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  • Articles  (33)
  • representation
  • 2015-2019
  • 1990-1994  (33)
  • 1
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    Springer
    Minds and machines 4 (1994), S. 215-231 
    ISSN: 1572-8641
    Keywords: Meaning ; representation ; disjunction problem ; Twin-Earth ; Fodor ; asymmetric causal dependency ; actual ; naturalized semantics ; information
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract In an earlier paper, we argued that Fodorian Semantics has serious difficulties. However, we suggested possible ways that one might attempt to fix this. Ted Warfield suggests that our arguments can be deflected and he does this by making the very moves that we suggested. In our current paper, we respond to Warfield's attempts to revise and defend Fodorian Semantics against our arguments that such a semantic theory is both too strong and too weak. To get around our objections, Warfield proposes a modified reading of one of Fodor's conditions and proposes adding a new condition to the theory. We show that neither the modified reading nor the additional condition saves the asymmetric causal dependency approach to naturalized semantics.
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  • 2
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    Minds and machines 4 (1994), S. 333-344 
    ISSN: 1572-8641
    Keywords: Emergence ; content ; information ; representation ; computers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract I examine whether it is possible for content relevant to a computer's behavior to be carried without an explicit internal representation. I consider three approaches. First, an example of a chess playing computer carrying ‘emergent’ content is offered from Dennett. Next I examine Cummins’ response to this example. Cummins says Dennett's computer executes a rule which is inexplicitly represented. Cummins describes a process wherein a computer interprets explicit rules in its program, implements them to form a chess-playing device, then this device executes the rules in a way that exhibits them inexplicitly. Though this approach is intriguing, I argue that the chess-playing device cannot exist as imagined. The processes of interpretation and implementation produce explicit representations of the content claimed to be inexplicit. Finally, the Chinese Room argument is examined and shown not to save the notion of inexplicit information. This means the strategy of attributing inexplicit content to a computer which is executing a rule, fails.
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  • 3
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    Applied mathematics & optimization 30 (1994), S. 51-78 
    ISSN: 1432-0606
    Keywords: Hidden Markov Model ; Discrete adaptive filter ; Martingale ; representation ; Girsanov theorem ; Smoothed estimate ; Zakai equation ; Expectation maximization ; 93E11 ; 93E12 ; 60G35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A discrete state and time Markov chain is observed through a finite state function which is subject to random perturbations. Such a situation is often called a Hidden Markov Model. A general filter is obtained which provides recursive updates of estimates of processes related to the Markov chain given the observations. In the unnormalized, or Zakai, form this provides particularly simple equations. Specializing this result provides recursive estimates and smoothers for the state of the process, for the number of jumps from one state to another, for the occupation time in any state and for a process related to the observations. These results allow a re-estimation of the parameters of the model, so that our procedures are adaptive or “self tuning” to the data. The main contributions of this paper are the introduction of an equivalent measure under which the observation values are independent and identically distributed, and the use of the idempotent property when the state space of the Markov chain is identified with canonical unit vectors in a Euclidean space.
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  • 4
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    Minds and machines 3 (1993), S. 183-200 
    ISSN: 1572-8641
    Keywords: Connectionism ; representation ; explicit rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract At present, the prevailing Connectionist methodology forrepresenting rules is toimplicitly embody rules in “neurally-wired” networks. That is, the methodology adopts the stance that rules must either be hard-wired or “trained into” neural structures, rather than represented via explicit symbolic structures. Even recent attempts to implementproduction systems within connectionist networks have assumed that condition-action rules (or rule schema) are to be embodied in thestructure of individual networks. Such networks must be grown or trained over a significant span of time. However, arguments are presented herein that humanssometimes follow rules which arevery rapidly assignedexplicit internal representations, and that humans possessgeneral mechanisms capable of interpreting and following such rules. In particular, arguments are presented that thespeed with which humans are able to follow rules ofnovel structure demonstrates the existence of general-purpose rule following mechanisms. It is further argued that the existence of general-purpose rule following mechanisms strongly indicates that explicit rule following is not anisolated phenomenon, but may well be a common and important aspect of cognition. The relationship of the foregoing conclusions to Smolensky's view of explicit rule following is also explored. The arguments presented here are pragmatic in nature, and are contrasted with thekind of arguments developed by Fodor and Pylyshyn in their recent, influential paper.
