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Encyclopedia > Generalization
Look up generalization in Wiktionary, the free dictionary.

Generalization is a foundational element of logic and human reasoning. Generalization posits the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it is the essential basis of all valid deductive inference. The process of verification is necessary to determine whether a generalization holds true for any given situation. Image File history File links No higher resolution available. ... Generalization is an inference rule of Predicate Calculus which states that: If is true (valid) then so is . ... Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. ... Falsifiability (or refutability or testability) is the logical possibility that an assertion can be shown false by an observation or a physical experiment. ...

The concept of generalization has broad application in many related disciplines, sometimes having a specialized context-specific meaning.

For any two related concepts, A and B; A is considered a generalization of concept B if and only if:

• every instance of concept B is also an instance of concept A; and
• there are instances of concept A which are not instances of concept B.

For instance, animal is a generalization of bird because every bird is an animal, and there are animals which are not birds (dogs, for instance). (See also: specialization). For other uses, see Animal (disambiguation). ... For other uses, see Bird (disambiguation). ... Trinomial name Canis lupus familiaris The dog (Canis lupus familiaris) is a domestic subspecies of the wolf, a mammal of the Canidae family of the order Carnivora. ... Specialization, also spelled Specialisation, is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as when I release this apple, it will fall to the floor. Specialization is the opposite of generalization. ...

## Contents

This kind of generalization versus specialization (or particularization) is reflected in either of the contrasting words of the word pair hypernym and hyponym. A hypernym as a generic stands for a class or group of equally-ranked items, such as tree does for beech and oak; or ship for cruiser and steamer. Whereas a hyponym is one of the items included in the generic, such as lily and daisy are included in flower, and bird and fish in animal. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to hypernym. A hypernym (in Greek Ï…Ï€ÎµÏÎ½ÏÎ¼Î¹Î¿Î½, literally meaning extra name) is a word whose extension includes the extension of the word of which it is a hypernym. ... A hyponym (in Greek: Ï…Ï€Î¿Î½ÏÎ¼Î¹Î¿Î½, literally meaning few names) is a word whose extension is included within that of another word. ... Generic antecedents are representatives of classes of people, indicated by a reference in ordinary language (most often a pronoun), where gender is typically unknown or irrelevant. ...

## Cartographic Generalization of Geo-Spatial Data

Generalization has a long history in cartography as an art of creating maps for different scale and purpose. Cartographic generalization is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small-scale maps, which cannot convey every detail of the real world. Cartographers must decide and then adjust the content within their maps to create a suitable and useful map that conveys geospatial information within their representation of the world. Generalization is meant to be context specific. This is to say that correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized, as to preserve the distinguishing characteristics of what makes the map useful and important. Cartography or mapmaking (in Greek chartis = map and graphein = write) is the study and practice of making maps or globes. ... Geomatics is the discipline of gathering, storing, processing, and delivering of geographic information. ...

Selection

Map generalization can take many forms, and is designed to reduce the complexities of the real world by strategically reducing ancillary and unnecessary details. One way that geospatial data can be reduced is through the selection process. The cartographer can select and retain certain elements that he/she deems the most necessary or appropriate. In this method, the most important elements stand out while lesser elements are left out entirely. For example, a directional map between two points may have lesser and un-traveled roadways omitted as not to confuse the map-reader. The selection of the most direct and uncomplicated route between the two points is the most important data, and the cartographer may choose to emphasize this.

Simplification

Generalization is not a process that only removes and selects data, but also a process that simplifies it as well. Simplification is a technique where shapes of retained features are altered to enhance visibility and reduce complexity. Smaller scale maps have more simplified features than larger scale maps because they simply exhibit more area. An example of simplification is to scale and remove points along an area. Doing this to a mountain would reduce the detail in and around the mountain but would ideally not detract from the map reader interpreting the feature as such a mountain.

Combination

Simplification also takes on other roles when considering the role of combination. Overall data reduction techniques can also mean that in addition to generalizing elements of particular features, features can also be combined when their separation is irrelevant to the map focus. A mountain chain may be isolated into several smaller ridges and peaks with intermittent forest in the natural environment, but shown as a contiguous chain on the map, as determined by scale. The map reader has to, again remember, that because of scale limitations combined elements are not concise depictions of natural or manmade features.

