Unreferenced date December 2009 Mergeinto reification computer science date July 2009 Expert subject Computer science date February 2009 Context date February 2009 Reification in knowledge representation involves the representation of factual assertions, that are referred to by other assertions which might then be manipulated in some way. e.g., to compare logical assertion s from different witness es in order to determine their credibility . says how it s used but not what it is The message John is six feet tall is an assertion involving truth, that commits the speaker to its factuality, whereas the reified statement, Mary reports that John is six feet tall defers such commitment to Mary. In this way, the statements can be incompatible without creating contradictions in reasoning . For example the statements John is six feet tall and John is five feet tall are mutually exclusive thus, incompatible but, the statements Mary reports that John is six feet tall, and Paul reports that John is five feet tall, are not incompatible, as they both are governed by a conclusive rationale, that either Mary or Paul or both is, in fact, incorrect. See also Reification linguistics Reification fallacy Reification computer science DEFAULTSORT Reification Knowledge Representation Category Knowledge representation ... more details
Multiple issues one source September 2010 refimprove September 2010 Knowledgerepresentation KR is an area ... network . ref name martin http www.webkb.org doc papers iccs02 iswc02.pdf Knowledgerepresentation ... Centre, QLD, Australia, July 15 19, 2002 ref Overview KnowledgeRepresentation KR research involves ... the concept of the Semantic Web , and development of XML based knowledgerepresentation languages and standards ... Language DAML , Ontology Inference Layer OIL ref Enabling knowledgerepresentation on the Web ... KR must be both declarative knowledge declarative and procedural knowledge . What is knowledgerepresentation ... 2011 ref A knowledgerepresentation KR is most fundamentally a surrogate, a substitute for the thing ... in which we say things about the world. Some issues that arise in knowledgerepresentation from an AI perspective are How do people represent knowledge? What is the nature of knowledge? Should a representation ... been very little top down discussion of the knowledgerepresentation KR issues and research in this area ... by an appropriate choice of knowledgerepresentation . Representing knowledge in some ways makes certain ... A good knowledgerepresentation covers six basic characteristics Coverage, which means the KR covers ... of why these characteristics represent a good knowledgerepresentation, think about how an encyclopedia ... formal computer knowledgerepresentation languages and systems arose. Major projects attempted to encode ... aimed at knowledgerepresentation itself. In 1995, the Dublin Core standard of metadata ... retrieval and data mining efforts, which have in recent years begun to relate to knowledgerepresentation. Development of the Semantic Web , has included development of XML based knowledgerepresentation ... OWL . Topics in Knowledgerepresentation and reasoning Language and notation Some Citation needed date ... and Behavior of Digital Hardware, IEEE Computer, Special Issue on KnowledgeRepresentation, 16 10 75 ... in Readings in KnowledgeRepresentation, pp. 288 295. ref , i.e., there is a correspondence ... more details
Cleanup date November 2008 Vague date February 2009 Semantic analysis is a method for eliciting and representing knowledge about organisation s. Liu, 1991 Initially the problem must be defined by domain experts and passed to the project analyst s . The next step is the generation of candidate affordances. This step will generate a list of semantic units that may be included in the schema. The candidate grouping follows where some of the semantic units that will appear in the schema are placed in simple groups. Finally the groups will be integrated together into an Ontology information science ontology chart. A case study of a library domain will be used to illustrate the process of semantic analysis. Semantic analysis always starts from the problem definition which if not clear, require the analyst to employ relevant literature , interview s with the Stakeholder corporate stakeholders and other techniques towards collecting supplementary information . All assumptions made must be genuine and not limiting the system. Liu Kecheng, 2000 Semiotics in information systems engineering , Cambridge University Press. See also Ontology chart Category Knowledge representation Library stub ... more details
Wiktionarypar representation represent Representation can refer to Representation politics , one s ability to influence the political process Representative democracy Permanent Representation, a type of diplomatic mission Representation of the International NGO the representative office of the International non governmental organization INGO mission Representation arts , the depiction and ethical concerns of construction in visual arts and literature. Depiction is meaning conveyed through pictures Representation psychology , a hypothetical internal cognitive symbol that represents external reality Representation mathematics and group representation Multiple representations mathematics education Representation chemistry Representation systemics Knowledgerepresentation , the study of formal ways to describe knowledge Legal representation or advocacy is provided by lawyers Lobbying for a group of individuals or companies In unionised workplaces, Union steward shop stewards and union executives can represent employees The legal status of a statement made with regards to Contract contract law A fiction of the law which causes a person to enter into another s right of succession, called Representation succession representation , and also called substitution . Represent can refer to Represent Fat Joe album Represent Fat Joe album , a 1993 album by Fat Joe Represent Compton s Most Wanted album Represent Compton s Most Wanted album , a 2000 album by Compton s Most Wanted Represent , a 1994 album by DJ Magic Mike Represent song Represent song , a song by Nas Represent , a 2009 song by The Red Jumpsuit Apparatus Represent Weezer song Represent , a 2010 single by Weezer released as an unofficial anthem for the United States men s national soccer team See also Reprazent disambig cs Reprezentace de Repr sentation es Representaci n fr Repr sentation homonymie nl Representatie pt Representa o ro Reprezentare ru simple Representation fi Representaatio sv Representation ... more details
