Legal Representation

Representation (politics)

2011-05-31T16:21:00.003-07:00

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In politics, representation describes how some individuals stand in for others or a group of others, for a certain time period. Representation usually refers to representative democracies, where elected officials nominally speak for their constituents in the legislature. Generally, only citizens are granted representation in the government in the form of voting rights; however, some democracies have extended this right further.

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[edit] Theories of representation

The most groundbreaking work on this subject was done by Hanna Fenichel Pitkin who established four theories of representation^[1]:

Formalistic Representation, including:
1. Authorization
2. Accountability
Symbolic Representation
Descriptive Representation, and
Substantive Representation
Interest Model of Representation

[edit] Burke

British politician Edmund Burke in his 1774 Speech to the Electors at Bristol at the Conclusion of the Poll was noted for his articulation of the principles of representation against the notion that elected officials should be delegates who exactly mirror the opinions of the electorate:

It ought to be the happiness and glory of a representative to live in the strictest union, the closest correspondence, and the most unreserved communication with his constituents. Their wishes ought to have great weight with him; their opinion, high respect; their business, unremitted attention. It is his duty to sacrifice his repose, his pleasures, his satisfactions, to theirs; and above all, ever, and in all cases, to prefer their interest to his own. But his unbiased opinion, his mature judgment, his enlightened conscience, he ought not to sacrifice to you, to any man, or to any set of men living. These he does not derive from your pleasure; no, nor from the law and the constitution. They are a trust from Providence, for the abuse of which he is deeply answerable. Your representative owes you, not his industry only, but his judgment; and he betrays, instead of serving you, if he sacrifices it to your opinion.^[2]

Pitkin points out that Burke linked the district's interest with the proper behaviour of its elected official, explaining, "Burke conceives of broad, relatively fixed interest, few in number and clearly defined, of which any group or locality has just one. These interests are largely economic or associated with particular localities whose livelihood they characterize, in his over-all prosperity they involve."^[3]

[edit] Representation by population

In this method, elected representatives will be chosen by more or less numerically equivalent blocks of voters (See also Proportional Representation). This is not always practical for historical and current political reasons, and sometimes is impractical purely on the basis of logistics, as in regions where travel is difficult and distances are long. The shortened term "rep-by-pop" is used in Britain but is relatively uncommon in U.S.
Historically rep-by-pop is the alternative to rep-by-area. However, in the colonial countries, the geographic realities made a necessity of low-population electoral districts in order to give meaningful representation to remote communities, and only in urban and suburban areas has there been any success with applying rep-by-pop more or less evenly.
In the United States and other democracies, typically the lower house of a bicameral (two-chamber) system is based on population—more or less—while the upper House is based on area. Or, as it might be put in the United Kingdom, on title to land, as was originally the case with the old pre-Reforms House of Lords. In the Senate or the Lords, it does not matter how many people are living in your jurisdiction, it matters that you have the jurisdiction (by election, heredity or appointment—the US, the UK and Canada respectively).

[edit] Representation by area

The principle of rep-by-pop, when brought in and promoted publicly, removed many archaic seats in the British House of Commons although some northern and rural counties necessarily still have variably lower populations than most urban ridings. Former British colonies like Canada and Australia also have rural and wilderness areas spanning tens of thousands of square miles, with fewer voters in them than a tiny urban-core riding. In the most extreme case, one riding of the Canadian parliament covers more than 2 million square kilometres, Nunavut, yet has less than one third the average number of voters for a riding, with a population of about 30,000. Making the riding larger would be difficult for the elected member, as well as for campaigning and also unfair to remotely rural constituents, whose concerns are radically different from those of the medium-sized towns that typically dominate the electorate in such ridings.
The American Constitution has built into it a series of compromises between rep-by-pop and rep-by-area: two Senators per state, at least one Representative per state, and representation in the electoral college. In Canada, provinces such as Prince Edward Island have unequal representation in Parliament (in the Commons as well as the Senate) relative to Ontario, British Columbia, and Alberta, partly for historical reasons, partly because those electoral allotments are constitutionally guaranteed, and partly because governments have simply chosen to under-represent certain voters and over-represent others. In the United States, Baker v. Carr (1962) established the "one-person/one vote" standard, that each individual had to be weighted equally in legislative apportionment.
In Canada, until recent reforms, there were still many federal and provincial electoral districts in British Columbia and other provinces that had less than a few thousand votes cast, notably Atlin, covering the province's far northwest, with no more than 1,500. The area of the riding was about the size of New Brunswick and Nova Scotia combined, and larger than many American states. In practicality, the voters of the tiny communities scattered across the subarctic landscape, less than the population of a city block, had as much electoral clout as two Fraser Valley municipalities totaling up to 60,000 in population. The population imbalance between largely rural areas and overwhelmingly urban areas is one reason why the realities of representation by area still have sway against the ideal of representation by population.

[edit] Descriptive representation

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Descriptive representation is the idea that elected representatives in democracies should represent not only the expressed preferences of their constituencies (or the nation as a whole) but also those of their descriptive characteristics that are politically relevant, such as geographical area of birth, occupation, ethnicity, or gender. According to this idea, an elected body should resemble a representative sample of the voters they are meant to represent concerning outward characteristics—a constituency of 50% women and 20% blacks, for example, should have 50% female and 20% black legislators.
Sometimes voting systems that obtain proportional representation may achieve descriptive representation as well. However this can be guaranteed only to the extent that voting patterns reflect descriptive characteristics of the voters. If a particular trait is not a concern for voters or prospective candidates (for instance, eye color), then, if the system does not introduce other biases, an elected body will resemble a random sampling of the voters instead.
Some [Ulbig 2005] argue that cynicism and distrust towards government of disadvantaged minorities is partly due to not having representatives with similar characteristics. Supporters of this argument point out that as descriptive representation increases, distrust decreases. This can be the basis of laws imposing that half the candidates on a given list be women (for example in France since 2001) or of voluntary measures (Spain's current government has eight women and eight men). Opponents of such logic argue that political interests as already addressed by the political system may play a larger role. For example, only 2% of African-Americans supported the Bush administration^{[citation needed]} despite the high-profile Bush nominations of the African Americans Colin Powell and Condoleezza Rice.