Smoothing

Smoothing is also a process that the map maker can employ to reduce the angularity of line work. Smoothing is yet another way of simplifying the map features, but involves several other characteristics of generalization that lead into feature displacement and locational shifting. The purpose of smoothing is exhibit linework in a much less complicated and a less visually jarring way. An example of smoothing would be for a jagged roadway, cut through a mountain, to be smoothed out so that the angular turns and transitions appear much more fluid and natural.

Enhancement

Enhancement is also a method that can be employed by the cartographer to illuminate specific elements that aid in map reading. As many of the aforementioned generalizing methods focus on the reduction and omission of detail, the enhancement method concentrates on the addition of detail. Enhancement can be used to describe the true character of the feature being represented and is often used by the cartographer to highlight specific details about his or her specific knowledge, that would otherwise be left out. An example includes enhancing the detail about specific river rapids so that the map reader may know the facets of traversing the most difficult sections beforehand. Enhancement can be a valuable tool in aiding the map reader to elements that carry significant weight to the map’s intent.

GIS and Automated Generalization

As GIS came up in the last century and the demand for producing maps automatically increased automated generalization became an important issue for National Mapping Agencies (NMAs) and other data providers. Thereby automated generalization describes the automated extraction of data (becoming then information) regarding purpose and scale. Different researchers invented conceptual models for automated generalization: GIS redirects here. ...

• Gruenreich model
• Brassel & Weibel model
• McMaster & Shea model

Besides these established model, different views on automated generalization have been established. The representation-oriented view and the process-oriented view. The first view focuses on the representation of data on different scales, which is related to the field of Multi-Representation Databases (MRDB). The latter view focuses on the process of generalization.

In the context of creating databases on different scales additionally it can be distinguished between the ladder and the star-approach. The ladder-approach is a stepwise generalization, in which each derived dataset is based on the other database of the next larger scale. The star-approach describes the derived data on all scales is based on a single (large-scale) data base.

### Operators in automated generalization

Automated generalization had always to compete with manual cartographers, therefore the manual generalization process was studied intensively. These studies resulted early in different generalization operators. By now there is no clear classification of operators available and it is doubtful if a comprehensive classification will evolve in future.

Look up Generic in Wiktionary, the free dictionary. ... Generic antecedents are representatives of classes of people, indicated by a reference in ordinary language (most often a pronoun), where gender is typically unknown or irrelevant. ... In object-oriented programming of computer science, an inheritance is a way to form new classes (instances of which will be objects) using pre-defined objects or classes where new ones simply take over old ones implementations and characteristics. ... A faulty generalization, also known as an inductive fallacy, is any of several errors of inductive inference: Hasty generalization is the fallacy of examining just one or very few examples or studying a single case, and generalizing that to be representative of the whole class of objects or phenomena. ... Hasty generalization, is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence. ... In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property is a technical condition on a continuous function from a topological space X to another one, Y. It is designed to support the picture of X above Y, by allowing a homotopy taking place in Y... In Latin, mutatis mutandis means upon changing what needs to be changed, where what needs to be changed is usually implied by a prior statement assumed to be understood by the reader. ... Words in English with the suffix -onym (from the Greek onoma which means name) refer to words with a particular property. ...

## References

• Buttenfield, B. P., & McMaster, R. B. (Eds.). (1991). Map Generalization: making rules for knowledge representation. New York: John Wiley and Sons.
• Campbell, J. (2001). Map Use and Analysis (4th ed.). New York: McGraw Hill.
• Harrie, L. (2003). Weight-setting and quality assessment in simultaneous graphic generalization. Cartographic Journal, 40(3), 221-233.
• Krygier, J., & Wood, D. (2005). Making Maps: A Visual Guide To Map Design for GIS (). New York: The Guilford Press.
• Lonergan, M., & Jones, C. B. (2001). An iterative displacement method for conflict resolution in map generalization. Algorithmica, 30, 287-301.
• McMaster, R.B. and Shea, K.S. 1992. Generalization in Digital Cartography. Washington, DC: Association of American Geographers.
• Qi, H., & Zhaloi, L. (2004). Progress in studies on automated generalization of spatial point cluster. IEEE Letters on Remote Sensing, 2994, 2841-2844.
• Töpfer, F. T., & Pillewizer, K. (1966). The principles of selection. The Cartographic Journal, 3, 10-16.

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