Hierarchy

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A hierarchy (from the Greek hierarkhia, "rule of a high priest", from hierarkhes , "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy).

Ancient Greek Version of the Greek language used from roughly the 9th century BC to the 6th century AD

The ancient Greek language includes the forms of Greek used in Ancient Greece and the ancient world from around the 9th century BC to the 6th century AD. It is often roughly divided into the Archaic period, Classical period, and Hellenistic period. It is antedated in the second millennium BC by Mycenaean Greek and succeeded by Medieval Greek.

Philosophy The rational investigation of the truths and principles of being, knowledge, or conduct.

Philosophy is the study of general and fundamental questions about existence, knowledge, values, reason, mind, and language. Such questions are often posed as problems to be studied or resolved. The term was probably coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will?

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.

Contents

A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy which are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form.

Path (graph theory) sequence of edges connecting a sequence of vertices in a graph, with no repeating vertices

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct. A directed path in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction.

Comrade friend, colleague, or ally

The term comrade is used to mean "mate", "colleague", or "ally", and derives from the Spanish term camarada, literally meaning "chamber mate", from Latin camera "chamber" or "room". Political use of the term was inspired by the French Revolution, after which it grew into a form of address between socialists and workers. Since the Russian Revolution, popular culture in the Western World has often associated it with communism.

A heterarchy is a system of organization where the elements of the organization are unranked (non-hierarchical) or where they possess the potential to be ranked a number of different ways. Definitions of the term vary among the disciplines: in social and information sciences, heterarchies are networks of elements in which each element shares the same "horizontal" position of power and authority, each playing a theoretically equal role. But in biological taxonomy, the requisite features of heterarchy involve, for example, a species sharing, with a species in a different family, a common ancestor which it does not share with members of its own family. This is theoretically possible under principles of "horizontal gene transfer".

Nomenclature

Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below).

In an organizational context, the following terms are often used related to hierarchies: [1] [2]

In ontology and the philosophy of mind, a non-physical entity is a spirit or being that exists outside physical reality. Their existence divides the philosophical school of physicalism from the schools of idealism and dualism; with the latter schools holding that they can exist and the former holding that they cannot. If one posits that non-physical entities can exist, there exist further debates as to their inherent natures and their position relative to physical entities.

Concept Mental representation or an abstract object

Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science.

A system is a group of interacting or interrelated entities that form a unified whole. A system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory.

In a mathematical context (in graph theory), the general terminology used is different.

Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures, objects are known as nodes, superiors are called parents and subordinates are called children. In a business setting, a superior is a supervisor/boss and a peer is a colleague.

Degree of branching

Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: linear and branching.

In a linear hierarchy, the maximum degree is 1. [1] In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the objects and not the levels; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the hierarchy of life.

In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). [1] For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. [1] Branching hierarchies are present within numerous systems, including organizations and classification schemes. The broad category of branching hierarchies can be further subdivided based on the degree.

A flat hierarchy is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. [2] Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms which can be further decomposed into subatomic particles.

An overlapping hierarchy is a branching hierarchy in which at least one object has two parent objects. [1] For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status).

History of the term

Possibly the first use of the English word "hierarchy" cited by the Oxford English Dictionary was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία hierarchia) both in reference to the celestial hierarchy and the ecclesiastical hierarchy. [3] The Greek term ἱεραρχία means "rule of a high priest" [4] (from ἱεράρχης hierarches, meaning "president of sacred rites, high-priest" [5] and that from ἱερεύς hiereus, "priest" [6] and ἀρχή arche, amongst others "first place or power, rule" [7] ), and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings.

Visually representing hierarchies

Maslow's hierarchy of human needs. This is an example of a hierarchy visualized with a triangle diagram. Maslow's hierarchy of needs.png
Maslow's hierarchy of human needs. This is an example of a hierarchy visualized with a triangle diagram.

A hierarchy is typically depicted as a pyramid, where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. [8] For example, the few Directors of a company could be at the apex, and the base could be thousands of people who have no subordinates.

These pyramids are typically diagrammed with a tree or triangle diagram (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An organizational chart is the diagram of a hierarchy within an organization, and is depicted in tree form in § Organizations, below.

More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees.

