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A computational approach to fuzzy quantifiers in natural languages. (English) Zbl 0517.94028


MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03B52 Fuzzy logic; logic of vagueness
68T99 Artificial intelligence
68P20 Information storage and retrieval of data
03E72 Theory of fuzzy sets, etc.
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[1] Adams, E. W., The logic of “almost all.”, J. Philos. Logic, 3, 3-17 (1974) · Zbl 0278.02022
[2] Adams, E. W.; Levine, H. F., On the uncertainties transmitted from premises to conclusions in deductive inferences, Synthese, 30, 429-460 (1975) · Zbl 0307.02031
[3] Adams, E. W.; Carlstrom, I. F., Representing approximate ordering and equivalence relations, J. Math. Psych., 19, 182-207 (1979) · Zbl 0411.92003
[4] Adams, E. W., Improbability transmissibility and marginal essentialness of premises in inferences involving indicative conditionals, J. Philos. Logic, 10, 149-177 (1981) · Zbl 0473.03012
[5] Barr, A.; Feigenbaum, E. W., The Handbook of Artificial Intelligence, Vols. 1-3 (1982), Kaufmann: Kaufmann Los Altos · Zbl 0509.68088
[6] Bartsch, R.; Vennemann, T., Semantic Structures (1972), Attenaum Verlag: Attenaum Verlag Frankfurt
[7] Barwise, J.; Cooper, R., Generalized quantifiers and natural language, Linguistics and Philos., 4, 159-219 (1981) · Zbl 0473.03033
[8] Bellmann, R. E.; Zadeh, L. A., Local and fuzzy logics, (Epstein, G., Modern Uses of Multiple-Valued Logic (1977), Reidel: Reidel Dordrecht), 103-165 · Zbl 0382.03017
[9] Blanchard, N., Theories cardinales et ordinales des ensembles flou: les multiensembles, (Thesis (1981), University of Claude Bernard: University of Claude Bernard Lyon)
[10] Carlstrom, I. F., Truth and entailment for a vague quantifier, Synthese, 30, 461-495 (1975) · Zbl 0309.02023
[11] Carnap, R., Meaning and Necessity (1952), University of Chicago Press · Zbl 0034.00106
[12] Cooper, W. S., Logical Linguistics (1978), Reidel: Reidel Dordrecht
[13] Cresswell, M. J., Logic and Languages (1973), Methuen: Methuen London · Zbl 0287.02009
[14] Cushing, S., The formal semantics of quantification, Indiana Univ. Linguistics Club (1977)
[15] Cushing, S., Quantifier Meanings—A Study in the Dimensions of Semantic Competence (1982), North-Holland: North-Holland Amsterdam
[16] Damerau, F. J., On fuzzy adjectives, (Memo. RC 5340 (1975), IBM Research Laboratory: IBM Research Laboratory Yorktown Heights, New York)
[17] DeLuca, A.; Termini, S., A definition of non-probabilistic entropy in the setting of fuzzy sets theory, Inform. Control, 20, 301-312 (1972) · Zbl 0239.94028
[18] Dowty, D. R., Introduction to Montague Semantics (1981), Reidel: Reidel Dordrecht
[19] Dubois, D., A new definition of fuzzy cardinality of finite fuzzy sets, BUSEFAL, 8, 65-67 (1981)
[20] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[21] Dubois, D.; Prade, H., Operations on fuzzy numbers, Int. J. Systems Sci., 9, 613-626 (1978) · Zbl 0383.94045
[22] Dubois, D.; Prade, H., Addition of interactive fuzzy numbers, IEEE Trans. on Automatic Control, 26, 926-936 (1981) · Zbl 1457.68262
[23] Dubois, D., Proprietes de la cardinalite floue d’un ensemble flou fini, BUSEFAL, 8, 11-12 (1981)
[24] Duda, R. O.; Gaschnig, J.; Hart, P. E., Model design in the PROSPECTOR consultation system for mineral exploration, (Michie, D., Expert Systems in the Micro-Electronic Age (1979), Edinburgh University Press: Edinburgh University Press Edinburgh), 153-167