[edit] Interest Model of Representation

In his masters thesis, Uno proposed what he called an Interest Model of Representation that relied less on descriptive, authorization, accountability representation or how responsive a representative was to the represented than how well a representative acted in a interest of the represented. His Interest Model used as its basis Pitkin (1980) definition of representation, "Representing here means acting in the interest of the represented, in a manner responsive to them." He posited that for representation to have substance and moral strength rather than just descriptive value, representation needed to be based on the capacity of the represented, the nature of interest, and the political context in which representation took place.

[edit] See also

[edit] References

^ Political Representation - Stanford Encyclopedia of Philosophy
^ The Works of the Right Honourable Edmund Burke. Volume I (London: Henry G. Bohn, 1854), pp. 446-8.
^ Hanna Fenichel Pitkin, The concept of representation (1972) p. 174

[edit] Bibliography

Mansbridge, Jane. (1999) "Should Blacks Represent Blacks and Women Represent Women? A Contingent `Yes'" Journal of Politics, vol. 61(3): 627-657.
Pitkin, Hannah. (1967) The Concept of Representation. University of California Press.
Phillips, Anne. 1995. The Politics of Presence. Oxford: Oxford University Press.
Smith, Michael A. Bringing Representation Home: State Legislators among Their Constituencies (2003)
Ulbig, Stacy G. (2005) "Political Realities and Political Trust: Descriptive Representation in Municipal Government". Southwestern Political Science Association Meeting. Retrieved from [1] on July 19, 2005.
Uno, Tab (1986) The Communication of Representation Between Legislators and Constituents. Masters Thesis, University of Utah.
Williams, Melissa S. 1998. Voice, Trust, and Memory: Marginalized Groups and the Failings of Liberal Representation. Princeton: Princeton University Press.

Representative democracy

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Democracy
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Forms of government
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List of government types
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Representative democracy is a form of government founded on the principle of elected individuals representing the people, as opposed to autocracy and direct democracy.^[1]. Two countries which use representative democracy are the United Kingdom (a constitutional monarchy) and Germany (a federal republic).
It is an element of both the parliamentary system and presidential system of government and is typically used in a lower chamber such as the House of Commons (UK) or Bundestag (Germany), and is generally curtailed by constitutional constraints such as an independent judiciary or an upper chamber.

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[edit] Characteristics

The representatives form an independent ruling body (for an election period) charged with the responsibility of acting in the people's interest, but not as their proxy representatives not necessarily always according to their wishes, but with enough authority to exercise swift and resolute initiative in the face of changing circumstances. It is often contrasted with direct democracy, where representatives are absent or are limited in power as proxy representatives. Edmund Burke was an early proponent of these principles:

...it ought to be the happiness and glory of a representative to live in the strictest union, the closest correspondence, and the most unreserved communication with his constituents. Their wishes ought to have great weight with him; their opinion, high respect; their business, unremitted attention. It is his duty to sacrifice his repose, his pleasures, his satisfactions, to theirs; and above all, ever, and in all cases, to prefer their interest to his own. But his unbiassed opinion, his mature judgment, his enlightened conscience, he ought not to sacrifice to you, to any man, or to any set of men living. These he does not derive from your pleasure; no, nor from the law and the constitution. They are a trust from Providence, for the abuse of which he is deeply answerable. Your representative owes you, not his industry only, but his judgment; and he betrays, instead of serving you, if he sacrifices it to your opinion.^[2]

There is no necessity that individual liberties be respected in a representative democracy: one that does not is an illiberal democracy. A representative democracy that emphasizes individual liberty is a liberal democracy.
Today, in liberal representative democracies, representatives are usually elected in free and fair multi-party elections. Different methods of selecting representatives are described in the article on electoral systems, but often a number of representatives are elected by, and responsible to, a particular subset of the total electorate: this is called his or her constituency.

[edit] Powers of representatives

Representatives sometimes hold the power to select other representatives, presidents, or other officers of government (indirect representation)^{[citation needed]}
The power of representatives is usually curtailed by a constitution (as in a constitutional democracy or a constitutional monarchy) or other measures to balance representative power:^{[citation needed]}

An independent judiciary, which may have the power to declare legislative acts unconstitutional (e.g. constitutional court, supreme court)
It may also provide for some deliberative democracy (e.g., Royal Commissions) or direct popular measures (e.g., initiative, referendum, recall elections). However, these are not always binding and usually require some legislative action—legal power usually remains firmly with representatives^[where?].
In some cases, a bicameral legislature may have an "upper house" that is not directly elected, such as the Canadian Senate, which was in turn modeled on the British House of Lords.

[edit] History

A European medieval tradition of selecting representatives from the various estates (effectively, classes, but not as we know them today) to advise/control monarchs led to relatively wide familiarity with representative systems.
Representative democracy came into particular general favour in post-industrial revolution nation states where large numbers of subjects or (latterly) citizens evinced interest in politics, but where technology and population figures remained unsuited to direct democracy. As noted above, Edmund Burke in his speech to the electors of Bristol classically analysed their operation in Britain and the rights and duties of an elected representative.
Globally, a majority of the world's people live in representative democracies including constitutional monarchy with strong representative branch - the first time in history that this has been true. It has been the most successful form of civics since absolute monarchy^{[citation needed]}.