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  • 5
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    Acta applicandae mathematicae 32 (1993), S. 89-98 
    ISSN: 1572-9036
    Keywords: 22D30 ; 46L89 ; Hilbert algebra ; representation ; Stone-von Neumann theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we give a simple proof of the Stone-von Neumann theorem about the irreducible unitary representations of Heisenberg groups. First of all, we prove a result about the representations of Hilbert algebras of Hilbert-Schmidt operators on a Hilbert space. Then we use it to give a simple proof of the Stone-von Neumann theorem. Applications to theoretical physics are mentioned.
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  • 6
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    Artificial intelligence review 7 (1993), S. 329-354 
    ISSN: 1573-7462
    Keywords: cognitive architecture ; cognitive map ; concept ; concept learning ; connectionism ; content ; context-sensitivity ; development ; generality ; intentionality ; representation ; non-conceptual content ; parallel distributed processing ; sub-symbolic computation ; systematicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract It is claimed that there are pre-objective phenomena, which cognitive science should explain by employing the notion of non-conceptual representational content. It is argued that a match between parallel distributed processing (PDP) and non-conceptual content (NCC) not only provides a means of refuting recent criticisms of PDP as a cognitive architecture; it also provides a vehicle for NCC that is required by naturalism. A connectionist cognitive mapping algorithm is used as a case study to examine the affinities between PDP and NCC.
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  • 7
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    Journal of automated reasoning 10 (1993), S. 421-422 
    ISSN: 1573-0670
    Keywords: Reasoning by analogy ; representation ; unsolved research problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This article is the twenty-seventh of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find criteria that an automated reasoning program can apply to determine whether to attack a given question with reasoning by analogy. The imprecise term ‘reasoning by analogy’ refers to a type of reasoning in which the type of proof being sought is sharply influenced by the style of proof that was successfully used to prove related theorems.
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  • 8
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    Journal of automated reasoning 11 (1993), S. 147-148 
    ISSN: 1573-0670
    Keywords: Automated reasoning ; function replacement ; naming ; representation ; unsolved research problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This article is the twenty-eighth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find criteria that an automated reasoning program can profitably use to remove functions present in the representation and replace them with appropriate predicates or constants thatname the entities that werenamed by the functions. The notation used to present a problem to a reasoning program can have a profound effect on the likelihood of the program's success.
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  • 9
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    Journal of algebraic combinatorics 1 (1992), S. 111-132 
    ISSN: 1572-9192
    Keywords: tiling ; domino ; alternating-sign matrix ; monotone triangle ; representation ; square ice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2 n(n+1)/2 domino tilings. In this, the first half of a two-part paper, we give two proofs of this formula. The first proof exploits a connection between domino tilings and the alternating-sign matrices of Mills, Robbins, and Rumsey. In particular, a domino tiling of an Aztec diamond corresponds to a compatible pair of alternating-sign matrices. The second proof of our formula uses monotone triangles, which constitute another form taken by alternating-sign matrices; by assigning each monotone triangle a suitable weight, we can count domino tilings of an Aztec diamond.
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  • 10
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    Journal of algebraic combinatorics 1 (1992), S. 235-255 
    ISSN: 1572-9192
    Keywords: symmetric group ; representation ; character ; Young tableau ; Möbius function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Murnaghan–Nakayama formula for the characters of S n is derived from Young's seminormal representation, by a direct combinatorial argument. The main idea is a rational function identity which when stated in a more general form involves Möbius functions of posets whose Hasse diagrams have a planar embedding. These ideas are also used to give an elementary exposition of the main properties of Young's seminormal representations.
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  • 11
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    Journal of algebraic combinatorics 1 (1992), S. 219-234 
    ISSN: 1572-9192
    Keywords: tiling ; domino ; alternating-sign matrix ; monotone triangle ; representation ; square ice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.
