Skip to main content
SpringerLink
Log in

A Glance at Non-Standard Models and Logics of Uncertainty and Vagueness

  • Chapter
Philosophy of Probability

Part of the book series: Philosophical Studies Series ((PSSP,volume 56))

Abstract

Historically, it is well known that the notion of probability emerged in the 17th century as a dual concept: chance, related to gaming problems, and subjective uncertainty, related to the question of reliability of testimonies. In the works of pioneers of probability theory, such as J. Bernoulli, chance, very soon connected to frequency of occurrence, was an additive notion but subjective probability was not so. However with the development of physical sciences, the non-additive side of probability was forgotten (see Shafer, 1978). So much so as 20th century researchers in decision theory have devoted much effort in the non-frequentist justification of additive probability as a model for subjective uncertainty in rational decision strategies.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adams, E.W. (1975) The Logic of Conditionals. Reidel, Dordrecht.

    Book  Google Scholar 

  • Adams, E.W., Levine, H.P. (1975) On the uncertainties transmitted from premises to conclusions in deductive inferences. Synthese, 30, 429–460.

    Article  Google Scholar 

  • Bacchus, F. (1990) Representing and Reasoning with Probabilistic Knowledge—A Logical Approach to Probabilities. MIT Press, Cambridge, MA & London.

    Google Scholar 

  • Bezdek, J.C. (1981) Pattern Classification with Fuzzy Objective Function Models. Plenum Press, New York.

    Book  Google Scholar 

  • Boole, G. (1854) An Investigation of the Laws of Thought on which are Founded the Mathematical Theory of Logic and Probabilities. MacMillan. (Reprinted by Dover, New York, 1958).

    Google Scholar 

  • Buchanan, B.G., Shortliffe, E.H. (1984) Rule-Based Expert Systems—The MYCIN Experiments of the Stanford Heuristic Programming Project. Addison-Wesley, Reading.

    Google Scholar 

  • Calabrese, P. (1987) An algebraic synthesis of the foundations of logic and probability. Information Sciences, 42, 187–237.

    Article  Google Scholar 

  • Carnap, R. (1950) Logical Foundations of Probability. Routlege & Kegan Paul, London.

    Google Scholar 

  • Chateauneuf, A. (1988a) Uncertainty aversion and risk aversion in models with nonadditive probabilities. In: Risk, Decision and Rationality (B.R. Munier, ed.), Reidel, Dordrecht, 615–629.

    Chapter  Google Scholar 

  • Chateauneuf, A. (1988b) Decomposable measures, distorted probabilities and concave capacities. FUR-IV Conf. Foundations of Utility and Risk Theories, Budapest, April.

    Google Scholar 

  • Choquet, G. (1953) Theory of capacities. Ann. Inst. Fourier (Grenoble), 5(4), 131–295.

    Google Scholar 

  • Cox, R.T., (1946) Probability, frequency and reasonable expectation. American Journal of Physics, 14, 1–13.

    Article  Google Scholar 

  • De Campos, L.M., Lamata, M.T., Moral, S. (1990) The concept of conditional fuzzy measure. Int. J. of Intelligent Systems, 5, 237–246.

    Article  Google Scholar 

  • De Finetti, B. (1937) La prévision: ses lois logiques, ses sources subjectives. Ann. Inst. Poincaré 7, 1937, 1–68. Translated in: Studies in Subjective Probability (H. Kyburg, Jr., H.E. Smokier, eds.), Wiley, New York, 1964.

    Google Scholar 

  • Dempster, A.P. (1967) Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist., 38, 325–339.

    Article  Google Scholar 

  • Dubois, D. (1986a) Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence (Bratislava), 5, 403–416.

    Google Scholar 

  • Dubois, D. (1986b) Generalized probabilistic independence and its implications for utility. Operations Research Letters, 5, 255–260.

    Article  Google Scholar 

  • Dubois, D., Lang, J., Prade, H. (1989) Automated reasoning using possibilistic logic: semantics, belief revision and variable certainty weights. Proc. of the 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Ontario, August 18–20, 81–87. To appear in IEEE Trans, on Data and Knowledge Engineering, 1993.

    Google Scholar 

  • Dubois, D., Prade, H. (1980) Fuzzy Sets and Systems: Theory and Applications. Mathematics in Sciences and Engineering Series, Vol. 144, Academic Press, New York.