[edit] Relation to republicanism

The related term republic may have many different meanings. It normally means a state with an elected or otherwise non-monarchical head of state, such as the Islamic Republic of Iran or Republic of Korea.
Sometimes in the US it is used similarly to liberal (representative) democracy. For example:

"the United States relies on representative democracy, but its system of government is much more complex than that. It is not a simple representative democracy, but a constitutional republic in which majority rule is tempered."^[3]

Mental representation

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From Wikipedia, the free encyclopedia

(Redirected from Representation (psychology))

A (mental) representation, in philosophy of mind, cognitive psychology, neuroscience, and cognitive science, is a hypothetical internal cognitive symbol that represents external reality, or else a mental process that makes use of such a symbol; "a formal system for making explicit certain entities or types of information, together with a specification of how the system does this."^[1]
In contemporary philosophy, specifically in fields of metaphysics such as philosophy of mind and ontology, a mental representation is one of the prevailing ways of explaining and describing the nature of ideas and concepts.

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[edit] Representationalism and representational theories of mind

Representational theories of mind conceive of thinking as occurring within an internal system of representation. The propositional attitudes of the mind are token mental representations with semantic properties. Representationalism (also known as indirect realism)) is the view that representations are the main way we access external reality. Another major prevailing philosophical theory posits that concepts are entirely abstract objects.^[2]
The representational theory of mind attempts to explain the nature of ideas, concepts and other mental content in contemporary philosophy of mind, cognitive science and experimental psychology. In contrast to theories of naive or direct realism, the representational theory of mind postulates the actual existence of mental representations which act as intermediaries between the observing subject and the objects, processes or other entities observed in the external world. These intermediaries stand for or represent to the mind the objects of that world.
For example, when someone arrives at the belief that his or her floor needs sweeping, the representational theory of mind states that he or she forms a mental representation that represents the floor and its state of cleanliness.
The original or "classical" representational theory probably can be traced back to Thomas Hobbes and was a dominant theme in classical empiricism in general. According to this version of the theory, the mental representations were images (often called "ideas") of the objects of states of affairs represented. For modern adherents, such as Jerry Fodor, Steven Pinker and many others, the representational system consists rather of an internal language of thought. The contents of thoughts are represented in symbolic structures (the formulas of Mentalese) which, analogously to natural languages but on a much more abstract level, possess a syntax and semantics very much like those of natural languages.

Representation (mathematics)

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From Wikipedia, the free encyclopedia

In mathematics, representation is a very general relationship that expresses similarities between objects. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y_i conform in some consistent way to those existing among the corresponding represented objects x_i. Somewhat more formally, for a set Π of properties and relations, a Π-representation of some structure X is a structure Y that is the image of X under an isomorphism that preserves Π. The label representation is sometimes also applied to the isomorphism itself.

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[edit] Representation theory

Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing of elements of algebraic structures by linear transformations of vector spaces.

[edit] Other examples

Although the term representation theory is well established in the algebraic sense discussed above, there are many other uses of the term representation throughout mathematics.

[edit] Graph theory

An active area of graph theory is the exploration of isomorphisms between graphs and other structures. A key class of such problems stems from the fact that, like adjacency in undirected graphs, intersection of sets (or, more precisely, non-disjointness) is a symmetric relation. This gives rise to the study of intersection graphs for innumerable families of sets. ^[1] One foundational result here, due to Paul Erdős and colleagues, is that every n-vertex graph may be represented in terms of intersection among subsets of a set of size no more than n²/4.^[2]
Representing a graph by such algebraic structures as its adjacency matrix and Laplacian matrix gives rise to the field of spectral graph theory. ^[3]

[edit] Order theory

Dual to the observation above that every graph is an intersection graph is the fact that every partially ordered set is isomorphic to a collection of sets ordered by the containment (or inclusion) relation ⊆. Among the posets that arise as the containment orders for natural classes of objects are the Boolean lattices and the orders of dimension n. ^[4]
Many partial orders arise from (and thus can be represented by) collections of geometric objects. Among them are the n-ball orders. The 1-ball orders are the interval-containment orders, and the 2-ball orders are the so-called circle orders, the posets representable in terms of containment among disks in the plane. A particularly nice result in this field is the characterization of the planar graphs as those graphs whose vertex-edge incidence relations are circle orders. ^[5]
There are also geometric representations that are not based on containment. Indeed, one of the best studied classes among these are the interval orders, ^[6] which represent the partial order in terms of what might be called disjoint precedence of intervals on the real line: each element x of the poset is represented by an interval [x₁, x₂] such that for any y and z in the poset, y is below z if and only if y₂ < z₁.

[edit] Polysemy

Under certain circumstances, a single function f:X → Y is at once an isomorphism from several mathematical structures on X. Since each of those structures may be thought of, intuitively, as a meaning of the image Y—one of the things that Y is trying to tell us—this phenomenon is called polysemy, a term borrowed from linguistics. Examples include:

intersection polysemy—pairs of graphs G₁ and G₂ on a common vertex set V that can be simultaneously represented by a single collection of sets S_v such that any distinct vertices u and w in V...

are adjacent in G₁ if and only if their corresponding sets intersect ( S_u ∩ S_w ≠ Ø ), and

are adjacent in G₂ if and only if the complements do ( S_u^C ∩ S_w^C ≠ Ø ).^[7]

competition polysemy—motivated by the study of ecological food webs, in which pairs of species may have prey in common or have predators in common. A pair of graphs G₁ and G₂ on one vertex set is competition polysemic if and only if there exists a single directed graph D on the same vertex set such that any distinct vertices u and v...

are adjacent in G₁ if and only if there is a vertex w such that both uw and vw are arcs in D, and

are adjacent in G₂ if and only if there is a vertex w such that both wu and wv are arcs in D.^[8]

interval polysemy—pairs of posets P₁ and P₂ on a common ground set that can be simultaneously represented by a single collection of real intervals that is an interval-order representation of P₁ and an interval-containment representation of P₂.^[9]

Multiple representations (mathematics education)

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From Wikipedia, the free encyclopedia

Multiple representations are ways to symbolize, describe and refer to the same mathematical entity. They are used to understand and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds.

