conceptual model that describes and represents the structure, behavior, and more viewsView model
A view model or viewpoints framework in systems engineering, software engineering, and enterprise engineering is a framework which defines a coherent set of views to be used in the construction of a system architecture, software architecture, or enterprise architecture. A view is a representation...
of a system
System
System is a set of interacting or interdependent components forming an integrated whole....
. A system model can represent multiple views
View model
A view model or viewpoints framework in systems engineering, software engineering, and enterprise engineering is a framework which defines a coherent set of views to be used in the construction of a system architecture, software architecture, or enterprise architecture. A view is a representation...
of a system by using two different approaches. The first one is the non-architectural approach and the second one is the architectural approach. The non-architectural approach respectively picks a model for each view. The architectural approach, also known as system architecture, instead of picking many heterogeneous and unrelated models, will use only one integrated architectural model.
Conceptual models of human activity systems
Conceptual models of human activity systems are used in Soft systems methodology (SSM) which is a method of systems analysis concerned with the structuring of problems in management. These models are models of concepts; the authors specifically state that they are not intended to represent a state of affairs in the physical world. They are also used in Information Requirements Analysis (IRA) which is a variant of SSM developed for information system design and software engineering.Logico-linguistic models
Logico-linguistic modeling is another variant of SSM that uses conceptual models. However, this method combines models of concepts with models of putative real world objects and events. It is a graphical representation of modal logic in which modal operators are used to distinguish statement about concepts from statements about real world objects and events.Entity-relationship model
In software engineering, an entity-relationship model (ERM) is an abstract and conceptual representation of data. Entity-relationship modeling is a database modeling method, used to produce a type of conceptual schema or semantic data model of a system, often a relational database, and its requirements in a top-down fashion. Diagrams created by this process are called entity-relationship diagrams, ER diagrams, or ERDs.Entity-relationship models have had wide application in the building of information systems intended to support activities involving objects and events in the real world. In these cases they are models that are conceptual. However, this modeling method can be used to build computer games or a family tree of the Greek Gods, in these cases it would be used to model concepts.
Domain model
A domain model is a type of conceptual model used to depict the structural elements and their conceptual constraints within a domain of interest (sometimes called the problem domainProblem domain
A problem domain is the area of expertise or application that needs to be examined to solve a problem. A problem domain is simply looking at only the topics you are interested in, and excluding everything else. For example, if you were developing a system trying to measure good practice in...
). A domain model includes the various entities, their attributes and relationships, plus the constraints governing the conceptual integrity of the structural model elements comprising that problem domain. A domain model may also include a number of conceptual views, where each view is pertinent to a particular subject area of the domain or to a particular subset of the domain model which is of interest to a stakeholder of the domain model.
Like entity-relationship models, domain models can be used to model concepts or to model real world objects and events.
See also
- Conceptual model (computer science)
- Conceptual schemaConceptual schemaA 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...
- paradigmParadigmThe word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...
- Interpretation (logic)Interpretation (logic)An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
- Concept mapping
- Scientific modellingScientific modellingScientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling...
- Conceptual systemConceptual systemA conceptual system is a system that is composed of non-physical objects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects".- Overview :...
- TheoryTheoryThe English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
- ConceptConceptThe word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...