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  • 12
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    Journal for general philosophy of science 23 (1992), S. 85-103 
    ISSN: 1572-8587
    Keywords: life ; teleology ; evolution ; reality ; representation ; experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Summary A comprehensive definition of the phenomenon called “life” led to the addition of many dimensions to the natural sciences, and especially the conscious mental dimension. Historical attention is paid not only to those employing the natural philosophical paradigms, but also to evolutionary theories and to the Kantian teleological philosophy. The belief that science can solve the riddle of life is a category of purposal thinking. A revised version of critical teleology is essential for comprehension of life.
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  • 13
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    Minds and machines 2 (1992), S. 185-201 
    ISSN: 1572-8641
    Keywords: Constraint ; individuation scheme ; infon ; information ; representation ; type
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract I argue that the role played by infons in the kind of mathematical theory of information being developed by several workers affiliated to CSLI is analogous to that of the various number systems in mathematics. In particular, I present a mathematical construction of infons in terms of representations and informational equivalences between them. The main theme of the paper arose from an electronic mail exchange with Pat Hayes of Xeroxparc. The exposition derives from a talk I gave at theTheories of Partial Information conference held at the University of Texas at Austin, January 1990.
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  • 14
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    Minds and machines 2 (1992), S. 175-183 
    ISSN: 1572-8641
    Keywords: Meaning ; representation ; disjunction problem ; information semantics ; Fodor ; asymmetric causal dependency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract InPsychosemantics Jerry Fodor offered a list of sufficient conditions for a symbol “X” to mean something X. The conditions are designed to reduce meaning to purely non-intentional natural relations. They are also designed to solve what Fodor has dubbed the “disjunction problem”. More recently, inA Theory of Content and Other Essays, Fodor has modified his list of sufficient conditions for naturalized meaning in light of objections to his earlier list. We look at his new set of conditions and give his motivation for them-tracing them to problems in the literature. Then we argue that Fodor's conditions still do not work. They are open to objections of two different varieties: they are too strong and too weak. We develop these objections and indicate why Fodor's new, improved list of conditions still do not work to naturalize meaning.
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  • 15
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    Acta mechanica solida Sinica 5 (1992), S. 135-146 
    ISSN: 0894-9166
    Keywords: representation ; rotation tensor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Through a variational approach, an explicit connection between the additive and the polar decompositions of deformation gradient has been established. An exact formula for determining the rotation tensor in polar decomposition is obtained. The formula is fundamental in continuum mechanics and can be used to separate the rotation and the pure strain in deformation, by which various approximate expressions can be easily obtained.
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  • 16
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    Acta applicandae mathematicae 27 (1992), S. 123-133 
    ISSN: 1572-9036
    Keywords: 46A40 ; 46B40 ; representation ; Archimedean Riesz space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A brief survey of representations of Archimedean Riesz spaces in spaces of continuous extended real-valued functions, together with an example of their use in proving results about Riesz spaces
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  • 17
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    Journal of mathematical imaging and vision 1 (1992), S. 7-21 
    ISSN: 1573-7683
    Keywords: morphology ; granulometry ; pattern spectrum ; representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A basic filter theory within mathematical morphology involves the binary granulometric theory of G. Matheron. This theory results in a size-distribution analysis that has proved beneficial in the characterization of random-grain image models. Of central importance are the Euclidean granulometries, which admit a particularly elegant representation. The present paper extends the Matheron binary Euclidean granulometric theory to the gray scale. In doing so, it draws on the lattice formulations of openings and abstract granulometric processes. Given these, the concept of gray-scale Euclidean granulometry is defined in terms of a signal scalar multiplication that is compatible with the umbra transform. Once the definition has been extended, the fundamental Matheron representation in terms of unit generators is generalized to the gray scale. Attention is then paid to the inducements of gray-scale-to-binary and binary-to-gray-scale operators that result naturally from the umbra methodology. It is demonstrated that this inducement results in the inducement of Euclidean granulometries in both directions.