unlike a mere book on its own . The knowledge must constitute some sort of representation of the outside ...other uses File Efez Celsus Library 5 RB.jpg thumb upright Personification of knowledge Greek language Greek , Episteme in Celsus Library in Ephesus , Turkey. Knowledge is a familiarity with someone ... view entry m en us1261368 m en us1261368 ref In philosophy , the study of knowledge is called epistemology , and the philosopher Plato famously defined knowledge as justified true belief . However no single agreed upon definition of knowledge exists, and there are numerous theories to explain it. Knowledge ..., association and reasoning while knowledge is also said to be related to the capacity of acknowledgment ... University Press, 2002 , 238 266. ref Theories of knowledge File Knowledge Reid Highsmith.jpeg thumb left Robert Reid painter Robert Reid , Knowledge 1896 . Thomas Jefferson Building , Washington ... possible by the notion that philosophy s core was theory of knowledge, a theory distinct from the sciences because it was their foundation Without this idea of a theory of knowledge, it is hard to imagine ... of Nature blockquote The definition of knowledge is a matter of on going debate among philosopher ... definitions of knowledgeknowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory ... to be considered knowledge it must be theory of justification justified , truth true , and belief ... that knowledge tracks the truth and Simon Blackburn Simon Blackburn s additional requirement ..., or failure have knowledge. Richard Kirkham suggests that our definition of knowledge requires that the evidence ... to the way knowledge is used in natural languages. He saw knowledge as a case of a family resemblance . Following this idea, knowledge has been reconstructed as a cluster concept that points out relevant ... and the flow of knowledge , in Hrachovec, H. Pichler, A. Hg. Philosophy of the Information Society ... more details
Adaptive representation is an extension by Francis Heylighen ref Heylighen, Francis 1990 . Representation and Change A Metarepresentational Framework for the Foundations of Physical and Cognitive Science . Communication and Cognition, Ghent, Belgium. ref to Kant s epistemology theory of knowledge . According to Kant, perception passes by the filters of the mind who observes the phenomena. In this line, there exists in the human mind invariant and a priori principles of experience. As an example, one may have imprinted in the brain a Dualism philosophy of mind Cartesian representation of space, a notion of time, color separation and others. This may be called static representation . Heylighen has proposed a revision of these Kantian ideas, in which these principles are not supposed to be invariant and necessary A priori and a posteriori philosophy a priori instead alternative principles exist for the organization of experience in adaptive representations. This opens a path for new investigations in the philosophy of mind and human cognition . References reflist External links http pcp.vub.ac.be books Rep&Change.pdf Web edition of Representation and Change 1999 . Epistemology stub Category Epistemology ... more details
Refimprove date December 2009 Genetic representation is a way of representing solutions individuals in evolutionary computation methods. Genetic representation can encode appearance, behavior, physical qualities of individuals. Designing a good genetic representation that is expressive and evolvable is a hard problem in evolutionary computation. Difference in genetic representations is one of the major criteria drawing a line between known classes of evolutionary computation. Genetic algorithm s use linear binary representations. The most standard one is an array of bit s. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size. This facilitates simple crossover operation. Variable length representations were also explored in Genetic algorithm s, but crossover implementation is more complex in this case. Evolution strategy uses linear real valued representations, e.g. an array of real values. It uses mostly gaussian mutation and blending averaging crossover. Genetic programming GP pioneered tree like representations and developed genetic operator s suitable for such representations. Tree like representations are used in GP to represent and evolve functional programs with desired properties. ref http www.sover.net nichael nlc publications icga85 index.html Cramer, 1985 ref Human based genetic algorithm HBGA offers a way to avoid solving hard representation problems by outsourcing all genetic operators to outside agents, in this case, humans. The algorithm has no need for knowledge of a particular fixed genetic representation as long as there are enough external agents capable of handling those representations, allowing for free form and evolving genetic representations. Common genetic representations Genetic algorithm ... DEFAULTSORT Genetic Representation Category Evolutionary algorithms ... more details
