Abstract
This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined here.
Since nominal comparatives involve plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed, and which maps (via abstract dimensions such asweight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantifiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determiners are first order, at least when restricted to nonparametric and noncollective predications.
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References
Atlas, J., 1984, “Comparative Adjectives and Adverbials of Degree: An Introduction to Radically Radical Pragmatics”,Linguistics and Philosophy bf 7(4), 347–377.
Ballard, B. 1989, “A general computational treatment of comparatives for natural language question answering”, inProc. of the 26th Annual Meeting of the Association for Computational Linguistics, pp. 41–48. author supply Town, publisher's name
Barwise, J. 1987, “Noun phrases, generalized quantifiers, and anaphora”, pp. 1–29 inGeneralized Quantifiers and Natural Language, P. Gärdenfors, ed., Dordrecht: Reidel.
Barwise, J. and Cooper, R. 1981, “Generalized quantifiers and natural language”,Linguistics and Philosophy 4(2), 159–219.
Benthem, J. van 1983, “Determiners and logic”,Linguistics and Philosophy 6, 447–478.
Bresnan, J. 1973, “Syntax of the comparative clause construction in English”,Linguistic Inquiry 4(2), 275–343.
Burris, S. and H. P. Sankappanavar, 1982,A Course in Universal Algebra, New York: Springer.
Carston, R., 1985, “A Re-Analysis of some ‘Quantity Implicatures’”, Manuscript. London: University College.
Cartwright, H., 1975, “Amounts and measures of amount”,Nous 9, 143–64, Also pp. 179–98 in Mass Terms: Some Philosophical Problems, F. J. Pelletier, ed., 1979, Dordrecht: Reidel.
Cresswell, M. J., 1976, “The semantics of degree”, pp. 261–292 inMontague Grammar, B. H. Partee, ed., New York: Academic Press.
Does, J. van der, 1993, “Sums and Quantifiers”,Linguistics and Philosophy,16(5), 509–550.
Horn, L. R., 1972,On the Semantic Properties of Logical Operators in English, Ph.D. thesis, University of California, Los Angeles.
Keenan, E. L. and Moss, L., 1984, “Generalized quantifiers and the expressive power of natural language”, pp. 73–124 inGeneralized Quantifiers, J. van Benthem and A. ter Meulen, eds., Dordrecht: Foris.
Klein, E., 1981, “The interpretation of adjectival, nominal and adverbial comparatives”, pp. 73–124 inFormal Methods in the Study of Language, J. Groenendijk, T. Janssen, and M. Stokhof, eds., Amsterdam: Mathematical Centre.
Krantz, D. H., Luce, R. D., Suppes, P., and Tversky, A., 1971,Foundations of Measurement, New York: Academic Press.
Krifka, M., 1987,Nominal Reference and Temporal Constitution: Toward a Semantics of Quantity, Technical Report 17, Forschungsstelle für natürlich-sprachliche Systeme, Universität Tübingen.
Krifka, M., 1989, “Nominal reference, temporal constitution, and quantification in event semantics”, pp. 75–115 inSemantics and Contextual Expressions, R. Bartsch, J. van Benthem, and P. van Emde Boas, eds., Dordrecht: Foris.
Krifka, M., 1990, “Four thousand ships passed through the lock: Object-induced measure functions on events”,Linguistics and Philosophy 13(5), 487–520.
Larson, R., 1988, “Scope and Comparatives”,Linguistics and Philosophy 11(1), 1–26.
Lasersohn, P., 1990, “Group Action and Spatio-Temporal Proximity”,Linguistics and Philosophy 13(2), 179–206.
Laubsch, J., 1989,Logical Form Simplification., STL report, Hewlett-Packard.
Link, G., 1983, “The logical analysis of plurals and mass terms: A lattice-theoretical approach”, pp. 302–323 inMeaning, Use, and the Interpretation of Language, R. Bäuerle, U. Egli, and A. von Stechow, eds., Berlin: de Gruyter.
Link, G., 1987, “Generalized quantifiers and plurals”, pp. 151–180 inGeneralized Quantifiers and Natural Language, P. Gärdenfors, ed., Dordrecht: Reidel.
Lønning, J. T., 1987, “Collective readings of definite and indefinite noun phrases”, pp. 203–235 inGeneralized Quantifiers and Natural Language, P. Gärdenfors, ed., Dordrecht: Reidel.
Lønning, J. T., 1989a, “Computational semantics of mass terms”, pp. 205–211 inEuropean ACL.
Lønning, J. T., 1989b,Some Aspects of the Logic of Plural Noun Phrases, Technical Report 11, Department of Mathematics, University of Oslo.
Meulen, A. ter, 1980,Substances, Quantities and Individuals: A Study in the Formal Semantics of Mass Terms, Ph.D. thesis, Stanford, Available throughIndiana University Linguistics Club.
Nerbonne, J., Iida, M., and Ladusaw, W., 1990, “Semantics of common noun phrase anaphora”, pp. 379–394 inProc. of the 9th West Coast Conference on Formal Linguistics, A. Halpern, ed., Stanford: CSLI.
Nerbonne, J., Laubsch, J., Diagne, A. K., and Oepen, S., 1993, “Software for applied semantics’, pp. 35–56 inProc. of Pacific Asia Conference on Formal and Computational Linguistics, C.-R. Huang, C. H. Hui Chang, K. Jiann Chen, and C.-H. Liu, eds., Taipei: Academica Sinica. Also available as DFKI Research Report RR-92-55.
Nerbonne, J. and Proudian, D., 1987,The HP-NL System, Technical report, Hewlett-Packard Labs.
Pollard, C. and Sag, I., 1987,Information-Based Syntax and Semantics, Vol.I, Stanford: CSLI Press.
Pollard, C. and Sag, I., 1994,Head-Driven Phrase Structure Grammar Stanford: CSLI Press.
Pinkal, M., 1989, “Die Semantik von Satzkomparativen”,Zeitschrift für Sprachwissenschaft 8(2), 206–256.
Rayner, M. and Banks, A., 1990, “An implementable semantics for comparative constructions”,Computational Linguistics 16(2), 86–112.
Roberts, C., 1987,Modal Subordination, Anaphora, and Distributivity, Ph.D. thesis, University of Massachusetts at Amherst.
Stechow, A. von, 1984, “Comparing semantic theories of comparison”,Journal of Semantics 3, 1–77.
Westerståhl, D., 1989, “Quantifiers in formal and natural languages”, pp. 1–132 inHandbook of Philosophical Logic, Vol.IV, D. Gabbay and F. Guenthner, eds., Dordrecht: Reidel.
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Nerbonne, J. Nominal comparatives and Generalized Quantifiers. J Logic Lang Inf 4, 273–300 (1995). https://doi.org/10.1007/BF01049471
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DOI: https://doi.org/10.1007/BF01049471