Skip to main content
SpringerLink
Log in

“Prototypes” and “fuzziness” in the logic of concepts

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

“Prototypes” and “fuzziness” are regarded in this paper as fundamental phenomena in the inherent logic of concepts whose relationship, however, has not been sufficiently clarified. Therefore, modifications are proposed in the definition of both. Prototypes are defined as the elements possessing maximal degree of membership in the given category such thatthis membership has maximal cognitive efficiency in representing theelement. A modified fuzzy set (m-fuzzy set) is defined on aclass (possibly self-contradictory collection) such that its core (the collection of elements with full membership) is aset (self-consistent collection) comprising the finite set of the prototypes. In this scheme of recursive representation the possibility of contradictions, which has been proven to be inevitable in the logic of concepts, islocalized. Finally a related model of the brain's pattern recognition mechanism is briefly summarized.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Armstrong, S. L., Gleitman, L. R. and Gleitman, H.: 1983, ‘What Some Concepts Might Not Be’,Cognition 13, 263–308.

    Google Scholar 

  • Barsalou, L. W.: 1983, ‘Ad Hoc Categories’,Memory and Cognition 11, 211–27.

    Google Scholar 

  • Berlin, B., Breedlove, D. E. and Raven, P. H.: 1973, ‘General Principles of Classification and Nomenclature in Folk Biology’,American Anthropologist 75, 214–42.

    Google Scholar 

  • Berlin, B. and Kay, P.: 1969,Basic Color Terms: Their Universality and Evolution, University of California Press, Berkeley.

    Google Scholar 

  • Cantor, N., Mischel, W. and Schwartz, J. C.: 1982, ‘A Prototype Analysis of Psychological Situations’,Cognitive Psychology 14, 45–77.

    Google Scholar 

  • Chen, C. H.: 1973,Statistical Pattern Recognition, Hayden, New York.

    Google Scholar 

  • Cohen, L. J.: 1981, ‘Can Human Irrationality Be Experimentally Demonstrated?’,Behavior and Brain Sciences 4 317–70.

    Google Scholar 

  • Cohen, B. and Murphy, G. L.: 1984, ‘Models of Concepts’,Cognitive Science 8, 27–58.

    Google Scholar 

  • Dahlgren, K.: 1985, ‘The Cognitive Structure of Social Categories’,Cognitive Science 9, 379–98.

    Google Scholar 

  • Dubois, D. and Prade, H.: 1980,Fuzzy Sets and Systems, Academic Press, New York.

    Google Scholar 

  • Fodor, J. A.: 1983,The Modularity of Mind, MIT Press, Cambridge.

    Google Scholar 

  • Fraenkel, A. A., Bar-Hillel, Y. and Levy, A.: 1973,Foundations of Set Theory, (2nd rev. ed.), North-Holland, Amsterdam.

    Google Scholar 

  • Fu, K. S.: 1982,Syntactic Pattern Recognition and Applications, Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Fuhrmann, Gy.: 1981, ‘Modelling the Visual Cortex with “Modulo System” Concept’,Biological Cybernetics 40, 39–48.

    Google Scholar 

  • Fuhrmann, Gy.: 1982, ‘A Recognizing Neural Network: Modulo System, for Extracting and Syntactically Processing of the Important Properties of Patterns’, in R. Trappl, G. Pask and L. M. Ricciardi (eds.),Progress in Cybernetics and Systems Research, IX, pp. 305–11, Hemisphere, Washington. Reprinted in R. K. Ragade (ed.),General Systems XXVII, pp. 147–53, Society for General Systems Research, Louisville, 1983.

    Google Scholar 

  • Fuhrmann, Gy.: 1984, ‘Syntax as the Model of Semantics in Brain Modelling’,Cybernetica 27, 39–56.

    Google Scholar 

  • Fuhrmann, Gy.: 1985a, ‘Interdisciplinary Approach to the Brain's Pattern Recognition’,Cybernetica 28, 107–45.

    Google Scholar 

  • Fuhrmann, Gy.: 1985b, ‘Arithmetic Model for the Distributed Encoding in the Neuron Module’,International Journal of Neuroscience 27, 131–48.

    Google Scholar 

  • Fuhrmann, Gy.: 1985c, ‘Mathematical Approach to Integrating the “Neuron-Module” and the “Cell-Assembly”’,International Journal of Neuroscience 28, 91–110.

    Google Scholar 

  • Fuhrmann, Gy.: 1986, ‘Arithmetic Codes Resembling Neural Encoding’,Information Sciences 39, 197–203.

    Google Scholar 

  • Fuhrmann, Gy.: 1988, ‘Fuzziness of Concepts and Concepts of Fuzziness’,Synthese 75, 349–372.