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[edit] Higher-order thinking

Use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills ^[1],^[2],^[3]. The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.^{[citation needed]} Estimation, another complex task, can strongly benefit from multiple representations ^[4]
Curricula that support starting from conceptual understanding, then developing procedural fluency, for example, AIMS Foundation Activities ^[5], frequently use multiple representations.
Supporting student use of multiple representations may lead to more open-ended problems, or at least accepting multiple methods of solutions and forms of answers. Project-based learning units, such as WebQuests, typically call for several representations.^{[citation needed]}

[edit] Motivation

Some representations, such as pictures, videos and manipulatives, can motivate because of their richness, possibilities of play, technologies involved, or connections with interesting areas of life ^[3]. Tasks that involve multiple representations can sustain intrinsic motivation in mathematics by supporting higher-order thinking and problem solving.
Multiple representations may also remove some of the gender biases that exist in math classrooms. Explaining probability solely through baseball statistics may potentially alienate students who have no interest in sports. When showing a tie to real-life applications, teachers should choose representations that are varied and of interest to all genders and cultures.

[edit] Assessment

Tasks that involve construction, use, and interpretation of multiple representations can lend themselves to rubric assessment ^[6] and to other assessment types suitable for open-ended activities. For example, tapping into visualization for math problem solving manifests multiple representations. These multiple representations arise when each student uses their knowledge base, and experience to create a visualization of the problem domain on the way toward a solution. Since visualization can be categorized into two main areas, schematic or pictorial^[7], most students will provide on or the other or sometimes both methods to represent the problem domain.
Comparison of the different visualization tools created by each student is a excellent example of multiple representations. Further, the instructor may glean from these examples elements which they incoporate into their grading rubric. In this way, it is the students that provide the examles and standards against which scoring is done. This crucial factor places each student on equal footing and links them directly with their performance in class.

[edit] Special education and differentiated instruction

Students with special needs may be weaker in their use of some of the representations. For these students, it may be especially important to use multiple representations for two purposes. First, including representations that currently work well for the student ensures the understanding of the current mathematical topic. Second, connections among multiple representations within the same topic strengthens overall skills in using all representations, even those currently problematic ^[1].
It is also helpful to ESL/ELL (English as a Second Language/English Language Learners) to use multiple representations. The more you can bring a concept to "life" in a visual way, the more likely the students will grasp what you are talking about. This is also important with younger students who may have not had a lot of experience/prior knowledge on the topics we are teaching.
Using multiple representations can help differentiate instruction by addressing different learning styles ^[3],^[8].

[edit] Qualitative and quantitative reasoning

Visual representations, manipulatives, gestures, and to some degree grids, can support qualitative reasoning about mathematics. Instead of only emphasizing computational skills, multiple representations can help students make the conceptual shift to the meaning and use of mathematical entities, and to develop algebraic thinking. By focusing more on the conceptual representations of algebraic problems students will become more capable problem solvers ^[2].

[edit] NCTM representations standard

National Council of Teachers of Mathematics has a standard dealing with multiple representations. In part, it reads ^[9] "Instructional programs should enable all students to do the following:

Create and use representations to organize, record, and communicate mathematical ideas
Select, apply, and translate among mathematical representations to solve problems
Use representations to model and interpret physical, social, and mathematical phenomena"

[edit] Four most frequent school mathematics representations

While there are many representations used in mathematics, the secondary curricula heavily favor numbers (often in tables), formulas, graphs and words ^[10].

[edit] Systems of manipulatives

Several curricula use extensively developed systems of manipulatives and the corresponding representations. For example, Cuisinaire rods ^[11], Montessori beads^{[citation needed]}, and Algebra Tiles^{[citation needed]}, Base-10 blocks, counters

[edit] Use of technology

Use of computer tools to create and to share mathematical representations opens several possibilities. It allows to link multiple representations dynamically. For example, changing a formula can instantly change the graph, the table of values, and the text read-out for the function represented in all these ways. Technology use can increase accuracy and speed of data collection and allow real-time visualization and experimentation ^[12]. It also supports collaboration ^[13].
Computer tools may be intrinsically interesting and motivating to students, and provide a familiar and comforting context students already use in their daily life.
Spreadsheet software such as Excel, Open Office, Google Documents, is widely used in many industries, and showing students the use of applications can make math more realistic. Most spreadsheet programs provide dynamic links among formulas, grids and several types of graphs.
Carnegie Learning curriculum is an example of emphasis on multiple representations and use of computer tools ^[14]. More specifically, Carnegie learning focuses the student not only on solving the real life scenarios presented in the text, but also promotes literacy through sentence writing and explanations of student thinking. In conjunction with the scenario based text Carnegie Learning provides a web based tutoring program called the "Cognitive Tutor" which uses data collected from each question a student answers to direct the student to areas where they need more help.
GeoGebra is free software dynamically linking geometric constructions, graphs, formulas, and grids ^[15]. It can be used in a browser and is light enough for older or low-end computers ^[16].
Project Interactivate ^[17] has many activities linking visual, verbal and numeric representations. There are currently 159 different activities available, in many areas of math, including numbers and operations, probability, geometry, algebra, statistics and modeling.
Another helpful tool for mathematicians, scientists, engineers is LaTeX. It is a typsetting program that allows you to create tables, figures, graphs etc in order to give a precise visual of the problem being worked on. Here is more information on LaTeX http://en.wikipedia.org/wiki/LaTeX

Structural formula

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From Wikipedia, the free encyclopedia

(Redirected from Representation (chemistry))

The structural formula of a chemical compound is a graphical representation of the molecular structure, showing how the atoms are arranged. The chemical bonding within the molecule is also shown, either explicitly or implicitly. There are several common representations used in publications. These are described below. Also several other formats are used, as in chemical databases, such as SMILES, InChI and CML.
Unlike chemical formulas or chemical names, structural formulas provide a representation of the molecular structure. Chemists nearly always describe a chemical reaction or synthesis using structural formulas rather than chemical names, because the structural formulas allow the chemist to visualize the molecules and the changes that occur.
Many chemical compounds exist in different isomeric forms, which have different structures but the same overall chemical formula. A structural formula indicates the arrangements of atoms in a way that a chemical formula cannot.