Visual hierarchy

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of visual hierarchy. Visual hierarchy is also important for proper organization of files on computers.

An example of visually representing hierarchy is through the Nested clusters. The Nested clusters represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure of representing hierarchy is most effective in representing simple relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located.

For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached.

Informal representation

In plain English, a hierarchy can be thought of as a set in which: [1]

  1. No element is superior to itself, and
  2. One element, the hierarch, is superior to all of the other elements in the set.

The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.

Mathematical representation

Mathematically, in its most general form, a hierarchy is a partially ordered set or poset. [9] The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps in order to solve. The use of hierarchy in mathematics is beneficial in order to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

Subtypes

Nested hierarchy

Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy. Russian-Matroshka no bg.jpg
Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.

A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets. [10] The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc.

Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae ), a human can be formulated as: [11]

Taxonomies may change frequently (as seen in biological taxonomy), but the underlying concept of nested hierarchies is always the same.

In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. [12]

Containment hierarchy

A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

The notation means x is a subset of y but is not equal to y.

A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.

Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "subsumes" its children, and a compositional hierarchy is "composed" of its children. A hierarchy can also be both subsumptive and compositional[ example needed ]. [13]

Subsumptive containment hierarchy

A subsumptive containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "IS-A hierarchy". [9] [14] [15] The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level Mammalia "is a" member of the level Animalia; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "concepts". [15] For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal.

Compositional containment hierarchy

A compositional containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts. [16] Most engineered structures, whether natural or artificial, can be broken down in this manner.

The compositional hierarchy that every person encounters at every moment is the hierarchy of life. Every person can be reduced to organ systems, which are composed of organs, which are composed of tissues, which are composed of cells, which are composed of molecules, which are composed of atoms. In fact, the last two levels apply to all matter, at least at the macroscopic scale. Moreover, each of these levels inherit all the properties of their children.

In this particular example, there are also emergent properties —functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain)—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These level hierarchies are characterized by bi-directional causation. [10] Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into a higher-level entity can have on x's properties and interactions. Furthermore, the entities found at each level are autonomous .

Contexts and applications

According to Kulish, V. V. (2002), almost every system of organization applied to the world is arranged hierarchically. [17] By their common definitions, every nation has a government and every government is hierarchical. [18] [19] Socioeconomic systems are stratified into a social hierarchy (the social stratification of societies), and all systematic classification schemes (taxonomies) are hierarchical. Most organized religions, regardless of their internal governance structures, operate as a hierarchy under God. Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership. Families are viewed as a hierarchical structure in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in a family tree) and inheritance (succession and heirship). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs. Learning must often follow a hierarchical scheme—to learn differential equations one must first learn calculus; to learn calculus one must first learn elementary algebra; and so on. Even nature itself has its own hierarchies, as numerous schemes such as Linnaean taxonomy, the organization of life, and biomass pyramids attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial. [1] [17]

While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept is the "postal district", and consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy, because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter position allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. [20]

A simple organizational hierarchy depicted in the form of a tree. Diagrams like this are called organizational charts. Organizational chart.svg
A simple organizational hierarchy depicted in the form of a tree. Diagrams like this are called organizational charts.

Organizations

Organizations can be structured as a dominance hierarchy. In an organizational hierarchy, there is a single person or group with the most power and authority, and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments, companies, militia and organized religions. The units or persons within an organization are depicted hierarchically in an organizational chart.

In a reverse hierarchy, the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.

Life

Empirically, we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, [21] [22] laid the empirical foundations for a field that would be, from the 1980s, hierarchical ecology. [23] [24] [25] [26] [27]

The theoretical foundations are summarized by Thermodynamics. When biological systems are modeled as physical systems, in its most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and the set/subset relations between dissipative structures can be characterized in a hierarchy.

Computer graphic imaging

CGI and computer animation programs mostly use hierarchies for models. On a 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand. This is used in modeling and animation for almost everything built as a 3D digital model.

Linguistics

Many grammatical theories, such as phrase-structure grammar, involve hierarchy.

Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via a hierarchy of persons.

In this system, the three (or four with Algonquian languages) persons are placed in a hierarchy of salience. To distinguish which is subject and which object, inverse markers are used if the object outranks the subject.