    Book  Google Scholar 

  • Dubois, D., Prade, H. (1982) A class of fuzzy measures based on triangular norms. Int. J. of General Systems, 8, 43–61.

    Article  Google Scholar 

  • Dubois, D, Prade, H. (1985a) Evidence measures based on fuzzy information. Automatica, 21, 547–562.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1985b) A review of fuzzy set aggregation connectives. Information Sciences, 36, 85–121.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1985c) (with the collaboration of Farreny, H., Martin-Clouaire, R., Testemale, C.) Théorie des Possibilités-Applications à la Représentation des Connaissances en Informatique. Masson, Paris. 2nd Revised and augmented edition, 1987). English translation: Possibility Theory—An Approach to the Computerized Processing of Uncertainty, Plenum Press, New York, 1988.

    Google Scholar 

  • Dubois, D., Prade, H. (1986a) The principle of minimum specificity as a basis for evidential reasoning. In: Uncertainty in Knowledge-Based Systems (Inter. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, France, June 30-July 4, 1986) (B. Bouchon, R.R. Yager, eds.), Lecture Notes in Computer Science, Springer Verlag, Berlin, 75–84.

    Google Scholar 

  • Dubois, D., Prade, H. (1986b) A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. Int. J. of General Systems, 12, 193–226.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1987a) The mean value of a fuzzy number. Fuzzy Sets and Systems, 24, 279–300.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1987b) Necessity measures and the resolution principle. IEEE Trans, on Systems, Man and Cybernetics, 17, 474–478.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1988a) Modelling uncertainty and inductive inference: a survey of recent non-additive probability systems. Acta Psychologica, 68, 53–78.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1988b) An introduction to possibilistic and fuzzy logics. In: Non-Standard Logics for Automated Reasoning (P. Smets, A. Mamdani, D. Dubois, H. Prade, eds.), Academic Press, New York, 287–326.

    Google Scholar 

  • Dubois, D., Prade, H. (1988c) On fuzzy syllogisms. Computation Intelligence (Canada), 4(2), 171–179.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1988d) Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence (Canada), 4(4), 244–264.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1989) Fuzzy sets, probability and measurement. Europ. J. of Operational Research, 40, 135–154.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1990a) The logical view of conditioning and its applications to possibility and evidence theories. Int. J. of Approximate Reasoning, 4, 23–46.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1990b) Rough fuzzy sets and fuzzy rough sets. Int. J. of General Systems, 17, 191–209.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1991a) Updating with belief functions, ordinal conditional functions and possibility measures. In: Uncertainty in Artificial Intelligence Vol. 6 (P.P. Bonissone, M. Henrion, L.N. Kanal, J.F. Lemmer, eds.), North-Holland, Amsterdam, 311–329.

    Google Scholar 

  • Dubois, D., Prade, H. (1991b) Conditional objects and non-monotonic reasoning. Proc. of the 2nd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’91), Cambridge, MA, April 22–25, 1991 (J. Allen, R. Fikes, E. Sandewall, eds.), Morgan Kaufmann, pp. 175–185.

    Google Scholar 

  • Dubois, D., Prade, H. (1991c) Possibilistic logic, preference models, non- monotonicity and related issues. Proceedings 12th Inter. Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Aus., 419–424.

    Google Scholar 

  • Dubois, D., Prade, H. (1991d) Fuzzy sets in approximate reasoning—Part 1: Inference with possibility distributions. Fuzzy Sets and Systems, 25th Anniversary Memorial Volume, 40, 143–202.

    Article  Google Scholar 

  • Dubois, D., Prade, H. (1991e) Epistemic entrenchment and possibilistic logic. Artificial Intelligence, 50, 223–239.

    Article  Google Scholar 

  • Dubucs, J.P. (1989) Logiques non-classiques. Encyclopedia Universalis, 977–992.

    Google Scholar 

  • Fagin, R., Halpern, J.Y. (1989a) Uncertainty, belief and probability. Proc. of the 11th Inter. Joint Conf. on Artificial Intelligence (IJCAI-89), Detroit, Michigan, 1161–1167.

    Google Scholar 

  • Fagin, R., Halpern, J.Y. (1989b) A new approach to updating beliefs. Research Report RJ 7222, IBM, Research Division, San Jose, CA.