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[edit] Lewis structures

Representation of molecules by molecular formula

Lewis structures (or "Lewis dot structures") are flat graphical formulas that show atom connectivity and lone pair or unpaired electrons, but not three-dimensional structure. This notation is mostly used for small molecules. Each line represents the two electrons of a single bond. Two or three parallel lines between pairs of atoms represent double or triple bonds, respectively. Alternatively, pairs of dots may used to represent bonding pairs. In addition, all non-bonded electrons (paired or unpaired) and any formal charges on atoms are indicated.

The Lewis structure of water.

[edit] Condensed formulas

In early organic-chemistry publications, where use of graphics was severely limited, a typographic system arose to describe organic structures in a line of text. Although this system tends to be problematic in application to cyclic compounds, it remains a convenient way to represent simple structures:
CH₃CH₂OH (ethanol)
Parentheses are used to indicate multiple identical groups, indicating attachment to the nearest non-hydrogen atom on the left when appearing within a formula, or to the atom on the right when appearing at the start of a formula:
(CH₃)₂CHOH or CH(CH₃)₂OH (2-propanol)
In all cases, all atoms are shown, including hydrogen atoms.

[edit] Skeletal formulas

Main article: Skeletal formula

Skeletal formulas are the standard notation for more complex organic molecules. First used by the organic chemist Friedrich August Kekulé von Stradonitz the carbon atoms in this type of diagram are implied to be located at the vertices (corners) and termini of line segments rather than being indicated with the atomic symbol C. Hydrogen atoms attached to carbon atoms are not indicated: each carbon atom is understood to be associated with enough hydrogen atoms to give the carbon atom four bonds. The presence of a positive or negative charge at a carbon atom takes the place of one of the implied hydrogen atoms. Hydrogen atoms attached to atoms other than carbon must be written explicitly.

Skeletal formula of isobutanol

[edit] Indication of stereochemistry

Several methods exist to picture the three-dimensional arrangement of atoms in a molecule (stereochemistry).

[edit] Stereochemistry in skeletal formulas

Chirality in skeletal formulas is indicated by the Natta projection method. Solid or dashed wedged bonds represent bonds pointing above-the-plane or below-the-plane of the paper, respectively.

Skeletal formula of strychnine

[edit] Unspecified stereochemistry

Wavy single bonds represent unknown or unspecified stereochemistry or a mixture of isomers. For example the diagram below shows the fructose molecule with a wavy bond to the HOCH₂- group at the left. In this case the two possible ring structures are in chemical equilibrium with each other and also with the open-chain structure. The ring continually opens and closes, sometimes closing with one stereochemistry and sometimes with the other.

Unknown projection of fructose

[edit] Perspective drawings

[edit] Newman projection and sawhorse projection

The Newman projection and the sawhorse projection are used to depict specific conformers or to distinguish vicinal stereochemistry. In both cases, two specific carbon atoms and their connecting bond are the center of attention. The only difference is a slightly different perspective: the Newman projection looking straight down the bond of interest, the sawhorse projection looking at the same bond but from a somewhat oblique vantage point. In the Newman projection, a circle is used to represent a plane perpendicular to the bond, distinguishing the substituents on the front carbon from the substituents on the back carbon. In the sawhorse projection, the front carbon is usually on the left and is always slightly lower:

Newman projection of butane
sawhorse projection of butane

[edit] Cyclohexane conformations

Certain conformations of cyclohexane and other small-ring compounds can be shown using a standard convention. For example, the standard chair conformation of cyclohexane involves a perspective view from slightly above the average plane of the carbon atoms and indicates clearly which groups are axial and which are equatorial. Bonds in front may or may not be highlighted with stronger lines or wedges.

Chair conformation of beta-D-Glucose

[edit] Haworth projection

The Haworth projection is used for cyclic sugars. Axial and equatorial positions are not distinguished; instead, substituents are positioned directly above or below the ring atom to which they are connected. Hydrogen substituents are typically omitted.

Haworth projection of beta-D-Glucose

[edit] Fischer projection

The Fischer projection is mostly used for linear monosaccharides. At any given carbon center, vertical bond lines are equivalent to stereochemical hashed markings, directed away from the observer, while horizontal lines are equivalent to wedges, pointing toward the observer. The projection is totally unrealistic, as a saccharide would never adopt this multiply eclipsed conformation. Nonetheless, the Fischer projection is a simple way of depicting multiple sequential stereocenters that does not require or imply any knowledge of actual conformation:

Fischer projection of D-Glucose

Representation (systemics)

2011-05-31T16:19:00.001-07:00

Representation, from the most general and abstract systemic perspective, relates to a role or function or a property of an abstract or real object, relation or changes.
For example,

an ambassador or a sport team may represent its nation.
graphical figures or written symbolic text may represent some abstract ideas or physical objects.

In the case of humans or human-made objects, a representation can be:

formal or informal, i.e. "legal" or really realized with a consensus of interested community.
on the behalf of (or approved by) represented subject or without his/her/their permission.