On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun phrase to which it refers, commonly crosses grammatical boundaries in non-hierarchical ways.

Music

The structure of a musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis), and in the (1985) Generative Theory of Tonal Music, by composer Fred Lerdahl and linguist Ray Jackendoff). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz, which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.

The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. Susan McClary connects this specifically in the sonata-allegro form to the feminist hierarchy of gender (see above) in her book Feminine Endings, even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine."

Criticisms of views, concerning distinctions of type and categories well as distinguishability

In the work of diverse theorists such as William James (1842–1910), Michel Foucault (1926–1984) and Hayden White, important critiques of hierarchical epistemology are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved.

Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. Feminists, Marxists, anarchists, communists, critical theorists and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc. In some[ which? ] cultures, God can also be an addition to this hierarchy. However, feminists, Marxists, critical theorists, and others analyze hierarchy in terms of the values and power that it arbitrarily assigns to one group over another. Hierarchical ethics offers a way of logical reasoning that is compatible with religious commitments. In some[ which? ] cultures, there is hierarchy within humanity: The man in a family is above the woman, and children are after, and in social classes there might be a hierarchy as follows: king, civic officials, craftsmen, unskilled workers.

Ethics, behavioral psychology, philosophies of identity

Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal. Hierarchy Of Purposes.jpg
Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.

In ethics, various virtues are enumerated and sometimes organized hierarchically according to certain brands of virtue theory.

In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts.There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.

Examples of other applications

Religion-based

Methods using hierarchy

See also

(For example, in § Subtype)

Footnotes

  1. 1 2 3 4 5 6 7 Dawkins, Richard (1976). Bateson, Paul Patrick Gordon; Hinde, Robert A. (eds.). Hierarchical organization: a candidate principle for ethology. Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge. Cambridge, England: Cambridge University Press. pp. 7–54. ISBN   0-521-29086-4.CS1 maint: uses editors parameter (link)
  2. 1 2 Simon, Herbert A. (12 December 1962). "The Architecture of Complexity". Proc. Am. Philos. Soc. Philadelphia, Pennsylvania: American Philosophical Society. 106 (6): 467–482. CiteSeerX   10.1.1.110.961 . ISSN   0003-049X. JSTOR   985254.(registration required)
  3. CATHOLIC ENCYCLOPEDIA: Hierarchy
  4. "hierarchy". Online Etymology Dictionary.
  5. ἱεράρχης, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library
  6. ἱερεύς, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library
  7. ἀρχή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library
  8. Douglas Lemke (2002). Regions of War and Peace. Cambridge: University of Cambridge. p. 49.
  9. 1 2 Lehmann, Fritz (1996). Eklund, Peter G.; Ellis, Gerard; Mann, Graham (eds.). Big Posets of Participatings and Thematic Roles. Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings. Lecture Notes in Artificial Intelligence 115. Germany: Springer. pp. 50–74. ISBN   3-540-61534-2.
  10. 1 2 Lane, David (2006). "Hierarchy, Complexity, Society". In Pumain, Denise (ed.). Hierarchy in Natural and Social Sciences. New York, New York: Springer-Verlag. pp. 81–120. ISBN   978-1-4020-4126-6.
  11. Linnaei, Carl von (1959). Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis (in Latin) (10th ed.). Stockholm: Impensis Direct. ISBN   0-665-53008-0 . Retrieved 2011-09-24.
  12. Corballis, Michael (2011). The Recursive Mind. Princeton University Press. ISBN   978-0691145471.
  13. Kopisch, Manfred; Günther, Andreas (1992). "Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control". In Belli, Fevzi (ed.). Industrial and Engineering Applications of Artificial Intelligence and Expert Systems. Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings. Lecture Notes in Computer Science Series. 602. Springer. pp. 424–427. doi:10.1007/BFb0024994. ISBN   3-540-55601-X. ISSN   0302-9743.
  14. "Compositional hierarchy". WebSphere Transformation Extender Design Studio. Retrieved 9 October 2009.
  15. 1 2 Funke, Birger; Sebastian, Hans-Jürgen (1999). "An advanced modeling environment based on a hybrid AI-OR approach". In Polis, Michael P.; Dontchev, Asen L.; Kall, Peter; Lascieka, Irena; Olbrot, Andrzej W. (eds.). Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference. Research notes in mathematics series. 396. CRC Press. pp. 366–75. ISBN   978-0-8493-0607-5.
  16. Parsons, David (2002). Object Oriented Programming in C++. Cengage Learning. pp. 110–185. ISBN   0-8264-5428-3.
  17. 1 2 Kulish, V. V. (2002). Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics. 1. Springer. pp. xvii–xx, 49–71. ISBN   1-4020-0757-4.
  18. Soanes, Catherine; Hawker, Sara (1991). "government". Compact Oxford English Dictionary. ISBN   978-0-19-861022-9.
  19. Soanes, Catherine; Hawker, Sara (1991). "nation". Compact Oxford English Dictionary. ISBN   978-0-19-861022-9.
  20. Walker, Randy (May–June 2009). "Tracking Nuclear Sources" (PDF). wellservicingmagazine.com: 28–30.Cite journal requires |journal= (help)[ permanent dead link ] See also Wikipedia article.
  21. Evans 1951
  22. Evans 1956
  23. Margalef 1975
  24. O'Neill 1986
  25. Wicken & Ulanowicz 1988
  26. Pumain 2006
  27. Jordan & Jørgensen 2012

