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Quantifiers in Formal and Natural Languages

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 14))

For a long time, the word ‘quantifier’ in linguistics and philosophy simply stood for the universal and existential quantifiers of standard predicate logic. In fact, this use is still prevalent in elementary textbooks. It seems fair to say that the dominance of predicate logic in these fields has obscured the fact that the quantifier expressions form a syntactic category, with characteristic interpretations, and with many more members than ∀ and ∃.

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Bibliography

  • [Aczel, 1975] P. Aczel. Quantifiers, games and inductive definitions. In Proc. of the 3rd Scandinavian Logic Symposium, pp. 1–14. North-Holland, Amsterdam, 1975.

    Google Scholar 

  • [Anapolitanos and Väänänen, 1981] Decidability of some logics with free quantifier variables. Zeit. Math. Logik und Grundl. der Math., 27, 17–22, 1981.

    Google Scholar 

  • [Barwise, 1978] J. Barwise. Monotone quantifiers and admissible sets. In Generalised Recursion Theory II, J. E. Fenstad et al., eds. pp. 1–38. North-Holland, Amsterdam, 1978.

    Google Scholar 

  • [Barwise, 1979] J. Barwise. On branching quantifiers in English. J. Phil. Logic, 8, 47–80, 1979.

    Google Scholar 

  • [Barwise and Cooper, 1981] J. Barwise and R. Cooper. Generalised quantifiers and natural language. Linguistics and Philosophy, 4, 159–219, 1981.

    Google Scholar 

  • [Barwise and Feferman, 1985] J. Barwise and S. Feferman, eds. Model-Theoretic Logics, Springer-Verlag, Berlin, 1985.

    Google Scholar 

  • [Barwise and Perry, 1983] J. Barwise and J. Perry. Situations and Attitudes. MIT Press/Bradford, Cambridge, USA, 1983.

    Google Scholar 

  • [Broesterhuizen, 1975] G. Broesterhuizen. Structures for a logic with additional generalised quantifier. Colloquium Mathematicum, 33, 1–12, 1975.

    Google Scholar 

  • [Bruce, 1978] K. Bruce. Ideal models and some not so ideal problems in the model theory of L(Q). J. Symbolic Logic, 43, 304–321, 1978.

    Google Scholar 

  • [Chang and Keisler, 1973] C.C. Chang and K. J. Keisler. Model Theory, North-Holland, Amsterdam.

    Google Scholar 

  • [Church, 1951] A. Church. A formulation of the logic of sense and denotation. In Structure, Method and Meaning. Essays in Honor of Henry M. Sheffer, E. Henle et al., eds. pp. 3–24. New York, 1951.

    Google Scholar 

  • [Cocchiarella, 1975] N. Cocchiarella. A second-order logic of variable-binding operators. Rep. Math. Logic, 5, 9–42, 1975.

    Google Scholar 

  • [Cooper, 1983] R. Cooper. Quantification and Syntactic Theory. D. Reidel, Dordrecht, 1983.

    Google Scholar 

  • [Cowles, 1981] J. R. Cowles. The Henkin quantifier and real closed fields. Zeit. Math. Logik und Grundl. der Math.. 27, 549–555, 1981.

    Google Scholar 

  • [Daniels and Freeman, 1978] C. B. Daniels and J. B. Freeman. A logic of generalised quantification. Rep. Math. Logic, 10, 9–42, 1978.

    Google Scholar 

  • [DeMorgan, 1847] A. DeMorgan. Formal Logic, London. Repr. (A. E. Taylor, ed) London, 1926.

    Google Scholar 

  • [Dummett, 1973] M. Dummett. Frege: Philosophy of Language, Duckworth, London, 1973.

    Google Scholar 

  • [Dummett, 1975] M. Dummett. The philosophical basis of intuitionistic logic. In Logic Colloquium 73, H. E. Rose and J. C. Shepherdson, eds. pp. 5–4. North Holland, Amsterdam, 1975.

    Google Scholar 

  • [Dummett, 1981] M. Dummett. The Interpretation of Frege’s Philosophy, Duckworth, London, 1981.

    Google Scholar 

  • [Enderton, 1970] H. B. Enderton. Finite partially-ordered quantifiers. Zeit. Math. Logik und Grundl. der Math., 16, 393–397, 1970.