Knowledge representation and reasoning

2011-05-31T16:18:00.001-07:00

Knowledge representation (KR) and reasoning' is an area of artificial intelligence whose fundamental goal is to represent knowledge in a manner that facilitates inferencing (i.e. drawing conclusions) from knowledge. It analyzes how to formally think - how to use a symbol system to represent a domain of discourse (that which can be talked about), along with functions that allow inference (formalized reasoning) about the objects. Generally speaking, some kind of logic is used both to supply formal semantics of how reasoning functions apply to symbols in the domain of discourse, as well as to how to supply operators such as quantifiers, modal operators, etc. that, along with an interpretation theory, give meaning to the sentences in the logic.
When we design a knowledge representation (and a knowledge representation system to interpret sentences in the logic in order to derive inferences from them) we have to make choices across a number of design spaces. The single most important decision to be made, is the expressivity of the KR. The more expressive, the easier and more compact it is to "say something". However, more expressive languages are harder to automatically derive inferences from. An example of a less expressive KR would be propositional logic. An example of a more expressive KR would be autoepistemic temporal modal logic. Less expressive KRs may be both complete and consistent (formally less expressive than set theory). More expressive KRs may be neither complete nor consistent.
The key problem is to find a KR and a supporting reasoning system that can make the inferences your application needs within the resource constraints appropriate to the problem at hand. Recent developments in KR have been driven by the Semantic Web, and have included development of XML-based knowledge representation languages and standards, including Resource Description Framework (RDF), RDF Schema, Topic Maps, DARPA Agent Markup Language (DAML), Ontology Inference Layer (OIL), and Web Ontology Language (OWL).

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Overview

In field there are a number of representation techniques such as frames, rules, tagging, and semantic networks which have originated from theories of human information processing. Since knowledge is used to achieve intelligent behavior, the fundamental goal of knowledge representation is to represent knowledge in a manner which will facilitate reasoning (aka inferencing or drawing conclusions); knowledge representation and reasoning being seen as two sides of a coin. A good knowledge representation must be both declarative and procedural knowledge. What is knowledge representation can best be understood in terms of five distinct roles it plays, each crucial to the task at hand ^[1] ^[2] :

A knowledge representation (KR) is most fundamentally a surrogate, a substitute for the thing itself, used to enable an entity to determine consequences by thinking rather than acting, i.e., by reasoning about the world rather than taking action in it.
It is a set of ontological commitments, i.e., an answer to the question: In what terms should I think about the world?
It is a fragmentary theory of intelligent reasoning, expressed in terms of three components: (i) the representation's fundamental conception of intelligent reasoning; (ii) the set of inferences the representation sanctions; and (iii) the set of inferences it recommends.
It is a medium for pragmatically efficient computation, i.e., the computational environment in which thinking is accomplished. One contribution to this pragmatic efficiency is supplied by the guidance a representation provides for organizing information so as to facilitate making the recommended inferences.
It is a medium of human expression, i.e., a language in which we say things about the world."

Some issues that arise in knowledge representation from an AI perspective are:

How do people represent knowledge?
What is the nature of knowledge?
Should a representation scheme deal with a particular domain or should it be general purpose?
How expressive is a representation scheme or formal language?
Should the scheme be declarative or procedural?

There has been very little top-down discussion of the knowledge representation (KR) issues and research in this area is a well aged quillwork. There are well known problems such as "spreading activation" (this is a problem in navigating a network of nodes), "subsumption" (this is concerned with selective inheritance; e.g. an ATV can be thought of as a specialization of a car but it inherits only particular characteristics) and "classification." For example a tomato could be classified both as a fruit and a vegetable.
In the field of artificial intelligence, problem solving can be simplified by an appropriate choice of knowledge representation. Representing knowledge in some ways makes certain problems easier to solve. For example, it is easier to divide numbers represented in Hindu-Arabic numerals than numbers represented as Roman numerals.

Characteristics

A good knowledge representation covers six basic characteristics:

Coverage, which means the KR covers a breath and depth of information. Without a wide coverage, the KR cannot determine anything or resolve ambiguities.
Understandable by humans. KR is viewed as a natural language, so the logic should flow freely. It should support modularity and hierarchies of classes (Polar bears are bears, which are animals). It should also have simple primitives that combine in complex forms.
Consistency. If John closed the door, it can also be interpreted as the door was closed by John. By being consistent, the KR can eliminate redundant or conflicting knowledge.
Efficient
Easy to modify and update.
Supports the intelligent activity which uses the knowledge base

To gain a better understanding of why these characteristics represent a good knowledge representation, think about how an encyclopedia (e.g. Wikipedia) is structured. There are millions of articles (coverage), and they are sorted into categories, content types, and similar topics (understandable). It redirects different titles but same content to the same article (consistency). It is efficient, easy to add new pages or update existing ones, and allows users on their mobile phones and desktops to view its knowledge base.

History of knowledge representation and reasoning

In computer science, particularly artificial intelligence, a number of representations have been devised to structure information.
KR is most commonly used to refer to representations intended for processing by modern computers, and in particular, for representations consisting of explicit objects (the class of all elephants, or Clyde a certain individual), and of assertions or claims about them ('Clyde is an elephant', or 'all elephants are grey'). Representing knowledge in such explicit form enables computers to draw conclusions from knowledge already stored ('Clyde is grey').
Many KR methods were tried in the 1970s and early 1980s, such as heuristic question-answering, neural networks, theorem proving, and expert systems, with varying success. Medical diagnosis (e.g., Mycin) was a major application area, as were games such as chess.
In the 1980s formal computer knowledge representation languages and systems arose. Major projects attempted to encode wide bodies of general knowledge; for example the "Cyc" project (still ongoing) went through a large encyclopedia, encoding not the information itself, but the information a reader would need in order to understand the encyclopedia: naive physics; notions of time, causality, motivation; commonplace objects and classes of objects.
Through such work, the difficulty of KR came to be better appreciated. In computational linguistics, meanwhile, much larger databases of language information were being built, and these, along with great increases in computer speed and capacity, made deeper KR more feasible.
Several programming languages have been developed that are oriented to KR. Prolog developed in 1972,^[3] but popularized much later, represents propositions and basic logic, and can derive conclusions from known premises. KL-ONE (1980s) is more specifically aimed at knowledge representation itself. In 1995, the Dublin Core standard of metadata was conceived.
In the electronic document world, languages were being developed to represent the structure of documents, such as SGML (from which HTML descended) and later XML. These facilitated information retrieval and data mining efforts, which have in recent years begun to relate to knowledge representation.
Development of the Semantic Web, has included development of XML-based knowledge representation languages and standards, including RDF, RDF Schema, Topic Maps, DARPA Agent Markup Language (DAML), Ontology Inference Layer (OIL), and Web Ontology Language (OWL).