    Google Scholar 

  • Farinas del Cerro, L., Orlowska, E. (1985) DAL—A logic for data analysis. Theoretical Computer Science, 36, 251–264.

    Article  Google Scholar 

  • Farinas del Cerro, Prade, H. (1986) Rough sets, twofold fuzzy sets and modal logic—Fuzziness in indiscernibility and partial information. In: The Mathematics of Fuzzy Systems (A. Di Nola, A.G.S. Ventre, eds.), Verlag TÜV Rheinland, Köln, 103–120.

    Google Scholar 

  • Fenstad, J.E. (1967) Representations of probabilities defined on first order languages. In: Sets, Models and Recursion Theory (J.N. Crossley, ed.), North-Holland, Amsterdam, 156–172.

    Chapter  Google Scholar 

  • Fine, K. (1975) Vagueness, truth and logic. Synthese, 30, 265–300.

    Article  Google Scholar 

  • Fine, T.L. (1973) Theories of Probability. Academic Press, New York.

    Google Scholar 

  • Fishburn, P.C. (1986a) The axioms of subjective probability. Statistical Science, 1, 335–358.

    Article  Google Scholar 

  • Fishburn, P.C. (1986b) Interval models for comparative probability on finite sets. J. of Mathematical Psychology, 30, 221–242.

    Article  Google Scholar 

  • Gabbay, D.M. (1985) Theoretical foundations for non-monotonic reasoning in expert systems. In: Logics and Models of Concurrent Systems (K.R. Apt., ed.), Springer Verlag, Berlin, 439–457.

    Chapter  Google Scholar 

  • Gärdenfors, P. (1988) Knowledge in Flux—Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge, MA & London.

    Google Scholar 

  • Gärdenfors, P., Hansson, B., Sahlin, N.E. (Eds.) (1983) Evidentiary Value: Philosophical, Judicial and Psychologuical aspects of a Theory. CWK Gleenrups, Lund, Library of Theoria n015.

    Google Scholar 

  • Gil, M.A. (1988) Probabilistic-possibilistic approach to some statistical problems with fuzzy experimental observations. In: Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision-Making (J. Kacprzyk, M. Fedrizzi, eds.) Lecture Notes in Economics and Mathematical Systems, Vol. 310, Springer Verlag, Berlin, 286–306.

    Chapter  Google Scholar 

  • Gilboa, I. (1987) Expected utility with purely subjective non-additive probabilities. J. Math. Econom., 16, 65–88.

    Article  Google Scholar 

  • Giles, R. (1982) Foundations for a theory of possibility. In: Fuzzy Information and Decision Processes (M.M. Gupta, E. Sanchez, eds.), North-Holland, Amsterdam, 183–195.

    Google Scholar 

  • Goguen, J. A. (1969) The logic of inexact concepts, Synthese, 19, 1–36.

    Article  Google Scholar 

  • Goodman, I.R., Nguyen, H.T. (1988) Conditional objects and the modeling of uncertainties. In: Fuzzy Computing—Theory, Hardware, and Applications (M.M. Gupta, T. Yamakawa, eds.), North-Holland, Amsterdam, 119–138.

    Google Scholar 

  • Halmos, P. (1950) Measure Theory. Van Nostrand.

    Google Scholar 

  • Hisdal, E. (1988) Are grades of membership probabilities? Fuzzy Sets and Systems, 25, 325–348.

    Article  Google Scholar 

  • Höhle, U. (1988) Quotients with respect to similarity relations. Fuzzy Sets and Systems, 27, 31–44.

    Article  Google Scholar 

  • Hughes, G.E., Cresswell, M.J. (1968) An Introduction to Modal Logic, Methuen, London.

    Google Scholar 

  • Jaffray, J.Y. (1990) Bayesian updating and belief functions. Proc. of the 3rd Inter. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU’90), Paris, July, 449–451 (published by ENSTA, Paris).

    Google Scholar 

  • Jardine, N., Sibson, R. (1977) Mathematical Taxonomy. Wiley, New York.

    Google Scholar 

  • Jeffrey, R. (1983) The Logic of Decision (2nd ed.). University of Chicago Press, Chicago, IL.