    Google Scholar 

  • [Fenstad et al., 1987] J. E. Fenstad, P.-K. Halvorsen, T. Langholm and J. van Benthem. Situations, Language and Logic, D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [Flum, 1985] J. Flum. Characterising logics. Chapter III in [Barwise and Feferman, 1985], pp. 77–120.

    Google Scholar 

  • [Frege, 1892] G. Frege. On concept and object. In Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black, eds. Blackwell, Oxford, 1952.

    Google Scholar 

  • [Frege, 1893] G. Frege. Grundgesetze der Arithmetik I, Jena; partial transl. and introduction by M. Furth: The Basic Laws of Arithmetic, Univ. Calif. Press, Berkeley, 1964.

    Google Scholar 

  • [Geach, 1972] P. Geach. A program for syntax. In Semantics of Natural Language, D. Davidson and G. Harman, eds. pp. 483–497. D. Reidel, Dordrecht, 1972.

    Google Scholar 

  • [Goldfarb, 1979] W. Goldfarb. Logic in the twenties: the nature of the quantifier. J. Symbolic Logic, 44, 351–368, 1979.

    Google Scholar 

  • [Hauschild, 1981] K. Hauschild. Zum Ergleich von Ha”artigquantor und Rescherquantor. Zeit. Math. Logik und Grundl. der Math., 27, 255–264, 1981.

    Google Scholar 

  • [Henkin, 1961] L. Henkin. Some remarks on infinitely long formulas. In Infinistic Methods, pp. 167–183. , Oxford, 1961.

    Google Scholar 

  • [Higginbotham and May, 1981] J. Higginbotham and R. May. Questions, quantifiers and crossing. The Linguistic Review, 1, 41–79, 1981.

    Google Scholar 

  • [Hintikka, 1973] J. Hintikka. Quantifiers vs. quantification theory. Dialectica, 27, 329–358, 1973.

    Google Scholar 

  • [Hodges, 1983] W. Hodges. Elementary predicate logic. This Handbook, Volume 1.

    Google Scholar 

  • [Hoeksema, 1983] J. Hoeksema. Plurality and conjunction. In Studies in Model-theoretic Semantics, A. ter Meulen, ed. pp. 63–83. Foris, Dordrecht, 1983.

    Google Scholar 

  • [Kamp, 1981] H. Kamp. A theory of truth and semantic representation. In Formal Methods in the Study of Language, J. Groenendijk et al., eds. pp 277–322. Math Centre, Amsterdam, 1981.

    Google Scholar 

  • [Keenen, 1981] E. L. Keenan. A Boolean approach to semantics. In Formal Methods in the Study of Language, J. Groenendijk et al., eds. pp 343–379. Math Centre, Amsterdam, 1981.

    Google Scholar 

  • [Keenan, 1989] E. L. Keenan. A semantic definition of ‘indefinite NP’. 1989.

    Google Scholar 

  • [Keenan, 1987] E. L. Keenan. Unreducible n-ary quantification in natural language. In Generalised Quantifiers: Linguistic and Logical Approaches, P. Gärdenfors, ed. pp. 109–50. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [Keenan and Moss, 1985] E. L. Keenan and L. S. Moss. Generalised quantifiers and the expressive power of natural language. In Generalised quantifiers in Natural Language, J. van Benthem and A. ter Meulen, eds. pp. 73–124. Foris, Dordrecht, 1985.

    Google Scholar 

  • [Keenan and Stavi, 1986] E. L. Keenan and J. Stavi. A semantic characterisation of natural language determiners. Linguistics and Philosophy, 9, 253–326, 1986.

    Google Scholar 

  • [Keisler, 1970] H. J. Keisler. Logic with the quantifier ‘there exists uncountably many’. Annals of Math Logic, 1, 1–93, 1097.

    Google Scholar 

  • [Kreisel, 1967] G. Kreisel. Informal rigour and completeness proofs. In Problems in the Philosophy of Mathematics, I. Lakatos, ed. pp. 138–157. North-Holland, Amsterdam, 1967.

    Google Scholar 

  • [Lachlan and Krynicki, 1979] A. H. Lachlan and M. Krynicki. On the semantics of the Henkin quantifier. J. Symbolic Logic, 44, 184–200, 1979.

    Google Scholar 

  • [Ladusaw, 1979] W. Ladusaw. Polarity Sensitivity and Inherent Scope Relations, diss., Univ. Texas, Austin, 1979.

    Google Scholar 

  • [Lindström, 1966] P. Lindström. First order predicate logic with generalised quantifiers. Theoria, 32, 186–195, 1966.

    Google Scholar 

  • [Lindström, 1969] P. Lindström. On extensions of elementary logic. Theoria, 35, 1–11, 1969.

    Google Scholar 

  • [Link, 1987] G. Link. Generalised quantifiers and plurals. In Generalised Quantifiers: Linguistic and Logical Approaches, P. Gärdenfors, ed. pp. 151–180. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [Lorenzen, 1958] P. Lorenzen. Formale Logik, w. de Gruyter, Berlin, 1958.

    Google Scholar 

  • [Lønning, 1987a] J. T. Lønning. Mass terms and quantification. Linguistics and Philosophy, 10, 1–52, 1987.

    Google Scholar 

  • [Lønning, 1987b] J. T. Lønning. Collective readings of definite and indefinite noun phrases. In Generalised Quantifers: Linguistic and Logical Approaches, P. Gärdenfors, ed. pp. 203–235. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [Łukasiewicz, 1957] J. Łukasiewicz. Aristotle’s Syllogistic. Clarendon Press, Oxford, 1957.

    Google Scholar 

  • [Makowski and Tulipani, 1977] J. Makowsky and S. Tulipani. Some model theory for monotone quantifiers. Archiv f. Math. Logik, 18, 115–134, 1977.

    Google Scholar 

  • [Montague, 1974] R. Montague. Formal Philosophy, R. M. Thomason, ed. Yale U. P. New Haven, 1974.

    Google Scholar 

  • [Mostowski, 1957] A. Mostowski. On a generalisation of quantifiers. Fund. Math, 44, 12–36, 1957.

    Google Scholar 

  • [Mundici, 1985] D. Mundici. Other quantifiers: an overview. Chapter VI in [Barwise and Feferman, 1985], pp. 211–233.

    Google Scholar 

  • [Partee, 1984a] B. Partee. Compositionality. In Varieties of Formal Semantics, F. Landman and F. Veltman, eds. Foris, Doredrecht, 1984.

    Google Scholar 

  • [Partee, 1984b] B. Partee. Genitives and ‘have’, abstract, UMass, Amherst, 1984.

    Google Scholar 

  • [Patzig, 1959] G. Patzig. De Aristotelische Syllogistik, van der Hoeck and Ruprecht, Göttingen; trans. Aristotle’s Theory of the Syllogism, D. Reidel, Doredrecht, 1968.

    Google Scholar 

  • [Prawitz, 1971] D. Prawitz. Ideas and results in proof theory. In Proc. 2nd Scandinavian Logic Symposium, J. E.Fenstad, ed. pp 235–307. North-Holland, Amsterdam, 1971.

    Google Scholar 

  • [Prawitz, 1977] D. Prawitz. Meaning and proofs. Theoria, 43, 2–40, 1977.

    Google Scholar 

  • [Rescher, 1962] N. Rescher. Plurality-quantification, abstract. J. Symbolic Logic, 27, 373–374, 1962.

    Google Scholar 

  • [Rooth, 1984] M. Rooth. How to get even with domain selection. In Proc. NELS14, pp. 377–401, UMas, Amherst, 1984.

    Google Scholar 

  • [Rooth, 1985] M. Rooth. Association with Focus, diss. UMass, Amherst, 1985.

    Google Scholar 

  • [Russell, 1903] B. Russell. The Principles of Mathematics, Allen and Unwin, London, 1903.

    Google Scholar 

  • [Russell, 1956] B. Russell. Logic and Knowledge. Essays 1901–1950, R. C. Marsh, ed. Allen and Unwin (reference to ‘Mathematical logic as based on the theory of types’, 1908 and ‘The philosophy of logical atomism, 1918).

    Google Scholar 

  • [Sgro, 1977] J. Sgro. Completeness theorems for topological models. Annals of Math. Logic, 11, 173– 193, 1977.

    Google Scholar 

  • [Thijsse, 1983] E. Thijsse. Laws of Language, thesis, Rijksunivesiteit Groningen, 1983.

    Google Scholar 

  • [van Benthem, 1983a] J. van Benthem. Five easy pieces. In Studies in Model theoretic Semantics, A. ter Meulen, ed. pp. 1–17. Foris,Dordrecht, 1983.

    Google Scholar 

  • [van Benthem, 1983b] J. van Benthem. Determiners and logic. Linguistics and Philosophy, 6, 447– 478, 1983.

    Google Scholar 

  • [van Benthem, 1983c] J. van Benthem. A linguistic turn: new directions in logic. In Proc. 7th Int. Cong. Logic, Methodology and Philosophy of Science, Salzburg, 1983. R. Barcan Marcus et al., eds. North Holland, Amsterdam, 1986.

    Google Scholar 

  • [van Benthem, 1984a] J. van Benthem. Questions about quantifiers. J. Symbolic Logic, 49, 443–466, 1984.

    Google Scholar 

  • [van Benthem, 1984b] J. van Benthem. Foundations of conditional logic. J. Phil Logic, 13, 303–349, 1984.

    Google Scholar 

  • [van Benthem, 1985] J. van Benthem. Semantic automata. Report No CSLI-85-27, Stanford, 1985.

    Google Scholar 

  • [van Benthem, 1986] J. van Benthem. Essays in Logical Semantics, D. Reidel, Dordrecht, 1985. (Contains among other things, revised version of van Benthem [1983b, c], [1984a, b], [1985].) [van Benthem, 1987a] J. van Benthem. Towards a computational semantics. In Generalised Quantifiers, Linguistic and Logical Approaches, P. Gärdenfors, ed. pp. 31–71. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [van Benthem, 1987b] J. van Benthem. Polyadic quantifiers. To appear in Linguistics and Philosophy, 1987.

    Google Scholar 

  • [van Benthem and Doets, 1983] J. van Benthem and K. Doets. Higher order logic. This Handbook.

    Google Scholar 

  • [van Deemter, 1985] K. van Deemter. Generalized quantifiers: finite versus infinite. In Generalised quantifiers in Natural Language, J. van Benthem and A. ter Meulen, eds. pp. 147–159. Foris, Dordrecht, 1985.

    Google Scholar 

  • [van Eijck, 1982] J. van Eijck. Discourse representation, anaphora and scope. In Varieties of S+Formal Semantics, F. Landman and F. Veltman, eds. Foris, Dordrecht, 1982.

    Google Scholar 

  • [van Eijck, 1985] J. van Eijck. Aspects of quantification in natural language, diss, Rijksuniversiteit, Groningen, 1985.

    Google Scholar 

  • [Väänänen, 1979] J. Väänänen. Remarks on free quantifier variables. In Essays on Mathematical and Philosophical Logic, J. Hintikka et al., eds. pp. 267–272. D. Reidel, Dordrecht, 1979.

    Google Scholar 

  • [Walkoe, 1970] W.Walkoe, Jr. Finite partially ordered quantification. J. Symbolic Logic, 35, 535–550, 1970.

    Google Scholar 

  • [Weese, 1981] M. Weese. Decidability with respect to the Härtig and Rescher quantifiers. Zeitschrift f. Math. Logik und Grundl. der Math, 27, 569–576, 1981.

    Google Scholar 

  • [Westerståhl, 1976] D.Westeståhl. Some Philosophical Aspects of Abstract Model Theory, diss., Dept Philosophy, Univ Göteborg, 1976.

    Google Scholar 

  • [Westerståhl, 1983] D. Westeståhl. On determiners. In Abstracts from the 7th Int. Congress of Logic, Methodology and Phil of Science, Vol 2, pp. 223–226, Salzburg, 1983.

    Google Scholar 

  • [Westerståhl, 1984] D.Westeståhl. Some results on quantifiers. Notre Dame J. Formal Logic, 25, 152– 170, 1984.

    Google Scholar 

  • [Westerståhl, 1985a] D.Westeståhl. Logical constants in quantifier languages. Linguistics and Philosophy, 8, 387–413, 1985.

    Google Scholar 

  • [Westerståhl, 1985b] D. Westeståhl. Determiners and context sets. In Generalised quantifiers in Natural Language, J. van Benthem and A. ter Meulen, eds. pp. 45–71. Foris, Dordrecht, 1985.

    Google Scholar 

  • [Westerståhl, 1987] D. Westeståhl. Branching generalised quantifiers and natural language. In Generalised Quantifiers, Linguistic and Logical Approaches, P. Gärdenfors, ed. pp. 269–298. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  • [Yasuhura, 1969] M. Yasuhara. The incompleteness of LP languages. Fund. Math., 66, 147–152, 1969.

    Google Scholar 

  • [Zucker, 1978] J. I. Zucker. The adequacy problem for classical logic. J. Phil. Logic, 7, 517–535, 1978.

    Google Scholar 

  • [Zwarts, 1983] F. Zwarts. Determiners: a relational perspective. In Studies in Model Theoretic Semantics, A. ter Meulen, ed. pp. 37–62, Foris, Dordrecht, 1983.

    Google Scholar 

  • [Zwarts, 1986] F. Zwarts. Model Theoretic Semantics and Natural Language: the case of modern Dutch, diss, Nederlands inst, Rijksunivesiteit Groningen, 1986.

    Google Scholar 

  • [Altman et al., 2005] A. Altman, Y. Peterzil and Y. Winter. Scope dominance with upward monotone quantifiers. Journal of Logic, Language and Information, 14, 445–55, 2005

    Google Scholar 

  • [Bach et al., 1995] E. Bach, E. Jelinek, A. Kratzer and B. H. Partee, eds. Quantification in Natural Languages, Dordrecht: Kluwer Academic Publishers, 1995.

    Google Scholar 

  • [Beaver, 1997] D. Beaver. Presupposition. In van Benthem and ter Meulen, 1997, pp. 939–1008.

    Google Scholar 

  • [Beghelli, 1994] F. Beghelli. Structured quantifiers. In Kanazawa and Piñón, 1994, pp. 119–45.

    Google Scholar 

  • [Ben-Avi and Winter, 2005] G. Ben-Avi and Y. Winger. Scope dominance with monotone quantifiers over finite domains. Journal of Logic, Language and Information, 13, 385–402, 2005.

    Google Scholar 

  • [Ben-Shalom, 1994] D. Ben-Shalom. A tree characterization of generalised quantifier reducibility. In Kanazawa and Piñón, 1994, pp. 147–71.

    Google Scholar 

  • [Boolos, 1998] G. Boolos. Logic, Logic, and Logic. Cambridge, MA: Harvard University Press, 1998.

    Google Scholar 

  • [Chierchia, 1992] G. Chierchia. Anaphora and dynamic binding. Linguistics and Philosophy, 15, 111– 84, 1992.

    Google Scholar 

  • [Cohen, 2001] A. Cohen. Relative readings of ‘many’, ‘often’ and generics. Natural Language Semantics, 9, 41–67, 2001.

    Google Scholar 

  • [Dalrymple et al., 1998] M. Dalrymple, M. Kanazawa, Y. Kim, S. Mchombo and S. Peters. Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy, 21, 159–210, 1998.

    Google Scholar 

  • [Feferman, 1999] S. Feferman. Logic, logics and Logicism. Notre Dame Journal of Formal Logic, 40, 31–54, 1999.

    Google Scholar 

  • [Fernando, 2001] T. Fernando. Conservative generalized quantifiers and presupposition. Semantics and Linguistic Theory, 11: 172–91, 2001.

    Google Scholar 

  • [Fernando and Kamp, 1996] T. Fernando and H. Kamp. Expecting many. In Proceedings of the Sixth Conference on Semantics and Linguistic Theory, T. Galloway and J. Spence, eds. pp. 53–68. Ithaca, NY: CLC Publications, 1996.

    Google Scholar 

  • [Ginzburg and Sag, 2000] J. Ginzburg and I. Sag. Interrogative Investigations. CSLI Lecture Notes 123, Stanford, CA: CSLI Publications, 2000.

    Google Scholar 

  • [Groenendijk and Stokhof, 1991] J. Groenendijk and M. Stokhof. Dynamic predicate logic. Linguistics and Philosophy, 14, 39–100, 1991.

    Google Scholar 

  • [Groenendijk and Stokhof, 1997] J. Groenendijk and M. Stokhof. Questions. In van Benthem and ter Meulen, 1997, pp. 1055–1124.

    Google Scholar 

  • [Hella et al., 1997] L. Hella, J. Väänänen and D. Westerståahl. Definability of polyadic lifts of generalised quantifiers. Journal of Logic, Language and Information, 6, 305–35, 1997.

    Google Scholar 

  • [Hendriks, 2001] H. Hendriks. Compositionality and model-theoretic interpretation. Journal of Logic, Language and Information, 10, 29–48, 2001.

    Google Scholar 

  • [Hodges, 1997] W. Hodges. Some strange quantifiers. In Structures in Logic and Computer Science, J. Mycielski et al., eds. pp. 51–65. Lecture Notes in Computer Science 1261, Berlin: Springer, 1997.

    Google Scholar 

  • [Hodges, 2001] W. Hodges. Formal features of compositionality. Journal of Logic, Language and Information, 10, 7–28, 2001.

    Google Scholar 

  • [Hodges, 2002] W. Hodges. The unexpected usefulness of model theory in semantics. MS, 2002.

    Google Scholar 

  • [Hodges, 2003] W. Hodges. Composition of meaning (A class at Düsseldorf). Unpublished lecture notes, 2003.

    Google Scholar 

  • [Kamp and Reyle, 1993] H. Kamp and U. Reyle. From Discourse to Logic. Dordrecht: Kluwer, 1993

    Google Scholar 

  • [Kanazawa, 1994] M. Kanazawa. Weak vs. strong readings of donkey sentences and monotonicity inference in a dynamic setting. Linguistics and Philosophy, 17, 109–58, 1994.

    Google Scholar 

  • [Kanazawa and Piñón, 1994] M. Kanazawa and C. Piñón, eds. Dynamics, Polarity and Quantification, Stanford, CA: CSLI Publications, 1994.

    Google Scholar 

  • [Keenan, 1992] E. Keenan. Beyond the Frege boundary. Linguistics and Philosophy, 15, 199–221, 1992.

    Google Scholar 

  • [Keenan, 1993] E. Keenan. Natural language, sortal reducibility, and generalized quantifiers. Journal of Symbolic Logic, 58, 314–24, 1993.

    Google Scholar 

  • [Keenan, 2000] E. Keenan. Logical objects. In Logic, Language and Computation: Essays in Honor of Alonzo Church, C. A. Anderson and M. Zeleny, eds, pp. 151–83. Dordrecht: Kluwer, 2000.

    Google Scholar 

  • [Keenan, 2003] E. Keenan. The definiteness effect: semantics or pragmatics? Natural language Semantics, 11, 187–216, 2003.

    Google Scholar 

  • [Keenan, 2005] E. Keenan. Excursions in natural logic. In Language and Grammar: Studies in Mathematical Linguistics and Natural Language, C. Casadio, P. Scott and R. Seely, eds., pp. 3–24. Stanford, CA: CSLI Publications, 2005.

    Google Scholar 

  • [Keenan and Stabler, 2004] E. Keenan and E. Stabler. Bare Grammar: A Study of Language Invariants. Stanford, CA: CSLI Publications, 2004.

    Google Scholar 

  • [Keenan and Westerståahl, 1997] E. Keenan and D. Westerståahl. Generalised quantifiers in linguistics and logic. In van Benthem and ter Meulen, 1997, pp. 837–93.

    Google Scholar 

  • [Landman, 1989] F. Landman. Groups, Linguistics and Philosophy, 12, 559–605, 723–44, 1989.

    Google Scholar 

  • [Lappin, 1996a] S. Lappin. Generalized quantifiers, exception sentences and logicality. Journal of Semantics, f 13, 197–220, 1996.

    Google Scholar 

  • [Lappin, 1996b] S. Lappin. The interpretation of ellipsis. In The Handbook of Semantic Theory, S¿ Lappin, ed., pp. 145–75. Oxford: Blackwell, 1996.

    Google Scholar 

  • [Lønning, 1997] J. T. Lønning. Plurals and collectivity. In van Benthem and ter Meulen, 1997, pp. 302–23.

    Google Scholar 

  • [McGee, 1996] V. McGee. Logical operations. Journal of Philosophical Logic, 25, 567–80, 1996.

    Google Scholar 

  • [Moltmann, 1995] F. Moltmann. Exception sentences and polyadic quantification. Linguistics and Philosophy, 18, 223–80, 1995.

    Google Scholar 

  • [Moltmann, 1996] F. Moltmann. Resumptive quantifiers in exception phrases. In Quantifiers, Deduction and Context, H. de Swart, M. Kanazawa and C. Piñón, eds., pp. 139–70. Stanford, CA: CSLI Publications, 1996.

    Google Scholar 

  • [Neale, 1990] S. Neale. Descriptions, Cambridge MA: MIT Press, 1990.

    Google Scholar 

  • [Perry, 2001] J. Perry. Reference and Reflexivity, Stanford, CA: CSLI Publications, 2001.

    Google Scholar 

  • [Peters and Westerståahl, 2002] S. Peters and D. Westerståahl. Does English really have resumptive quantification? In The Construction of Meaning, D. Beaver et al., eds, pp. 181–95. Stanford, CA: CSLI Publications, 2002.

    Google Scholar 

  • [Pustejovsky, 1995] J. Pustejovsky. The Generative Lexicon, Cambridge MA, MIT Press, 1995.

    Google Scholar 

  • [Ranta, 1994] A. Ranta. Type Theoretical Grammar. Oxford: Oxford University Press, 1994.

    Google Scholar 

  • [Recanati, 2002] F. Recanati. Unarticulated constituents. Linguistics and Philosophy, 25, 299–345, 2002.

    Google Scholar 

  • [Recanati, 2004] F. Recanati. Literal Meaning, Cambridge: Cambridge University Press, 2004.

    Google Scholar 

  • [Sher, 1991] G, Sher. The Bounds of Logic, Cambridge, MA: MIT Press, 1991.

    Google Scholar 

  • [Sher, 1997] G, Sher. Partially-ordered (branching) generalized quantifiers: a general definition. Journal of Philosophical Logic, 26, 1–43, 1997.

    Google Scholar 

  • [Sperber and Wilson, 1995] D. Sperber and D. Wilson. Relevance: Communication and Cognition, Oxford: Oxford University Press, 1995.

    Google Scholar 

  • [Stanley, 2000] J. Stanley. Context and logical form. Linguistics and Philosophy, 23, 391–434, 2000.

    Google Scholar 

  • [Stanley, 2002] J. Stanley. Nominal restriction. In Logical Form and Language, G. Peters and G. Preyer, eds;, pp. 365–88. Oxford: Oxford University Press, 2002.

    Google Scholar 

  • [Stanley and Szabo, 2000] J. Stanley and Z. Szabo. On quantifier domain restriction. Mind and Language, 15, 219–61, 2000.

    Google Scholar 

  • [Sundholm, 1989] G. Sundholm. Constructive generalized quantifiers. Synthese, 79, 1–12, 1989.

    Google Scholar 

  • [Szabolcsi, 2004] A. Szabolcsi. Positive polarity—negative polarity. Natural Language and Linguistic Theory, 22, 409–52, 2004.

    Google Scholar 

  • [Thijsse, 1985] E. Thijsse. Counting quantifiers. In em General Quantifiers in Natural Language, J. van Benthem and A. ter Meulen, eds. GRASS 4, Foris, Dordrecht, 1985.

    Google Scholar 

  • [Väänänen, 1997] J. Väänänen. Unary quantifiers on finite models. Journal of Logic, Language and Information, 6, 275–304, 1997.

    Google Scholar 

  • [Väänänen, 2001] J. Väänänen. Second-order logic and foundations of mathematics. Bulletin of Symbolic Logic, 7, 504–20, 2001.

    Google Scholar 

  • [Väänänen, 2002] J. Väänänen. On the semantics of informational independence. Logic Journal of the IGPL, 10, 339–52, 2002.

    Google Scholar 

  • [Väänänen and Westerståahl, 2002] J. Väänänen and D. Westerståahl. On the expressive power of monotone natural language quantifiers over finite models. Journal of Philosophical Logic, 31, 327– 58, 2002.

    Google Scholar 

  • [Valludví and Engdahl, 1996] E. Valludví and E. Engdah. The linguistic realization of information packaging, Linguistics, 34, 459–519, 1996.

    Google Scholar 

  • [van Benthem, 1984] J. van Benthem. Questions about quantifiers. Journal of Symbolic Logic, 49, 443–66, 1984. Also in van Benthem, 1986.

    Google Scholar 

  • [van Benthem, 1986] J. van Benthem. Essays in Logical Semantics, Dordrecht: D. Reidel, 1986.

    Google Scholar 

  • [van Benthem, 1989] J. van Benthem. Polyadic quantifiers. Linguistics and Philosophy, 12, 437–64, 1989.

    Google Scholar 

  • [van Benthem, 1991] J. van Benthem. Language in Action, Amsterdam: North-Holland, 1991; also Boston, MIT Press, 1995.

    Google Scholar 

  • [van Benthem, 2002] J. van Benthem. Invariance and definability: two faces of logical constants. In Reflections of the Foundations of Mathematics: Essays in Honor of Sol Feferman, W. Sieg, R. Sommer and C. Talcott, eds., pp. 426–46. ASL Lecture Notes in Logic, 15, Natick, MA: The Association for Symbolic Logic, 2002.

    Google Scholar 

  • [van Benthem, 2003] J. van Benthem. Is there still logic in Bolzano’s key? In Bernard Bolzano’s Leistungen in Logik, Mathematik und Psysik, E. Morscher, ed., pp. 11–34. Beiträge zur Bolzano–Forschung, 16, Sankt Augustin: Academia Verlag, 2003.

    Google Scholar 

  • [van der Does, 1993] J. van der Does. Sums and quantifiers. Linguistics and Philosophy, 16, 509–50, 1993.

    Google Scholar 

  • [van der Does, 1996] J. van der Does. Quantification and nominal anaphora. In Proceedings of the Konstanz Workshop “Reference and Anaphoric Relations, K. von Heusinger and U. Egli, eds;, pp. 27–56, Universität Konstanz, 1996.

    Google Scholar 

  • [von Fintel, 1993] K. von Fintel. Exceptive constructions. Natural Language Semantics, 1, 123–48, 1993.

    Google Scholar 

  • [von Fintel, 1994] K. von Fintel. Restrictions on Quantifier Domains. PhD Dissertation, University of Massachusetts, Amherst, 1994.

    Google Scholar 

  • [Westerståahl, 1991] D. Westerståahl. Relativization of quantifiers in finite models. In generalized Quantifier Theory and Applications, j. van der Does and J. van Eijck, eds., pp. 187–205, Amsterdam: ILLC. Also in idem (eds.), Quantifiers: Logic, Models and Computation, pp. 375–83 Stanford, CA: CSLI Publications.

    Google Scholar 

  • [Westerståahl, 1994] D.Westerståahl. Iterated quantifiers. In Kanazawa and Piñón, 194, pp. 173–209.

    Google Scholar 

  • [Westerståahl, 1995] D. Westerståahl. Quantifiers in natural language. A survey of some recent work. In M. Krynicki, M. Mostowski and L. W. Szczerba (eds.), Quantifiers: Logics, Models and Computation, pp. 359–408. Kluwer Academic Publishers, 1995.

    Google Scholar 

  • [Westerståahl, 1996] D. Westerståahl. Self-commuting quantifiers. Journal of Symbolic Logic, 61, 212–24, 1996.

    Google Scholar 

  • [Westerståahl, 1998] D.Westerståahl. On mathematical proofs of the vacuity of compositionality. Linguistics and Philosophy, 21, 635–43, 1998.

    Google Scholar 

  • [Westerståahl, 2004] D.Westerståahl. On the compositional extension problem. Journal of Philosophical Logic, 33, 549–82, 2004.

    Google Scholar 

  • [Zimmermann, 1993] T. E. Zimmermann. Scopeless quantifiers and operators. Journal of Philosophical Logic, 22, 545–61, 1993.

    Google Scholar 

  • [Zucchi, 1995] S. Zucchi. The ingredients of definiteness and the indefiniteness effect. Natural Language Semantics, 3 33–78, 1995.

    Google Scholar 

  • [Zwarts, 1998] F. Zwarts. Three types of polarity. In Plurality and Quantification, F. Hamma and E. Hinrichs, eds., pp. 177–238. Dordrecht: Kluwer, 1998.

    Google Scholar 

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Authors
  1. Dag Westerstaåhl
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  1. King’s College, London, U.K

    D.M. Gabbay

  2. Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

    F. Guenthner

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Westerstaåhl, D. (2007). Quantifiers in Formal and Natural Languages. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6324-4_4

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