The term complex representation has slightly different meanings in mathematics and physics. In mathematics , a complex representation is a group representation of a group or Lie algebra on a complex vector space. In physics , a complex representation is a group representation of a group or Lie algebra on a complex vector space that is neither real representation real nor pseudoreal representation pseudoreal . In other words, the Group mathematics group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non equivalent representation. For compact groups, the Frobenius Schur indicator can be used to tell whether a representation is real, complex, or pseudo real. For example, the N dimensional fundamental representation of SU N for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation . algebra stub Category Representation theory of groups ... more details
In mathematics , an antifundamental representation is the complex conjugate of the fundamental representation , although the distinction between the fundamental and the antifundamental representation is a matter of convention. However, these two are often non equivalent, because each of them is a complex representation . Category Representation theory of Lie groups geometry stub ... more details
of natural languages. See also Object of the mind Knowledgerepresentation Perception Representative ...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. ref David Marr Vision. 1982 ref 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 explanation explaining and description describing the nature of idea s and concept s. Representationalism and representational theories of mind Representational theories of mind conceive of thinking as occurring within an internal system of representation. The propositional attitude s of the mind are Type token distinction token mental representations with semantics semantic Property philosophy properties . Representationalism also known as Direct and indirect realism 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 object s. ref The Ontology of Concepts Abstract Objects or Mental Representations? , Eric Margolis and Stephen Laurence ref The representational theory of mind attempts to explanation explain the nature of idea s, concept s and other mental content in contemporary ... existence of mental representation s which act as intermediaries between the observation observing ... theory of mind states that he or she forms a mental representation that represents the floor and its ... links http plato.stanford.edu entries mental representation Stanford Encyclopedia of Philosophy Mental Representation philosophy of language philosophy of mind Category Perception Category Cognitive ... more details
Orphan date February 2009 Management representation is a letter issued by an auditor s client to the auditor in writing as one of audit evidence s. The date of the document must not be later than the date of audit work completion. It is used to let the client s management declare in writing that the financial statements and other presentations to the auditor are sufficient and appropriate and without omission of material facts to the financial statements, to the best of the management s knowledge. For audit evidence, it is reliable if the auditor has no other means of obtaining evidence. Examples may include situations involving contingent liabilities or off balance sheet liabilities . The person issuing the letter should have the appropriate authority or seniority in the organization to vouch on the issue. In the case of contradictions between other sources of evidence and management representations, the auditor should conduct further investigations. See also ISA 500 Audit Evidence International Standards on Auditing ISA 580 Management Representations References unreferenced date November 2007 Category Auditing accounting stub ... more details
of the visual representation of rape. One of the myths which is perpetuated by these representations ... the relationship between the visual representation of rape and post feminism , examining depictions ... group Grrl Activistas who catalogue what they term as the mis representation of rape in British broadcast ... communication technologies allow rape survivors to counteract this so called mis representation ... reflist cite book title Rape and Representation author Higgins, Lynn A, and Silver, Brenda R ... more details
In mathematics and theoretical physics , a bifundamental representation is a representation theory representation obtained as a tensor product of two fundamental representation fundamental or antifundamental representation antifundamental representations. For example, the MN dimensional representation M , N of the group math SU M times SU N math is a bifundamental representation. These representations occur in quiver diagram s. algebra stub Category Abstract algebra ... more details
The adjoint representation can refer to Ad the adjoint representation of a Lie group G ad the adjoint representation of a Lie algebra math mathfrak g math , see adjoint endomorphism . mathdab ... more details
In mathematics , a linear representation &rho of a group G is a monomial representation if there is a finite index subgroup H and a one dimensional linear representation &sigma of H , such that &rho is equivalent to the induced representation Ind sub H sub sup G sup &sigma . Alternatively, one may define it as a representation whose image is in the monomial matrices . Here for example G and H may be finite group s, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the coset s of H . It is necessary only to keep track of scalars coming from &sigma applied to elements of H . References Springer id m m064780 title Monomial representation Category Representation theory of groups Algebra stub it Rappresentazione monomiale ... more details