    Google Scholar 

  • Fuhrmann, Gy.: forthcoming a, Note on the Generality of Fuzzy Sets. (Submitted for publication.)

  • Fuhrmann, Gy.: forthcoming b, Note on the Integration of Prototype Theory and Fuzzy-set Theory. (Submitted for publication.)

  • Goguen, J. A.: 1969, ‘The Logic of Inexact Concepts’,Synthese 19, 325–73.

    Google Scholar 

  • Goguen, J. A.: 1974, ‘Concept Representation in Natural and Artificial Languages: Axioms, Extensions, and Applications for Fuzzy Sets’,International Journal of Man-Machine Studies 6, 513–61. Reprinted in E. H. Mamdani and B. R. Gaines (eds.): 1981,Fuzzy Reasoning and Its Applications, Academic Press, New York, pp. 67–115.

    Google Scholar 

  • Hampton, J. A.: 1982, ‘A Demonstration of Intransitivity in Natural Categories’,Cognition 12, 151–64.

    Google Scholar 

  • Hebb, D. O.: 1949,The Organization of Behavior, Wiley, New York.

    Google Scholar 

  • Hersch, H. M. and Caramazza, A.: 1976, ‘A Fuzzy Set Approach to Modifiers and Vagueness in Natural Language’,Journal of Experimental Psychology: General 105, 245–67.

    Google Scholar 

  • Herskovits, A.: 1985, ‘Semantics and Pragmatics of Locative Expressions’,Cognitive Science 9, 341–78.

    Google Scholar 

  • Jones, G. V.: 1982, ‘Stacks Not Fuzzy Sets: An Ordinal Basis for Prototype Theory of Concepts’,Cognition 12, 281–90.

    Google Scholar 

  • Kandel, A.: 1986,Fuzzy Mathematical Techniques with Applications, Addison-Wesley, Reading.

    Google Scholar 

  • Kaufmann, A.: 1975,Introduction to the Theory of Fuzzy Subsets 1, Academic Press, New York.

    Google Scholar 

  • Lewis, E. R.: 1983, ‘The Elements of Single Neurons: A Review’,IEEE Transactions on Systems, Man, and Cybernetics 13, 702–10.

    Google Scholar 

  • Loftus, E. F.: 1975, ‘Spreading Activation within Semantic Categories: Comments on Rosch's ‘Cognitive representations of semantic categories’’,Journal of Experimental Psychology: General 104, 234–40.

    Google Scholar 

  • Maurer, H. A., Salomaa, A. and Wood, D.: 1980, ‘Pure Grammars’,Information and Control 44, 47–72.

    Google Scholar 

  • Mervis, C. B. and Rosch, E.: 1981, ‘Categorization of Natural Objects’,Annual Review of Psychology 32, 89–115.

    Google Scholar 

  • Miller, G. A. and Johnson-Laird, P. N.: 1976,Language and Perception, Harvard University Press, Cambridge.

    Google Scholar 

  • Mountcastle, V. B.: 1978, ‘An Organizing Principle for Cerebral Function: The Unit Module and the Distributed System’, in G. M. Edelman and V. B. Mountcastle:The Mindful Brain, MIT Press, Cambridge, pp. 7–50. Reprinted in F. O. Schmitt and F. G. Worden (eds.),The Neurosciences: Fourth Study Program, pp. 21–42, MIT Press, Cambridge, 1979.

    Google Scholar 

  • Murphy, G. L. and Smith, E. E.: 1982, ‘Basic-level Superiority in Picture Categorization’,Journal of Verbal Learning and Verbal Behavior 21, 1–20.

    Google Scholar 

  • Oden, G. C.: 1977, ‘Integration of Fuzzy Logical Information’,Journal of Experimental Psychology: Human Perception and Performance 3, 565–75.

    Google Scholar 

  • Osheron, D. N. and Smith, E. E.: 1981, ‘On the Adequacy of Prototype Theory as a Theory of Concepts’,Cognition 9, 35–58.

    Google Scholar 

  • Osheron, D. N. and Smith, E. E.: 1982, ‘Gradedness and Conceptual Combination’,Cognition 12, 299–318.

    Google Scholar 

  • Piaget, J.: 1963, ‘L'explication en psychologie et le parallélisme psychophysiologique’, in J. Piaget, P. Fraisse and M. Reuchlin,Traité de psychologie expérimentale, I. Histoire et méthode, Presses Universitaires de France, Paris, pp. 121–52.

    Google Scholar 

  • Posner, M. I. and Keele, S. W.: 1968, ‘On the Genesis of Abstract Ideas’,Journal of Experimental Psychology 77, 353–63.