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  • 18
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    Journal of mathematical imaging and vision 2 (1992), S. 173-183 
    ISSN: 1573-7683
    Keywords: nonlinear filter ; morphological filter ; image algebra ; representation ; cellular logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The mathematical structure of nonlinear filtering is expressed in the context of binary logic. This first part of a two-part study concerns the binary setting. Operator properties, such as antiextensivity and idempotence, are expressed in finite logical expressions, as are the Matheron representation for morphological filters and its extension to translation-invariant operators, thereby giving simplicity to both operational properties and representations and also exposing the manner in which logic methods can be used for filter design and analysis. The second part of the study treats gray-scale filters.
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  • 19
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    Journal of mathematical imaging and vision 2 (1992), S. 185-192 
    ISSN: 1573-7683
    Keywords: nonlinear filter ; morphological filter ; stack filter ; image algebra ; representation ; cellular logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This second part of a two-part study concerning the logical structure of nonlinear filters treats gray-scale filters. The algebraic framework of threshold decomposition is dedscribed in terms of the appropriate underlying commuting diagram, along with the manner in which generalized stack filters fall out of the framework when it is interpreted in the context of logical calculus. Relationships between representations for morphological and generalized stack filters are expressed in cellular logic.
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  • 20
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    Journal of science education and technology 1 (1992), S. 177-189 
    ISSN: 1573-1839
    Keywords: Mathematics ; representation ; videotape ; elementary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General , Technology
    Notes: Abstract Videotaping small groups of students in a regular classroom environment makes it possible to study individual student cognitive growth in a social setting. The present report deals with student development of some new mathematical ideas over an extended period of time.
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  • 21
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    Journal of statistical physics 67 (1992), S. 667-673 
    ISSN: 1572-9613
    Keywords: Mixing ; correlation ; exponential ; geodesic ; representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We give a short and direct proof of exponential mixing of geodesic flows on compact hyperbolic three-manifolds with respect to the Liouville measure. This complements earlier results of Collet-Epstein-Gallovotti, Moore, and Ratner for hyperbolic surfaces. Furthermore, since the analysis is even easier in three dimensions than in two dimensions (because of the absence of discrete series and the simplicity of the zonal spherical functions in this case), this apparently gives the simplest example of a flow with exponential mixing.
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  • 22
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    Minds and machines 1 (1991), S. 129-165 
    ISSN: 1572-8641
    Keywords: Computation ; cognition ; representation ; information processing ; physical symbol systems ; language of thought
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract Cognitive science uses the notion of computational information processing to explain cognitive information processing. Some philosophers have argued that anything can be described as doing computational information processing; if so, it is a vacuous notion for explanatory purposes. An attempt is made to explicate the notions of cognitive information processing and computational information processing and to specify the relationship between them. It is demonstrated that the resulting notion of computational information processing can only be realized in a restrictive class of dynamical systems called physical notational systems (after Goodman's theory of notationality), and that the systems generally appealed to by cognitive science-physical symbol systems-are indeed such systems. Furthermore, it turns out that other alternative conceptions of computational information processing, Fodor's (1975) Language of Thought and Cummins' (1989) Interpretational Semantics appeal to substantially the same restrictive class of systems. The necessary connection of computational information processing with notationality saves the enterprise from charges of vacuousness and has some interesting implications for connectionism. But, unfortunately, it distorts the subject matter and entails some troubling consequences for a cognitive science which tries to make notationality do the work of genuine mental representations.
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  • 23
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    Minds and machines 1 (1991), S. 167-184 
    ISSN: 1572-8641
    Keywords: Connectionism ; eliminativism ; propositional attitudes ; representation ; symbols
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract Ramsey, Stich and Garon's recent paper ‘Connectionism, Eliminativism, and the Future of Folk Psychology’ claims a certain style of connectionism to be the final nail in the coffin of folk psychology. I argue that their paper fails to show this, and that the style of connectionism they illustrate can in fact supplement, rather than compete with, the claims of a theory of cognition based in folk psychology's ontology. Ramsey, Stich and Garon's argument relies on the lack of easily identifiable symbols inside the connectionist network they discuss, and they suggest that the existence of a system which behaves in a cognitively interesting way, but which cannot be explained by appeal to internal symbol processing, falsifies central assumptions of folk psychology. My claim is that this argument is flawed, and that the theorist need not discard folk psychology in order to accept that the network illustrated exhibits cognitively interesting behaviour, even if it is conceded that symbols cannot be readily identified within the network.