Unreferenced date December 2009 Orphan date December 2009 This article addresses the notion of quasiregularity in the context of representation theory and topological algebra . For other notions of quasiregularity in mathematics , see the disambiguation page quasiregular . In mathematics , quasiregular representation is a concept of representation theory , for a locally compact group G and a homogeneous space G H where H is a closed subgroup . In line with the concepts of regular representation and induced representation , G acts on functions on G H . If however Haar measure s give rise only to a quasi invariant measure on G H , certain correction factors have to be made to the action on functions, for L sup 2 sup G H to afford a unitary representation of G on square integrable function s. With appropriate scaling factors, therefore, introduced into the action of G , this is the quasiregular representation or modified induced representation. DEFAULTSORT Quasiregular Representation Category Unitary representation theory Category Topological groups ... more details
Image Schop welt 2ed.jpg right thumb The title page of the expanded 1844 publication The World as Will and Representation ... this title The World as Will and Representation appeared by E.F.J.Payne who also translated several other works of Schopenhauer as late as in 1958 ref Arthur Schopenhauer The world as will and representation ... in 1966 and 1969 . ref Arthur Schopenhauer The world as will and representation , Courier Dover ... prior knowledge of Immanuel Kant s theories, ref WWR I, xv. ref and Schopenhauer is regarded by some ... form of experience. Schopenhauer saw the human will as our one window to the world behind the representation the Kantian thing in itself . He believed, therefore, that we could gain knowledge about ... representation and thing in itself could be understood by analogy to the relationship between human will and human body. According to Schopenhauer, the entire world is the representation of a single ... forms as existing on an intermediate ontology ontological level between the representation ... in his career 1814 1818 and culminated in the publication of the first volume of Will and Representation ... . Representation He used the word representation Vorstellung to signify the mental idea or image of any ... . This concept includes the representation of the observing subject s own body. Schopenhauer ... reality behind the representation that provided the matter of perception, but lacked form. Kant ... imposed on the world by the human mind in order to create the representation, and these factors were ... of the noumenal realm and the will is the inner kernel of every being. All knowledge gained of objects ... Vol. 1, Book 2 In Book Two, electricity and gravity are described as fundamental forces of the will. Knowledge ... between perceptual, intuitive knowledge and conceptual, discursive knowledge. One of Kant s greatest ... are as follows. Supplements to the First Book First Half The Doctrine of the Representation of Perception Through 1 &ndash 7 of Volume I I. On the Fundamental View of Idealism II. On the Doctrine of Knowledge ... more details
In mathematics , if G is a group mathematics group and &rho is a linear representation of it on the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 1 of Fulton Harris ref Overline &rho g is the transpose of a linear map transpose of &rho g sup &minus 1 sup for all g in G . Then Overline &rho is also a representation, as may be checked explicitly. The dual representation is also known as the contragredient representation . If math mathfrak g math is a Lie algebra and &rho is a representation of it over the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 8 of Fulton Harris ref Overline &rho u is the transpose of &minus &rho u for all u in math mathfrak g math . Overline &rho is also a representation, as can be explicitly checked. For a unitary representation , the conjugate representation and the dual representation coincide, up to equivalence of representations. Generalization A general ring Module mathematics module does not admit a dual representation. Modules of Hopf algebra s do, however. See also Complex conjugate representation Kirillov Character Formula References references Category Representation theory of groups fr Repr sentation duale ... more details
Representation is the use of signs that stand in for and take the place of something else. ref name Mitchell1995 Mitchell, W. 1995, Representation , in F Lentricchia & T McLaughlin eds , Critical Terms for Literary Study , 2nd edn, University of Chicago Press, Chicago ref It is through representation ... Representation has been associated with aesthetics art and semiotics signs . Mitchell says representation .... 13 The term representation carries a range of meanings and interpretations. In literary theory , representation ..., Media and society an introduction , 3rd edn, Oxford University Press, South Melbourne, 2005 ref Representation .... ref name Stadler2005 Defining representation Image Mona Lisa, by Leonardo da Vinci, from C2RMF retouched.jpg ... re , intensive prefix, praesentare to present, lit. to place before . A representation is a type of recording ... in a Media arts medium . The degree to which an artistic representation resembles the object it represents ... in Hadrian s Villa mosaic Since ancient times representation has played a central role in understanding ... theory who considered literature as simply one form of representation. ref name Childers1995 Childers ..., New York, 1995 ref Aristotle for instance, considered each mode of representation, verbal, visual or musical, as being natural to human beings. ref name Vukcevich2002 Vukcevich, M 2002, Representation ... animals is their ability to create and manipulate signs. ref name Mitchell1990 Mitchell, W, Representation ..., in contrast, looked upon representation with more caution. He recognised that literature is a representation ... Practice , Open University Press, London, 1997. ref For Plato, representation, like contemporary ... things . Plato believed that representation needs therefore, to be controlled and monitored due to the possible ... name Mitchell1995 From childhood man has an instinct for representation, and in this respect man differs ... things. ref name Mitchell1995 p. 11 Aristotle discusses representation in three ways The object ... to represent it. The means of literary representation is language . An important part of representation ... more details