[25] Ebbinghaus, H.-D., Uber fur-fast-alle quantoren, Archiv fur Math. Logik und Grundlageusforschung, 12, 39-53 (1969) · Zbl 0182.31502
[26] Gaines, B. R.; Kohout, L. J., The fuzzy decade: a bibliography of fuzzy systems and closely related topics, Int. J. Man-Machine Studies, 9, 1-68 (1977) · Zbl 0353.02011
[27] Gaines, B. R., Logical foundations for database systems, Int. J. Man-Machine Studies, 11, 481-500 (1979) · Zbl 0404.68098
[28] Goguen, J. A., The logic of inexact concepts, Synthese, 19, 325-373 (1969) · Zbl 0184.00903
[29] Hersh, H. M.; Caramazza, A., A fuzzy set approach to modifiers and vagueness in natural language, J. Exper. Psych., 105, 254-276 (1976)
[30] Hilpinen, R., (Przelecki, M.; Wojcicki, R., Approximate truth and truthlikeness. Approximate truth and truthlikeness, Proc. Conf. Formal Methods in the Methodology of the Empirical Sciences, Warsaw, 1974 (1976), Reidel: Reidel Dordrecht) · Zbl 0374.02007
[31] Hintikka, J. K., Logic, Language-Games, and Information: Kantian Themes in the Philosophy of Logic (1973), Oxford University Press: Oxford University Press Oxford · Zbl 0253.02005
[32] Hobbs, J., Making computational sense of Montague’s intensional logic, Artificial Intell., 9, 287-306 (1978) · Zbl 0379.02005
[33] Hofmann, T. R., Qualitative terms for quantity, (Trappl, R., Proc. 6th European Meeting on Cybernetics and Systems Research (1982), North-Holland: North-Holland Amsterdam)
[34] Hoover, D. N., Probability logic, Annals Math. Logic, 14, 287-313 (1978) · Zbl 0394.03033
[35] Ishizuka, M.; Fu, K. S.; Yao, J. T.P., A rule-based inference with fuzzy set for structural damage assessment, (Gupta, M.; Sanchez, E., Fuzzy Information and Decision Processes (1982), North-Holland: North-Holland Amsterdam)
[36] Johnson-Laird, P. N., Procedural semantics, Cognition, 5, 189-214 (1977)
[37] Kaufmann, A., La theorie des numbres hybrides, BUSEFAL, 8, 105-113 (1981)
[38] Keenan, E. L., Quantifier structures in English, Foundations of Language, 7, 255-336 (1971)
[39] Klement, E. P.; Schwyhla, W.; Lowen, R., Fuzzy probability measures, Fuzzy Sets and Systems, 5, 83-108 (1981)
[40] Klement, E. P., Operations on fuzzy sets and fuzzy numbers related to triangular norms, (Proc. 11th Conf. Multiple-Valued Logic (1981), Univ. of Oklahoma: Univ. of Oklahoma Norman), 218-225 · Zbl 0547.04003
[41] Klement, E. P., (An axiomatic theory of operations on fuzzy sets (1981), Institut fur Mathematik, Johannes Kepler Universitat Linz: Institut fur Mathematik, Johannes Kepler Universitat Linz Institutsbericht), 159
[42] Lakoff, G., (Jockney, D.; Harper, W.; Freed, B., Contemporary Research in Philosophical Logic and Linguistic Semantics (1973), Reidel: Reidel Dordrecht), 221-271, Also in · Zbl 0209.30101
[43] Lambert, K.; van Fraassen, B. C., Meaning relations, possible objects and possible worlds, Philos. Problems in Logic, 1-19 (1970) · Zbl 0188.32001
[44] Mamdani, E. H.; Gaines, B. R., Fuzzy Reasoning and its Applications (1981), Academic Press: Academic Press London · Zbl 0488.03001
[45] McCarthy, J., Circumscription: A non-monotonic inference rule, Artificial Intell., 13, 27-40 (1980) · Zbl 0435.68073
[46] McCawley, J. D., Everything that Linguists have Always Wanted to Know about Logic (1981), University of Chicago Press: University of Chicago Press Chicago
[47] McDermott, D. V.; Doyle, J., Non-monotonic logic. I., Artificial Intell., 13, 41-72 (1980) · Zbl 0435.68074