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  • 24
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    Minds and machines 1 (1991), S. 1-30 
    ISSN: 1572-8641
    Keywords: Artificial intelligence ; content ; cognitive science ; mind-body problem ; representation ; semantic ; syntax
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Philosophy
    Notes: Abstract I argue that there are no mental representations, in the sense of “representation” used in standard computational theories of the mind. I take Cummins' Meaning and Mental Representation as my stalking-horse, and argue that his view, once properly developed, is self-defeating. The argument implicitly undermines Fodor's view of the mind; I draw that conclusion out explicitly. The idea of mental representations can then only be saved by appeal to a Dennett-like instrumentalism; so I argue against that too. Finally, I argue that there is no good metaphysical reason in favour of believing in mental representations and that cognitive science can manage perfectly well without them.
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  • 25
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    Biology and philosophy 6 (1991), S. 205-226 
    ISSN: 1572-8404
    Keywords: Diagrams ; ethnomethodology ; knowledge ; photography ; representation ; science ; sociology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Philosophy
    Notes: Abstract Sociologists, philosophers and historians of science are gradually recognizing the importance of visual representation. This is part of a more general movement away from a theory-centric view of science and towards an interest in practical aspects of observation and experimentation. Rather than treating science as a matter of demonstrating the logical connection between theoretical and empirical statements, an increasing number of investigations are examining how scientists compose and use diagrams, graphs, photographs, micrographs, maps, charts, and related visual displays. This paper focuses on diagrams in biology, and tries to demonstrate how diagrams are an integral part of the production of scientific knowledge. In order to disclose some of the distinctive practical and analytical uses of diagrams, the paper contrasts the way diagrams and photographs are used in biological texts. Both diagrams and photographs are shown to be “constructions” that separately and together mediate the investigation of scientific phenoman.
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    Biology and philosophy 6 (1991), S. 255-274 
    ISSN: 1572-8404
    Keywords: Classification ; diagrams ; evolution ; history ; natural history ; natural system ; ornithology ; phylogeny ; representation ; systematics ; taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Philosophy
    Notes: Abstract ‘The Natural System’ is the abstract notion of the order in living diversity. The richness and complexity of this notion is revealed by the diversity of representations of the Natural System drawn by ornithologists in the Nineteenth Century. These representations varied in overall form from stars, to circles, to maps, to evolutionary trees and cross-sections through trees. They differed in their depiction of affinity, analogy, continuity, directionality, symmetry, reticulation and branching, evolution, and morphological convergence and divergence. Some representations were two-dimensional, and some were three-dimensional; n-dimensional representations were discussed but never illustrated. The study of diagrammatic representations of the Natural System is made difficult by the frequent failure of authors to discuss them in their texts, and by the consequent problem of distinguishing features which carried meaning from arbitrary features and printing conventions which did not. Many of the systematics controversies of the last thirty years have their roots in the conceptual problems which surrounded the Natural System in the late 1800s, problems which were left unresolved when interest in higher-level systematics declined at the turn of this century.
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    Journal of systems integration 1 (1991), S. 235-256 
    ISSN: 1573-8787
    Keywords: image processing ; graphics ; computer vision ; morphology ; integration ; computer-aided design ; recognition ; representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The integration of representation and recognition of rigid solid objects is becoming increasingly important in computer-aided design (CAD), computer-aided manufacturing (CAM), computer graphics, computer vision, and other fields that deal with spatial phenomena. The mathematical framework used for modeling solid objects is mathematical morphology, which is based on set-theoretic concept. The mathematical characteristics of these operators are investigated in order to achieve a formal theory. Using mathematical morphology as a tool, our theoretical research aims at studying the representation schemes for the dimension and tolerance of the geometric structure. Object features can be also extracted by using the mathematical morphology approach. Through a distance transformation, we can obtain the shape number, significant points database, and skeleton. We have also developed the object recognition, localization, and corner and circle detection algorithms.