In the mathematics mathematical field of representation theory , a trivial representation is a group representationrepresentation V , &phi of a Group mathematics group G on which all elements of G act as the identity mapping of V . A trivial Representation mathematics representation of an associative algebra associative or Lie algebra is a Lie algebra representation Lie algebra representation for which all elements of the algebra act as the zero endomorphism which sends every element of V to the zero vector. For any group or Lie algebra, an irreducible representation irreducible trivial representation always exists over any field, and is one dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebra s and unital representations. Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors so that searching for such subrepresentations is the whole topic of invariant theory . The trivial character is the character mathematics character that takes the value of one for all group elements. References Fulton Harris . Category Representation theory algebra stub zh ... more details
Symbolic representation may refer to Symbolism disambiguation Symbolic linguistic representation In politics, it has to do with a representative in congress or in a group that is seen as being there to represent a group of minorities whether it be gender or cultural groups. See also Symbolic disambiguation Representation disambiguation disambig ... more details
In mathematics , in the representation theory of algebraic group s, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties. Finite direct sums and products of rational representations are rational. A rational math G math module is a module that can be expressed as a sum not necessarily direct of rational representations. see Group representation References http www.jstor.org view 00029327 di994362 99p00143 Extensions of Representations of Algebraic Linear Groups http www.encyclopediaofmath.org index.php Rational representation Springer Online Reference Works Rational Representation Category Representation theory of algebraic groups algebra stub ... more details
In mathematics , especially in the area of abstract algebra known as representation theory , a faithful representation of a group mathematics group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings g . In more abstract language, this means that the group homomorphism G GL V is injective . Caveat While representations of G over a field K are de facto the same as math K G math modules with math K G math denoting the Group ring Group algebra over a finite group group algebra of the group G , a faithful representation of G is not necessarily a faithful module for the group algebra. In fact each faithful math K G math module is a faithful representation of G , but the converse does not hold. Consider for example the natural representation of the symmetric group S sub n sub in n dimensions by permutation matrices , which is certainly faithful. Here the order of the group is n while the n × n matrices form a vector space of dimension n sup 2 sup . As soon as n is at least 4, dimension counting means that some linear dependence must occur between permutation matrices since 24 16 this relation means that the module for the group algebra is not faithful. Properties A representation V of a finite group G over an algebraically closed field K of characteristic zero is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of S sup n sup V the n th symmetric power of the representation V for a sufficiently high n . Also, V is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of math V otimes n underbrace V otimes V otimes cdots otimes V n text times math the n th tensor power of the representation V for a sufficiently high n . References Springer id F f038170 title faithful representation Category Representation theory algebra stub ... more details
In the mathematics mathematical field of representation theory a real representation is usually a group representationrepresentation on a real number real vector space U , but it can also mean a representation on a complex number complex vector space V with an invariant real structure , i.e., an antilinear ... C is a representation on a complex vector space with an antilinear equivariant map given by complex conjugation . Conversely, if V is such a complex representation, then U can be recovered as the fixed ... concretely in terms of matrices, a real representation is one in which the entries of the matrices ... column vectors. A real representation on a complex vector space is isomorphic to its complex conjugate representation , but the converse is not true a representation which is isomorphic to its complex conjugate but which is not real is called a pseudoreal representation . An irreducible pseudoreal representation V is necessarily a quaternionic representation it admits an invariant quaternionic ... real nor quaternionic in general. A representation on a complex vector space can also be isomorphic to the dual representation of its complex conjugate. This happens precisely when the representation ... of the representation and is the Haar measure with G 1. For a finite group, this is given by math ... is 1, then the representation is real. If the indicator is zero, the representation is complex hermitian , ref Any complex representation V of a compact group has an invariant hermitian form ... form on V . ref and if the indicator is &minus 1, the representation is quaternionic. Examples All representation of the symmetric group symmetric groups are real and in fact rational , since we can ... of copies of the fundamental representation, which is real. Further examples of real representations ... representation . Notes reflist 1 References Fulton Harris . citation first Jean Pierre last Serre ... 6 . Category Representation theory pt Representa o real ... more details
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