Topics in Knowledge representation and reasoning

Language and notation

Some^{[citation needed]} think it is best to represent knowledge in the same way that it is represented in the human mind, or to represent knowledge in the form of human language.
Psycholinguistics investigates how the human mind stores and manipulates language. Other branches of cognitive science examine how human memory stores sounds, sights, smells, emotions, procedures, and abstract ideas. Science has not yet completely described the internal mechanisms of the brain to the point where they can simply be replicated by computer programmers.
Various^[which?] artificial languages and notations have been proposed for representing knowledge. They are typically based on logic and mathematics, and have easily parsed grammars to ease machine processing. They usually fall into the broad domain of ontologies.

Ontology Engineering

Main article: Ontology engineering

Main article: Ontology language

After CycL, a number of ontology languages have been developed. Most are declarative languages, and are either frame languages, or are based on first-order logic. Most of these languages only define an upper ontology with generic concepts, whereas the domain concepts are not part of the language definition. These languages all use special-purpose knowledge engineering because as stated by Tom Gruber, "Every ontology is a treaty- a social agreement among people with common motive in sharing." There are always many competing and differing views that make any general purpose ontology impossible. A general purpose ontology would have to be applicable in any domain and different areas of knowledge need to be unified.^[4] Gellish English is an example of an ontological language that includes a full engineering English Dictionary.
There is a long history of work attempting to build good ontologies for a variety of task domains, including early work on an ontology for liquids ^[5], the lumped element model widely used in representing electronic circuits (e.g., ^[6]), as well as ontologies for time, belief, and even programming itself. Each of these offers a way to see some part of the world. The lumped element model, for instance, suggests that we think of circuits in terms of components with connections between them, with signals flowing instantaneously along the connections. This is a useful view, but not the only possible one. A different ontology arises if we need to attend to the electrodynamics in the device: Here signals propagate at finite speed and an object (like a resistor) that was previously viewed as a single component with an I/O behavior may now have to be thought of as an extended medium through which an electromagnetic wave flows.
Ontologies can of course be written down in a wide variety of languages and notations (e.g., logic, LISP, etc.); the essential information is not the form of that language but the content, i.e., the set of concepts offered as a way of thinking about the world. Simply put, the important part is notions like connections and components, not whether we choose to write them as predicates or LISP constructs.
The commitment we make by selecting one or another ontology can produce a sharply different view of the task at hand. Consider the difference that arises in selecting the lumped element view of a circuit rather than the electrodynamic view of the same device. As a second example, medical diagnosis viewed in terms of rules (e.g., MYCIN) looks substantially different from the same task viewed in terms of frames (e.g., INTERNIST). Where MYCIN sees the medical world as made up of empirical associations connecting symptom to disease, INTERNIST sees a set of prototypes, in particular prototypical diseases, to be matched against the case at hand.

Commitment begins with the earliest choices

The INTERNIST example also demonstrates that there is significant and unavoidable ontological commitment even at the level of the familiar representation technologies. Logic, rules, frames, etc., each embody a viewpoint on the kinds of things that are important in the world. Logic, for instance, involves a (fairly minimal) commitment to viewing the world in terms of individual entities and relations between them. Rule-based systems view the world in terms of attribute-object-value triples and the rules of plausible inference that connect them, while frames have us thinking in terms of prototypical objects. Each of these thus supplies its own view of what is important to attend to, and each suggests, conversely, that anything not easily seen in those terms may be ignored. This is of course not guaranteed to be correct, since anything ignored may later prove to be relevant. But the task is hopeless in principle--every representation ignores something about the world--hence the best we can do is start with a good guess. The existing representation technologies supply one set of guesses about what to attend to and what to ignore. Selecting any of them thus involves a degree of ontological commitment: the selection will have a significant impact on our perception of and approach to the task, and on our perception of the world being modeled.

The commitments accumulate in layers

The ontologic commitment of a representation thus begins at the level of the representation technologies and accumulates from there. Additional layers of commitment are made as we put the technology to work. The use of frame-like structures in INTERNIST offers an illustrative example. At the most fundamental level, the decision to view diagnosis in terms of frames suggests thinking in terms of prototypes, defaults, and a taxonomic hierarchy. But prototypes of what, and how shall the taxonomy be organized? An early description of the system ^[7] shows how these questions were answered in the task at hand, supplying the second layer of commitment:

The knowledge base underlying the INTERNIST system is composed of two basic types of elements: disease entities and manifestations.... [It] also contains a...hierarchy of disease categories, organized primarily around the concept of organ systems, having at the top level such categories as "liver disease," "kidney disease," etc.