[48] McDermott, D. V., Non-monotonic logic II: non-monotonic modal theories, J. Assoc. Comp. Mach., 29, 33-57 (1982) · Zbl 0477.68099
[49] Mill, J. S., A System of Logic (1895), Harper: Harper New York
[50] Miller, D., Popper’s qualitative theory of verisimilitude, Brit. J. Philos. Sci., 25, 166-177 (1974) · Zbl 0377.02007
[51] Miller, G. A.; Johnson-Laird, P. N., Language and Perception (1976), Harvard University Press: Harvard University Press Cambridge
[52] Mizumoto, M.; Fukame, S.; Tanaka, K., Fuzzy reasoning Methods by Zadeh and Mamdani, and improved methods, (Proc. 3rd Workshop on Fuzzy Reasoning (1978), Queen Mary College: Queen Mary College London)
[53] Mizumoto, M.; Tanaka, K., Some properties of fuzzy numbers, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 153-164 · Zbl 0434.94026
[54] Mizumoto, M.; Umano, M.; Tanaka, K., Implementation of a fuzzy-set-theoretic data structure system, Tokyo. Tokyo, 3rd Int. Conf. Very Large Data Bases (1977)
[55] Moisil, G. C., Lectures on the Logic of Fuzzy Reasoning (1975), Bucarest
[56] Montague, R., Formal Philosophy, (Thomason, R., Selected Papers (1974), Yale University Press: Yale University Press New Haven)
[57] Moore, R. E., Interval Analysis (1966), Prentice-Hall: Prentice-Hall Englewood Cliffs · Zbl 0176.13301
[58] Morgenstern, C. F., The measure quantifier, J. Symbolic Logic, 44, 103-108 (1979) · Zbl 0404.03025
[59] Mostowski, A., On a generalization of quantifiers, Fund. Math., 44, 17-36 (1957) · Zbl 0078.24401
[60] Naranyani, A. S., Methods of modeling incompleteness of data in knowledge bases, (Knowledge Representation and Modeling of Processes of Understanding (1980), Academy of Sciences of U.S.S.R: Academy of Sciences of U.S.S.R Novosibirsk), 153-162
[61] Nguyen, H. T., Toward a calculus of the mathematical notion of possibility, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 235-246
[62] Niiniluoto, I.; Tuomela, R., Theoretical Concepts and Hypothetico-inductive Inference (1973), Reidel: Reidel Dordrecht · Zbl 0281.02003
[63] Niiniluoto, I., On the truthlikeness of generalizations, (Hintikka, J.; Butts, R., Basic Problems in Methodology and Linguistics (1977), Reidel: Reidel Dordrecht), 121-147
[64] Noguchi, K.; Umano, M.; Mizumoto, M.; Tanaka, K., Implementation of fuzzy artificial intelligence language FLOU, (Tech. Rep. (1976), Automation and Language of IECE)
[65] Orlov, A. I., Problems of Optimization and Fuzzy Variables (1980), Znaniye: Znaniye Moscow
[66] Partee, B., Montague Grammar (1976), Academic Press: Academic Press New York
[67] Peterson, P., On the logic of few, many and most, Notre Dame. J. Formal Logic, 20, 155-179 (1979) · Zbl 0299.02012
[68] Reiter, R., A logic for default reasoning, Artificial Intell., 13, 81-132 (1980) · Zbl 0435.68069
[69] Rescher, N., Plausible Reasoning (1976), Van Gorcum: Van Gorcum Amsterdam
[70] Schubert, L. K.; Goebel, R. G.; Cercone, N., The structure and organization of a semantic net for comprehension and inference, (Findler, N. V., Associative Networks (1979), Academic Press: Academic Press New York), 122-178
[71] (Searle, J., The Philosophy of Language (1971), Oxford University Press: Oxford University Press Oxford)
[72] Shortliffe, E. H., Computer-based Medical Consultations: MYCIN (1976), American Elsevier: American Elsevier New York
[73] Slomson, A. B., Some problems in mathematical logic, (Thesis (1967), Oxford University)