    Google Scholar 

  • Klement, E.P. (1982) Construction of fuzzy σ-algebras using triangular norms. J. of Mathematical Analysis and Applications, 85, 543–566.

    Article  Google Scholar 

  • Klir, G. J. (ed.) (1987) Special Issue on “Measures of Uncertainty. ” Fuzzy Sets and Systems, 24(2).

    Google Scholar 

  • Kruse, R., Meyer, K.D. (1987) Statistics with Vague Data. D. Reidel, Dordrecht.

    Book  Google Scholar 

  • Kyburg, H.E., Jr. (1974) The Logical Foundations of Statistical Inference. D. Reidel, Dordrecht.

    Book  Google Scholar 

  • Kyburg, H.E., Jr. (1987) Bayesian and non-Bayesian evidential updating. Artificial Intelligence, 31, 271–293.

    Article  Google Scholar 

  • Lang, J., Dubois, D., Prade, H. (1991) A logic of graded possibility and certainty coping with partial inconsistency. Proc. 7th Conference on Uncertainty in Artificial Intelligence, Los Angeles (Edited by B. D’Ambrosio, P. Smets, P. Bonissone) Morgan Kaufmann Pub. San Mateo, Ca., pp. 188–196.

    Google Scholar 

  • Lehrer, K., Wagner, C. (1981) Rational Consensus in Science and Society. D. Reidel Publishing Company, Boston.

    Book  Google Scholar 

  • Lewis, D. (1976) Probabilities of conditionals and conditional probabilities. Phil. Rev., 85, 297–315.

    Article  Google Scholar 

  • Løs, J. (1963) Semantic representations of the probability of formulas in formalized theories. Studia Logica, 14, 183–194.

    Article  Google Scholar 

  • Makinson D., Gärdenfors, P. (1991) Relations between the logic of theory change and non-monotonic logic. In: The Logic of Theory Change (A. Fuhrmann, M. Morreau, Eds) Lecture Notes in Artificial Intelligence vol. 465, Springer Verlag, Berlin, 185–205.

    Chapter  Google Scholar 

  • Mamdani, E.H. (1977) Application of fuzzy logic to approximate reasoning using linguistic systems. IEEE Trans, on Computers, 26, 1182–1191.

    Article  Google Scholar 

  • Menger, K. (1951) Probabilistic theories of relations. Proc. Nat. Acad. Sci. USA, 37, 178–180.

    Article  Google Scholar 

  • Murofushi, T., Sugeno, M. (1989) An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets and Systems, 29, 201–227.

    Article  Google Scholar 

  • Neufeld, E. (1990) A probabilistic commonsense reasoner. Int. J. of Intelligent Systems, 5, 565–594.

    Article  Google Scholar 

  • Nguyen, H.T. (1978) On random sets and belief functions. J. of Mathematical Analysis and Applications, 65, 531–542.

    Article  Google Scholar 

  • Nilsson, N. (1986) Probabilistic logic. Artificial Intelligence, 28, 71–87.

    Article  Google Scholar 

  • Norwich, A.M., Turksen, I.B. (1982) The fundamental measurement of fuzziness. In: Fuzzy Set and Possibility Theory: Recent Developments (R.R. Yager, ed.), Pergamon Press, Oxford, 49–50.

    Google Scholar 

  • Novak, V. (1990) On the Syntactico-semantical completeness of first-order fuzzy logic—Part I: syntax and semantics. Kybernetika, 26(1), 47–66; Part II: Main results, Kybernetika, (26)2, 134–154.

    Google Scholar 

  • Paass, G. (1988) Probabilistic logic. In: Non-Standard Logics for Automated Reasoning (P. Smets, E.H. Mamdani, D. Dubois, H. Prade, eds.), Academic Press, New York, 213–251.

    Google Scholar 

  • Pavelka, J. (1979) On fuzzy logic. Zeitschr. f. Math. Logik und Grundlagen d. Math., 25, Part I: 45–72; Part II: 119–134; Part III: 447–464.

    Article  Google Scholar 

  • Pawlak, Z. (1982) Rough sets. Int. J. of Computer and Informatics Sciences, 11, 341–356.

    Article  Google Scholar 

  • Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufman, San Mateo, CA.

    Google Scholar 

  • Poincaré, H. (1902) La Science et l’Hypothèse. Flammarion, Paris.