The prototypes are thus intended to capture prototypical diseases (e.g., a "classic case" of a disease), and they will be organized in a taxonomy indexed around organ systems. This is a sensible and intuitive set of choices but clearly not the only way to apply frames to the task; hence it is another layer of ontological commitment.
At the third (and in this case final) layer, this set of choices is instantiated: which diseases will be included and in which branches of the hierarchy will they appear? Ontologic questions that arise even at this level can be quite fundamental. Consider for example determining which of the following are to be considered diseases (i.e., abnormal states requiring cure): alcoholism, homosexuality, and chronic fatigue syndrome. The ontologic commitment here is sufficiently obvious and sufficiently important that it is often a subject of debate in the field itself, quite independent of building automated reasoners.
Similar sorts of decisions have to be made with all the representation technologies, because each of them supplies only a first order guess about how to see the world: they offer a way of seeing but don't indicate how to instantiate that view. As frames suggest prototypes and taxonomies but do not tell us which things to select as prototypes, rules suggest thinking in terms of plausible inferences, but don't tell us which plausible inferences to attend to. Similarly logic tells us to view the world in terms of individuals and relations, but does not specify which individuals and relations to use.
Commitment to a particular view of the world thus starts with the choice of a representation technology, and accumulates as subsequent choices are made about how to see the world in those terms.
Reminder: A KR is not a data structure
Note that at each layer, even the first (e.g., selecting rules or frames), the choices being made are about representation, not data structures. Part of what makes a language representational is that it carries meaning ^[8], i.e., there is a correspondence between its constructs and things in the external world. That correspondence in turn carries with it constraint. A semantic net, for example, is a representation, while a graph is a data structure. They are different kinds of entities, even though one is invariably used to implement the other, precisely because the net has (should have) a semantics. That semantics will be manifest in part because it constrains the network topology: a network purporting to describe family memberships as we know them cannot have a cycle in its parent links, while graphs (i.e., data structures) are of course under no such constraint and may have arbitrary cycles.
While every representation must be implemented in the machine by some data structure, the representational property is in the correspondence to something in the world and in the constraint that

Links and structures

While hyperlinks have come into widespread use, the closely related semantic link is not yet widely used. The mathematical table has been used since Babylonian times. More recently, these tables have been used to represent the outcomes of logic operations, such as truth tables, which were used to study and model Boolean logic, for example. Spreadsheets are yet another tabular representation of knowledge. Other knowledge representations are trees, graphs and hypergraphs, by means of which the connections among fundamental concepts and derivative concepts can be shown.
Visual representations are relatively new in the field of knowledge management but give the user a way to visualise how one thought or idea is connected to other ideas enabling the possibility of moving from one thought to another in order to locate required information.

Notation

The recent fashion in knowledge representation languages is to use XML as the low-level syntax. This tends to make the output of these KR languages easy for machines to parse, at the expense of human readability and often space-efficiency.
First-order predicate calculus is commonly used as a mathematical basis for these systems, to avoid excessive complexity. However, even simple systems based on this simple logic can be used to represent data that is well beyond the processing capability of current computer systems: see computability for reasons.
Examples of notations:

DATR is an example for representing lexical knowledge
RDF is a simple notation for representing relationships between and among objects

Storage and manipulation

One problem in knowledge representation is how to store and manipulate knowledge in an information system in a formal way so that it may be used by mechanisms to accomplish a given task. Examples of applications are expert systems, machine translation systems, computer-aided maintenance systems and information retrieval systems (including database front-ends).
Semantic networks may be used to represent knowledge. Each node represents a concept and arcs are used to define relations between the concepts.The Conceptual graph model is probably the oldest model still alive. One of the most expressive and comprehensively described knowledge representation paradigms along the lines of semantic networks is MultiNet (an acronym for Multilayered Extended Semantic Networks).
From the 1960s, the knowledge frame or just frame has been used. Each frame has its own name and a set of attributes, or slots which contain values; for instance, the frame for house might contain a color slot, number of floors slot, etc.
Using frames for expert systems is an application of object-oriented programming, with inheritance of features described by the "is-a" link. However, there has been no small amount of inconsistency in the usage of the "is-a" link: Ronald J. Brachman wrote a paper titled "What IS-A is and isn't", wherein 29 different semantics were found in projects whose knowledge representation schemes involved an "is-a" link. Other links include the "part-of" link.
Frame structures are well-suited for the representation of schematic knowledge and stereotypical cognitive patterns. The elements of such schematic patterns are weighted unequally, attributing higher weights to the more typical elements of a schema. A pattern is activated by certain expectations: If a person sees a big bird, he or she will classify it rather as a sea eagle than a golden eagle, assuming that his or her "sea-scheme" is currently activated and his "land-scheme" is not.
Frame representations are object-centered in the same sense as semantic networks are: All the facts and properties connected with a concept are located in one place - there is no need for costly search processes in the database.
A behavioral script is a type of frame that describes what happens temporally; the usual example given is that of describing going to a restaurant. The steps include waiting to be seated, receiving a menu, ordering, etc. The different solutions can be arranged in a so-called semantic spectrum with respect to their semantic expressivity.

Legal Representation

Representation (politics)

Contents

[edit] Theories of representation

[edit] Burke

[edit] Representation by population

[edit] Representation by area

[edit] Descriptive representation

[edit] Interest Model of Representation

[edit] See also

[edit] References

[edit] Bibliography

Representative democracy

Contents

[edit] Characteristics

[edit] Powers of representatives

[edit] History

[edit] Relation to republicanism

Mental representation

Contents

[edit] Representationalism and representational theories of mind

Representation (mathematics)

Contents

[edit] Representation theory

[edit] Other examples

[edit] Graph theory

[edit] Order theory

[edit] Polysemy

Multiple representations (mathematics education)

Contents

[edit] Higher-order thinking

[edit] Motivation

[edit] Assessment

[edit] Special education and differentiated instruction

[edit] Qualitative and quantitative reasoning

[edit] NCTM representations standard

[edit] Four most frequent school mathematics representations

[edit] Systems of manipulatives

[edit] Use of technology

Structural formula

Contents

[edit] Lewis structures

[edit] Condensed formulas

[edit] Skeletal formulas

[edit] Indication of stereochemistry

[edit] Stereochemistry in skeletal formulas

[edit] Unspecified stereochemistry

[edit] Perspective drawings

[edit] Newman projection and sawhorse projection

[edit] Cyclohexane conformations

[edit] Haworth projection

[edit] Fischer projection

Representation (systemics)

Knowledge representation and reasoning

Contents

Overview

Characteristics

History of knowledge representation and reasoning

Topics in Knowledge representation and reasoning

Language and notation

Ontology Engineering

Links and structures

Notation

Storage and manipulation