×

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.
PDF BibTeX XML Cite
Full Text: DOI

References:

[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 Los Altos · Zbl 0509.68088
[6] Bartsch, R.; Vennemann, T., Semantic structures, (1972), 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, (), 103-165
[9] Blanchard, N., Theories cardinales et ordinales des ensembles flou: LES multiensembles, ()
[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 Dordrecht
[13] Cresswell, M.J., Logic and languages, (1973), 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 Amsterdam
[16] Damerau, F.J., On fuzzy adjectives, ()
[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 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 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)
[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, (), 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., ()
[31] Hintikka, J.K., Logic, language-games, and information: Kantian themes in the philosophy of logic, (1973), 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, ()
[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, ()
[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, (), 218-225 · Zbl 0547.04003
[41] Klement, E.P., (), 159
[42] Lakoff, G.; Lakoff, G., Hedges: A study in meaning criteria and the logic of fuzzy concepts, (), 2, 221-271, (1973), 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 London · Zbl 0488.03001
[45] McCarthy, J., Circumscription: A non-monotonic inference rule, Artificial intell., 13, 27-40, (1980)
[46] McCawley, J.D., Everything that linguists have always wanted to know about logic, (1981), 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)
[49] Mill, J.S., A system of logic, (1895), 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 Cambridge
[52] Mizumoto, M.; Fukame, S.; Tanaka, K., Fuzzy reasoning methods by zadeh and mamdani, and improved methods, ()
[53] Mizumoto, M.; Tanaka, K., Some properties of fuzzy numbers, (), 153-164
[54] Mizumoto, M.; Umano, M.; Tanaka, K., Implementation of a fuzzy-set-theoretic data structure system, 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, ()
[57] Moore, R.E., Interval analysis, (1966), 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, (), 153-162
[61] Nguyen, H.T., Toward a calculus of the mathematical notion of possibility, (), 235-246
[62] Niiniluoto, I.; Tuomela, R., Theoretical concepts and hypothetico-inductive inference, (1973), Reidel Dordrecht · Zbl 0281.02003
[63] Niiniluoto, I., On the truthlikeness of generalizations, (), 121-147
[64] Noguchi, K.; Umano, M.; Mizumoto, M.; Tanaka, K., Implementation of fuzzy artificial intelligence language FLOU, ()
[65] Orlov, A.I., Problems of optimization and fuzzy variables, (1980), Znaniye Moscow
[66] Partee, B., Montague grammar, (1976), 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 Amsterdam
[70] Schubert, L.K.; Goebel, R.G.; Cercone, N., The structure and organization of a semantic net for comprehension and inference, (), 122-178
[71] ()
[72] Shortliffe, E.H., Computer-based medical consultations: MYCIN, (1976), American Elsevier New York
[73] Slomson, A.B., Some problems in mathematical logic, ()
[74] Sugeno, M., Fuzzy measures and fuzzy integrals: a survey, (), 89-102
[75] Suppes, P.; Suppes, P., Elimination of quantifiers in the semantics of natural languages by use of extended relation algebras, Revue int. philosphie, Revue int. philosphie, 243-259, (1976)
[76] Terano, T.; Sugeno, M., Conditional fuzzy measures and their applications, (), 151-170 · Zbl 0316.60005
[77] Van Lehn, K., Determining the scope of English quantifiers, ()
[78] Wilks, Y., Philosophy of language, (), 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, () · 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, (), 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.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, Inform. sci., Inform. sci., 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.; Zadeh, L.A., A theory of approximate reasoning, (), 149-194, also in · Zbl 0397.68071
[90] Zadeh, L.A., Inference in fuzzy logic, (), 124-131 · Zbl 0546.03014
[91] Zadeh, L.A.; Zadeh, L.A., Possibility theory and soft data analysis, (), 69-129, also in · Zbl 0484.94046
[92] Zadeh, L.A.; Zadeh, L.A., Test-score semantics for natural languages and meaning-representation via PRUF, (), 281-349, also in · Zbl 0406.68063
[93] Zadeh, L.A., Fuzzy probabilities and their role in decision analysis, (), 159-179 · Zbl 0532.90003
[94] Zimmer, A., Some experiments concerning the fuzzy meaning of logical quantifiers, (), 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.