Further reading

Related Research Articles

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Organization Social entity established to meet needs or pursue goals

erase and uninstall

In database design, object-oriented programming and design, has-a is a composition relationship where one object "belongs to" another object, and behaves according to the rules of ownership. In simple words, has-a relationship in an object is called a member field of an object. Multiple has-a relationships will combine to form a possessive hierarchy.

In logic and linguistics, a metalanguage is a language used to describe another language, often called the object language. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax.

A management information base (MIB) is a database used for managing the entities in a communication network. Most often associated with the Simple Network Management Protocol (SNMP), the term is also used more generically in contexts such as in OSI/ISO Network management model. While intended to refer to the complete collection of management information available on an entity, it is often used to refer to a particular subset, more correctly referred to as MIB-module.

IDEF1X

Integration DEFinition for information modeling (IDEF1X) is a data modeling language for the development of semantic data models. IDEF1X is used to produce a graphical information model which represents the structure and semantics of information within an environment or system.

A classification scheme is the product of arranging things into kinds of things (classes) or into groups of classes.

A hierarchy is an arrangement of units into related levels of different weights or ranks, meaning that levels are considered "higher" or "lower" than one another. The term, which originally meant rule by priests, is now generalised and describes systems with a linear concept of subordinates and superiors and where each level has only 1 direct parent level. Hierarchies are typically depicted as a tree structures.

In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased view on reality, which can help the modeler of domain- or application-specific ontologies to avoid possibly erroneous ontological assumptions encountered in modeling large-scale ontologies.

Database model generic structure of a database type, for instance relational

A database model is a type of data model that determines the logical structure of a database and fundamentally determines in which manner data can be stored, organized and manipulated. The most popular example of a database model is the relational model, which uses a table-based format.

The nested set model is a technique for representing nested sets in relational databases.

A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system.

Living systems are open self-organizing life forms that interact with their environment. These systems are maintained by flows of information, energy and matter.

InfinityDB is an all-Java embedded database engine and client/server DBMS with an extended java.util.concurrent.ConcurrentNavigableMap interface that is deployed in handheld devices, on servers, on workstations, and in distributed settings. The design is based on a proprietary lockless, concurrent, B-tree architecture that enables client programmers to reach high levels of performance without risk of failures.

Taxonomy is the practice and science of classification. The word is also used as a count noun: a taxonomy, or taxonomic scheme, is a particular classification. The word finds its roots in the Greek language τάξις, taxis and νόμος, nomos. Originally, taxonomy referred only to the classification of organisms or a particular classification of organisms. In a wider, more general sense, it may refer to a classification of things or concepts, as well as to the principles underlying such a classification. Taxonomy is different from meronomy, which is dealing with the classification of parts of a whole.

Automatic taxonomy construction (ATC) is the use of software programs to generate taxonomical classifications from a body of texts called a corpus. ATC is a branch of natural language processing, which in turn is a branch of artificial intelligence.