    Google Scholar 

  • Prade, H. (1985) A computational approach to approximate reasoning with applications to expert systems. IEEE Trans, on Pattern Analysis and Machine Intelligence, 7, 260–283. Corrections, 7, 747–748.

    Article  Google Scholar 

  • Reichenbach, H. (1949) The Theory of Probability. University of California Press, Berkeley and Los Angeles.

    Google Scholar 

  • Ruspini, E.H. (1991) On the semantics of fuzzy logic. Int. J. of Approximate Reasoning, 5, 45–88.

    Article  Google Scholar 

  • Schay, G. (1968) An algebra of conditional events. J. Math. Anal. & Appl., 24, 334–344.

    Article  Google Scholar 

  • Schmeidler, D. (1986) Integral representation without additivity. Proc. Amer. Math. Soc., 97, 255–261.

    Article  Google Scholar 

  • Schweizer, B., Sklar, A. (1983) Probabilistic Metric Spaces. North-Holland, Amsterdam.

    Google Scholar 

  • Shackle, G.L.S. (1961) Decision, Order and Time in Human Affairs. (2nd edition) Cambridge University Press, Cambridge.

    Google Scholar 

  • Shafer, G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton, N.J.

    Google Scholar 

  • Shafer, G. (1978) Non-additive probabilities in the work of Bernoulli and Lambert. Archive for History of Exact Sciences, 19, 309–370.

    Article  Google Scholar 

  • Shafer, G. (1986) The combination of evidence. Int. J. of Intelligent Systems, 1, 155–180.

    Article  Google Scholar 

  • Shafer, G., (1990) The unicity of probability. In: Acting Under Uncertainty: Multidisciplinary Conceptions (G.M. von Furstenberg, ed.), Kluwer Academic Pub., Boston.

    Google Scholar 

  • Shoham, Y. (1988) Reasoning About Change—Time and Causation from the Standpoint of Artificial Intelligence. The MIT Press, Cambridge, Mass.

    Google Scholar 

  • Smets, P. (1978) Un modèle mathématico-statistique simulant le processus du diagnostic médical. Doctoral Dissertation, Free University of Brussels, Presses Universitaires de Bruxelles. Available through University Microfilm International, 30–32 Mortimer Street, London WIN 7RA, Thesis 80–70,003).

    Google Scholar 

  • Smets, P. (1981) The degree of belief in a fuzzy event. Information Sciences, 25, 1–19.

    Article  Google Scholar 

  • Smets, P. (1988) Belief functions. In: Non-Standard Logics for Approximate Reasoning (P. Smets, A. Mamdani, D. Dubois, H. Prade, eds.), Academic Press, New York, 253–286.

    Google Scholar 

  • Smith, C.A.B. (1961) Consistency in statistical inference and decision. J. Royal Statist. Soc., B-23, 1–23.

    Google Scholar 

  • Spohn, W. (1988) Ordinal conditional functions: a dynamic theory of epistemic states. In: Causation in Decision, Belief Change, and Statistics (W.L. Harper, B. Skyrms, eds.), Kluwer Academic Publ., 105–134.

    Chapter  Google Scholar 

  • Spohn, W. (1990) A general non-probabilistic theory of inductive reasoning. In: Uncertainty in Artificial Intelligence 4 (R.D. Shachter, T.S. Levitt, L.N. Kanal, J.F. Lemmer, eds.), North-Holland, Amsterdam, 149–158.

    Google Scholar 

  • Sugeno, M. (1977) Fuzzy measures and fuzzy integral: a survey. In: Fuzzy Automata and Decision Processes (M.M. Gupta, G.N. Sardis, B.R. Gaines, eds.), North-Holland, Amsterdam, 89–102.

    Google Scholar 

  • Suppes, P. (1974) The measurement of belief. J. of Royal Statist. Soc., B-26, 160–191.

    Google Scholar 

  • Suppes, P., Zanotti, M. (1977) On using random relations to generate upper and lower probabilities. Synthese, 36, 427–440.

    Article  Google Scholar 

  • Turksen, I.B. (1991) Measurement of membership functions and their acquisition. Fuzzy Sets and Systems, Silver Anniversary Issue, 40, 5–38.

    Google Scholar 

  • Valverde, L. (1985) On the structure of F-indistinguishability operators. Fuzzy Sets and Systems, 17, 313–328.