    Google Scholar 

  • Reed, S. K.: 1972, ‘Pattern Recognition and Categorization’,Cognitive Psychology 3, 382–407.

    Google Scholar 

  • Reed, S. K.: 1973,Psychological Processes in Pattern Recognition, Academic Press, New York.

    Google Scholar 

  • Rescher, N.: 1969,Many-Valued Logic, McGraw-Hill, New York.

    Google Scholar 

  • Rosch, E.: 1973, ‘On the Internal Structure of Perceptual and Semantic Categories’, in T. E. Moore (ed.),Cognitive Development and the Acquisition of Language, Academic Press, New York, pp. 111–44.

    Google Scholar 

  • Rosch, E.: 1975a, ‘Cognitive Representations of Semantic Categories’,Journal of Experimental Psychology: General 104, 192–233.

    Google Scholar 

  • Rosch, E.: 1975b, ‘Cognitive Reference Points’,Cognitive Psychology 7, 532–47.

    Google Scholar 

  • Rosch, E.: 1978, ‘Principles of categorization’, in Rosch and Lloyd (1978), pp. 27–48.

    Google Scholar 

  • Rosch, E. and Lloyd, B. B. (eds.): 1978,Cognition and Categorization, Erlbaum, Hillsdale.

    Google Scholar 

  • Rosch, E. and Mervis, C. B.: 1975, ‘Family Resemblances: Studies in the Internal Structure of Categories’,Cognitive Psychology 7, 573–605.

    Google Scholar 

  • Rosch, E., Mervis, C. B., Gray, W. D., Johnson, D. M. and Boyes-Braem, P.: 1976, ‘Basic Objects in Natural Categories’,Cognitive Psychology 8, 382–439.

    Google Scholar 

  • Rosch, E., Simpson, C. and Miller, R. S.: 1976, ‘Structural Basis of Typicality Effects’,Journal of Experimental Psychology: Human Perception and Performance 2, 491–502.

    Google Scholar 

  • Roth, E. M. and Mervis, C. B.: 1983, ‘Fuzzy Set Theory and Class Inclusion Relations in Semantic Categories’,Journal of Verbal Learning and Verbal Behavior 22, 509–25.

    Google Scholar 

  • Salomaa, A.: 1973,Formal Languages, Academic Press, New York. (Chapter V, ‘Regulated Rewriting’, pp. 142–94.)

    Google Scholar 

  • Simpson, G. G.: 1961,Principles of Animal Taxonomy, Columbia University, New York.

    Google Scholar 

  • Smith, E. E. and Osheron, D. N.: 1984, ‘Conceptual Combination with Prototype Concepts’,Cognitive Science 8, 337–61.

    Google Scholar 

  • Szentágothai, J.: 1975, ‘The “Module Concept’ in Cerebral Cortex Architecture’,Brain Research 95, 475–96.

    Google Scholar 

  • Szentágothai, J.: 1978, ‘The Neuron Network of the Cerebral Cortex: A Functional Interpretation’,Proceedings of the Royal Society of London B 201, 219–48.

    Google Scholar 

  • Tversky, A.: 1977, ‘Features of Similarity’,Psychological Review 84, 317–52.

    Google Scholar 

  • Tversky, A. and Hemenway, K.: 1983, ‘Categories of Environmental Scenes’,Cognitive Psychology 15, 121–49.

    Google Scholar 

  • Vizi, E. S.: 1984,Non-synaptic Interactions Among Neurons, Wiley, New York.

    Google Scholar 

  • Zadeh, L. A.: 1965, ‘Fuzzy Sets’,Information and Control 8, 338–53.

    Google Scholar 

  • Zadeh, L. A.: 1975, ‘Calculus of Fuzzy Restrictions’, in L. A. Zadeh, K. S. Fu, K. Tanaka and M. Shimura (eds.),Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, pp. 1–39.

    Google Scholar 

  • Zadeh, L. A.: 1976, ‘A Fuzzy Algorithmic Approach to the Definition of Complex or Imprecise Concepts’,International Journal of Man-Machine Studies 8, 249–91.

    Google Scholar 

  • Zadeh, L. A.: 1982, ‘A Note on Prototype Theory and Fuzzy Sets’,Cognition 12, 291–97.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IGAC Computer Science Laboratory, Technical University of Budapest, Pöttyös u.4., 1098, Budapest, Hungary

    Gy. Fuhrmann

Authors
  1. Gy. Fuhrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fuhrmann, G. “Prototypes” and “fuzziness” in the logic of concepts. Synthese 75, 317–347 (1988). https://doi.org/10.1007/BF00869404

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00869404

Keywords

Search

Navigation