[74] Sugeno, M., Fuzzy measures and fuzzy integrals: a survey, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 89-102
[75] Suppes, P., Elimination of quantifiers in the semantics of natural languages by use of extended relation algebras, Revue Int. Philosphie, 243-259 (1976)
[76] Terano, T.; Sugeno, M., Conditional fuzzy measures and their applications, (Zadeh, L. A.; Fu, K. S.; Tanaka, K.; Shimura, M., Fuzzy Sets and Their Applications to Cognitive and Decision Processes (1975), Academic Press: Academic Press New York), 151-170 · Zbl 0316.60005
[77] Van Lehn, K., Determining the scope of English quantifiers, (Tech. Rep. 483 (1978), AI Laboratory, M.I.T)
[78] Wilks, Y., Philosophy of language, (Charniak, E.; Wilks, Y., Computational Linguistics (1976), North-Holland: North-Holland Amsterdam), 205-233
[79] Yager, R. R., A note on probabilities of fuzzy events, Inform. Sci., 18, 113-129 (1974) · Zbl 0438.60006
[80] Yager, R. R., Quantified propositions in a linguistic logic, (Klement, E. P., Proc. 2nd Int. Seminar on Fuzzy Set Theory (1980), Johannes Kepler University: Johannes Kepler University Linz, Austria) · Zbl 0472.03019
[81] Yager, R. R., A foundation for a theory of possibility, J. Cybernetics, 10, 177-204 (1980) · Zbl 0438.94042
[82] Zadeh, L. A., Probability measures of fuzzy events, J. Math. Anal. Appl., 23, 421-427 (1968) · Zbl 0174.49002
[83] Zadeh, L. A., Similarity relations and fuzzy orderings, Inform. Sci., 3, 177-200 (1971) · Zbl 0218.02058
[84] Zadeh, L. A., Fuzzy languages and their relation to human and machine intelligence, (Proc. Int. Conf. on Man and Computer. Proc. Int. Conf. on Man and Computer, Bordeaux, France (1972), Karger: Karger Basel), 130-165
[85] Zadeh, L. A., Fuzzy logic and approximate reasoning (in memory of Grigore Moisil), Synthese, 30, 407-428 (1975) · Zbl 0319.02016
[86] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci., 9, 43-80 (1975) · Zbl 0404.68075
[87] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 3-28 (1978) · Zbl 0377.04002
[88] Zadeh, L. A., PRUF—a meaning representation language for natural languages, Int. J. Man-Machine Studies, 10, 395-460 (1978) · Zbl 0406.68063
[89] Zadeh, L. A., (Hayes, J. E.; Michie, D.; Kulich, L. I., Machine Intelligence, 9 (1979), Wiley: Wiley New York), 149-194, also in · Zbl 0397.68071
[90] Zadeh, L. A., Inference in fuzzy logic, (Proc. 10th Inter. Symp. on Multiple-valued Logic (1980), Northwestern University), 124-131 · Zbl 0546.03014
[91] Zadeh, L. A., (Cobb, L.; Thrall, R. M., Mathematical Frontiers of the Social and Policy Sciences (1981), Westview Press: Westview Press Boulder), 69-129, also in · Zbl 0484.94046
[92] Zadeh, L. A., (Rieger, B. B., Empirical Semantics (1981), Brockmeyer: Brockmeyer Bochum), 281-349, also in · Zbl 0406.68063
[93] Zadeh, L. A., Fuzzy probabilities and their role in decision analysis, (Proc. 4th MIT/ONR Workshop on Command, Control and Communications (1981), M.I.T), 159-179 · Zbl 0532.90003
[94] Zimmer, A., Some experiments concerning the fuzzy meaning of logical quantifiers, (Troncoli, L., General Surveys of Systems Methodology (1982), Society for General Systems Research: Society for General Systems Research Louisville), 435-441
[95] Zimmermann, H.-J.; Zysno, P., Latent connectives in human decision making, Fuzzy Sets and Systems, 4, 37-52 (1980) · Zbl 0435.90009
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