    Article  Google Scholar 

  • Wagner, C.G. (1989) Consensus for belief functions and related uncertainty measures. Theory and Decision, 26, 295–304.

    Article  Google Scholar 

  • Wajsberg, M. (1935) Beiträge zum Metaaussagenkalk ül I. Monatshefte für Mathematik und Physik, 42, 221–242.

    Article  Google Scholar 

  • Wakker, P.P. (1989) Continuous subjective expected utility with non-additive probabilities. J. Math. Econom., 18, 1–27.

    Article  Google Scholar 

  • Walley, P. (1991) Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London.

    Google Scholar 

  • Weber, S. (1984) Decomposable measures and integrals for Archimedean t-conorms. J. of Mathematical Analysis and Applications, 101, 114–138.

    Article  Google Scholar 

  • Weber, S. (1988) Conditional measures based on archimedean semigroups. Fuzzy Sets and Systems, 27, 63–72.

    Article  Google Scholar 

  • Wellman, M.P. (1990) Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence, 44, 257–303.

    Article  Google Scholar 

  • Weston, T. (1987) Approximate truth. J. Philos. Logic, 16, 203–227.

    Article  Google Scholar 

  • Williams, P. (1980) Bayesian conditionalization and the principle of minimum information. British J. for the Philosophy of Science, 31, 131–144.

    Article  Google Scholar 

  • Wong, S.K.M. (1991) Propagation of preference relations in qualitative inference networks. 12th Inter. Joint Conf. on Artificial Intelligence, Sydney, Aus. pp. 1204–1209.

    Google Scholar 

  • Yaari, M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95–115.

    Article  Google Scholar 

  • Yager, R.R. (1984) Probabilities from fuzzy observations. Information Sciences, 32, 1–131.

    Article  Google Scholar 

  • Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353.

    Article  Google Scholar 

  • Zadeh, L.A. (1968) Probability measures of fuzzy events. J. of Mathematical analysis and Applications, 23, 421–427.

    Article  Google Scholar 

  • Zadeh, L.A. (1971) Similarity relations and fuzzy orderings. Information Sciences, 3, 177–200.

    Article  Google Scholar 

  • Zadeh, L. A. (1975) The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, Part I: 8, 199–249;

    Article  Google Scholar 

  • Zadeh, L. A. (1975) The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, Part II: 8, 301–357;

    Article  Google Scholar 

  • Zadeh, L. A. (1975) The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, Part III: 9, 43–80.

    Article  Google Scholar 

  • Zadeh, L.A. (1978a) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.

    Article  Google Scholar 

  • Zadeh, L.A. (1978b) PRUF: a meaning representation language for natural languages. Int. J. of Man-Machine Studies, 10(4), 395–460.

    Article  Google Scholar 

  • Zadeh, L.A. (1979a) Fuzzy sets and information granularity. In: Advances in Fuzzy Set Theory and Applications (M.M. Gupta, R.K. Ragade, R.R. Yager, eds.), North-Holland, Amsterdam, 3–18.

    Google Scholar 

  • Zadeh, L.A. (1979b) A theory of approximate reasoning. In: Machine Intelligence, Vol. 9 (J.E. Hayes, D. Michie, L.I. Mikulich, eds.), Elsevier, New York, 149–194.

    Google Scholar 

  • Zadeh, L.A. (1982) Test-score semantics for natural languages and meaning representation via PRUF. In: Empirical Semantics (B.B. Rieger, ed.), Brockmeyer, Bochum, Germany, 281–349.

    Google Scholar 

  • Zadeh, L.A. (1987) A computational theory of dispositions. Int. J. of Intelligent Systems, 2, 39–63.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche en Informatique de Toulouse, Toulouse, France

    Didier Dubois & Henri Prade

Authors
  1. Didier Dubois
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henri Prade
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Paris I — Sorbonne and C.N.R.S., France

    Jacques-Paul Dubucs

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Dubois, D., Prade, H. (1993). A Glance at Non-Standard Models and Logics of Uncertainty and Vagueness. In: Dubucs, JP. (eds) Philosophy of Probability. Philosophical Studies Series, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8208-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8208-7_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4301-6

  • Online ISBN: 978-94-015-8208-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation