Abstract
In an attempt to accommodate natural language phenomena involving nominalization and self-application, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briefly review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version ofsubsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained in the type of individuals. Russell's paradox is avoided by placing a type-constraint on lambda-abstraction, rather than by restricting comprehension.
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References
Aczel, P., 1980, “Frege structures and the notions of proposition, truth and setz,” inThe Kleene Symposium, J. Barwise, H. J. Keisler, and K. Kunen, eds., Amsterdam: North Holland, pp. 31–59.
Bach, E., 1979, “Control in Montague grammar,”Linguistic Inquiry 10, 515–531.
Bealer, G., 1982,Quality and Concept, Oxford: Clarendon Press.
Bealer, G., 1989, “On the identification of properties and propositional functions,”Linguistics and Philosophy 12, 1–14.
Cardelli, L. and Wegner, P., 1985, “On understanding types, data abstraction and polymorphism,”Computing Surveys 17, 471–522.
Chierchia, G., 1984,Topics in the Syntax and Semantics of Infinitives and Gerunds, Unpublished PhD Thesis, University of Massachusetts.
Chierchia, G., 1985, “Formal semantics and the grammar of predication,”Linguistic Inquiry 16, 417–443.
Chierchia, G. and Turner, R., 1988, “Semantics and property theory,”Linguistics and Philosophy 11, 261–302.
Curien, P.-L. and Ghelli, G., 1989, “Coherence of subsumption,” Unpublished ms, Liens (CNRS), Paris.
Dowty, D., 1982, “Grammatical relations and Montague grammar,” inThe Nature of Syntactic Representation, P. Jacobson and G. K. Pullum, eds., Dordrecht: D. Reidel, pp. 79–130.
Emms, M., 1991, “Polymorphic quantifiers,” inStudies in Categorial Grammar, G. Barry and G. Morrill, eds., Edinburgh: Centre for Cognitive Science, Univ. of Edinburgh, pp. 65–112.
Frege, G., 1977,Translations from the Philosophical Writings of Gottlob Frege, P. Geach, and M. Black, eds., 3rd Edition, Oxford: Basil Blackwell, pp. 56–78.
Gazdar, G., Klein, E., Pullum, G.K., and Sag, I. A., 1985,Generalized Phrase Structure Grammar, Oxford: Basil Blackwell.
Harper, R., Honsell, F., and Plotkin, G., 1987, “A framework for defining logics,”Second Annual Symposium on Logic in Computer Science, IEEE, pp. 194–204.
Jacobson, P., 1990, “Raising as function composition,”Linguistics and Philosophy 13, 423–475.
Martin-Löf, P., 1978, “Constructive mathematics and computer programming,” inLogic,Methodology and Philosophy of Science, VI, 1979, North-Holland, pp. 153–175.
Milner, R., 1978, “A theory of type polymorphism in programming,”Journal of Computer and System Sciences 17, 348–375.
Mitchell, J. C., 1988, “Polymorphic type inference and containment,”Information and Computation 76, 211–249.
Montague, R., 1973, “The proper treatment of quantification in ordinary English,” inApproaches to Natural Language, J. Hintikka, J. M. E. Moravcsik, and P. Suppes, eds., Dordrecht: D. Reidel, Reprinted in R. H. Thomason, ed., 1974,Formal Philosophy: Selected Papers of Richard Montague, New Haven, Conn.: Yale University Press, pp. 247–270.
Parsons, T., 1979, “The theory of types and ordinary language,” inLinguistics, Philosophy and Montague Grammar, S. Davies and M. Mithun, eds., Austin: University of Texas Press.
Partee, B. H. and M. Rooth, 1983, “Generalized conjunction and type ambiguity,” inMeaning,Use, and Interpretation of Language, R. Bäuerle, C. Schwarze, and A. von Stechow, eds., De Gruyter.
Partee,B. H., 1984, “Compositionality,” inVarieties of Formal Semantics: Proceedings of The Fourth Amsterdam Colloquium, Sept 1982, F. Landman and F. Veltman, eds., Dordrecht: Foris Press.
Partee, B. H., 1986, “Ambiguous pseudo-clefts with ambiguous be,” inProceedings of the Sixteenth Annual Meeting of the North Eastern Linguistic Society, S. Berman, J. Choe, and J. McDonough, eds., Amherst: University of Massachusetts.
Pereira, F., 1991, “Deductive interpretation,” inNatural Language and Speech, E. Klein and F. Veltman, eds., Berlin: Springer-Verlag, pp. 117–133.
Pollard, C. and Sag, I. A., 1987,Information-Based Syntax and Semantics, Vol. 1., CSLI Lecture Notes, No. 13.
Rooth, M. and Partee, B. H., 1982, “Conjunction, type ambiguity, and wide scope ‘or’,” inProceedings of the Second West Coast Conference on Formal Linguistics, M. Barlow, D. Flickinger, and M. Westcoat, eds., pp. 353–362.
Scott, D., 1976, “Data types as lattices,”SIAM Journal of Computing 5, 522–587.
Thomason, R. H., 1976, “On the semantic interpretation of the Thomason 1972 fragment,” Distributed by Indiana University Linguistics Club, Bloomington, Indiana.
Turner, R., 1987, “A theory of properties,”Journal of Symbolic Logic 52, 63–86.
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Kamareddine is grateful to the Department of Mathematics and Computing Science, Technical University of Eindhoven, for their financial support and hospitality during the academic year 1991–92.
Klein's work has been carried out as part of the research programmes of the dyana project (BR 3175 and BR 6852), funded by CEC esprit Basic Research Division, and of the Human Communication Research Centre, supported by the UK Economic and Social Research Council.
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Kamareddine, F., Klein, E. Nominalization, predication and type containment. J Logic Lang Inf 2, 171–215 (1993). https://doi.org/10.1007/BF01050787
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DOI: https://doi.org/10.1007/BF01050787