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    Journal of automated reasoning 7 (1991), S. 631-634 
    ISSN: 1573-0670
    Keywords: Automated reasoning ; inference rule ; metarules ; representation ; strategy ; unsolved research problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This article is the nineteenth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find guidelines for simultaneously choosing the most effective representation, inference rule, and strategy. Since the three areas are tightly coupled, formulation of such guidelines requires understanding the precise nature of this coupling. For evaluating a proposed solution to this research problem, we suggest possible test problems from group theory, Gödel's finite axiomatization of set theory, and program verification.
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    Acta applicandae mathematicae 25 (1991), S. 277-299 
    ISSN: 1572-9036
    Keywords: 16S80 ; 17B37 ; 22D25 ; 46L89 ; 47A67 ; Duality ; quantum group ; C *-algebra ; Hopf algebra ; representation
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    Topics: Mathematics
    Notes: Abstract In this paper, we consider the *-representations of compact quantum groups and group duality. The main results in the paper are: (1) there is a one-to-one correspondence between the *-representations of compact quantum groups and *-representations of the dual Banach *-algebra; (2) the category of commutative compact quantum groups (semigroups) is a dual category to the category of compact groups (semigroups); (3) the dual category of the category of locally compact groups (semigroups) is the category of commutative Hopf C*-algebras with a particular property. Our group duality has the flavor of a Gelfand-Naimark type theorem for compact quantum groups, and for Hopf C*-algebras.
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    Journal for general philosophy of science 21 (1990), S. 347-358 
    ISSN: 1572-8587
    Keywords: artificial intelligence ; understanding ; representation ; meaning ; intentionality ; teleology ; subjectivity ; semiotics ; philosophical anthropology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Summary Artificial Intelligence can be considered as the so far last attempt to decode the anthropological comparison between human beings and machines. Thereby it also represents in a prominent way what can be called “systemic thought”. Searle's conclusive argument against strong AI (that is the idea of computers having intention in a literal way) refers to his precise distinction between syntax and semantics. This difference obviously opposing some of Searle's other essential ideas will only convince if it also explains the genetic-pragmatic aspect. A theory explaining the “life of mind” and the possibility of understanding needs to combine representation and intention with the subjective causation of signs. At the same time they have to be contextualized within a model of teleologically interpreted life recognized with the help of self-experience and self-reflection. This suggests that AI is a simulation which wrongly believes to be a real duplication. Actually it is a semiotic reduction (syntax and semantic surface of signs only) and a psychological compensation (Turing test) connected with a genetic or abductive fallacy. The biological decontextualization, in fact the elimination of teleology and intention, the deconstruction of subjectivity, the loss of the genetic-pragmatic dimension and the abductive fallacy induce the strong AI to confuse its surface-illusion of simulated understanding with the real process itself.
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    Mathematical programming 49 (1990), S. 1-5 
    ISSN: 1436-4646
    Keywords: Formulation ; linear inequalities ; representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We are given finitely many polyhedra defined by linear constraints, using the same constraint matrix and different right-hand sides. We consider a simple constraint system and give necessary and sufficient conditions for this system to define the union of the polyhedra. We also show that deciding whether the system does define the union is NP-hard.
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    Multidimensional systems and signal processing 1 (1990), S. 251-278 
    ISSN: 1573-0824
    Keywords: AR 2-D system ; behavior ; representation ; polynomial ideal (module) ; Gröbner basis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A canonical form for AR 2-D systems representations is introduced. This yields a method for computing the system trajectories by means of a line-by-line recursion, and displays some relevant information about the system structure such as the choice of inputs and initial conditions.
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    Journal of automated reasoning 6 (1990), S. 463-464 
    ISSN: 1573-0670
    Keywords: Automated reasoning ; functions ; notation ; predicates ; representation ; unsolved research problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This article is the sixteenth of a series of articles discussing various open research problems in automated reasoning. Here we focus on choosing between the use of predicates and the use of functions for representing information to an automated reasoning program. The problem proposed for research asks one to find criteria that dictate the most effective choice of notation-functions or predicates-for presenting the question to be studied. The criteria must reflect the close coupling between inference rule, strategy, and representation. We suggest possible test problems for evaluating a proposed solution to this research problem.
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