Abstract
Categorial Grammar and logical Type Theory stem from the same historical source, viz. the Fregean and Russellian idea of a pervasive function/ argument structure in Language. Nevertheless, the two fields have developed in quite different ways, one becoming a more linguistic enterprise, the other a more mathematical one. (For the former, see Bach et al., 1986, Buszkowski et al., 1986 — for the latter, Gallin 1975, Barendregt, 1981.) Even so, there is also a more theoretical logical component to Categorial Grammar, which has been studied recently by various authors (cf. Buszkowski, 1982, Došen, 1986, van Benthem, 1986a,e). And in that direction, various connections have emerged with research in Type Theory and Lambda Calculus — exploiting analogies between categorial grammars, Gentzen calculi for implication and fragments of typed lambda-languages. In this paper, we shall survey this development, adding various new results on definability and preservation.
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References
E. Bach, R. Oehrle and D. Wheeler, eds, 1986, Categorial Grammars and Natural Language Structures, Reidel, Dordrecht.
J. Bacon, 1985, ‘The Completeness of a Predicate-Functor Logic’, Journal of Symbolic Logic 50, 903–926.
H. Barendregt, 1981, The Lambda Calculus; its Syntax and Semantics, North-Holland, Amsterdam.
J. van Benthem, 1983, The Semantics of Variety in Categorial Grammar, report 83-26, Department of Mathematics, Simon Fraser University, Burnaby (B.C.). (To appear in Buszkowski, Marciszewski & van Benthem (eds), 1986.)
J. van Benthem, 1986a, Essays in Logical Semantics, Reidel, Dordrecht.
J. van Benthem, 1986b, ‘Logical Syntax’, manuscript, Mathematisch Instituut, Universiteit van Amsterdam.
J. van Benthem, 1986c, ‘Meaning: Interpretation and Inference’, to appear in Synthese, (M-L dalla Chiara and G. Toraldo di Francia, eds, ‘Proceedings Conference on Theories of Meaning, Florence 1985’).
J. van Benthem, 1986d, ‘Strategies of Intensionalisation’, to appear in Filozófiai Figyelö, (L. Pólos, ed, ‘Festschrift for Imre Ruzsa’).
J. van Benthem, 1986e, ‘The Lambek Calculus’, report 86-06, Mathematical Institute, University of Amsterdam. (To appear in Bach, Oehrle & Wheeler (eds), 1986.)
W. Buszkowski, 1982, Lambek’s Categorial Grammars, Instytut Matematicki, Adam Mickiewicz University, Poznan, Poland.
W. Buszkowski, W. Marciszewski and J. van Benthem, eds, 1986, Categorial Grammar, John Benjamin, Amsterdam.
G. Chierchia, 1985, ‘Formal Semantics and the Grammar of Predication’, Linguistic Inquiry 16:3, 417–443.
K. Došen, 1986, ‘Sequent Systems and Groupoid Models’, Mathematical Institute, University of Beograd.
J-E Fenstad, ed, 1971, Proceedings of the Second Scandinavian Logic Symposium, North-Holland, Amsterdam.
H. Friedman, 1975, ‘Equality between Functionals’, in Dold and Eckmann, eds, Logic Colloquium, Boston 72-73, Springer, Heidelberg, (Lecture Notes in Mathematics, vol. 453), 22–37.
D. Gallin, 1975, Intensional and Higher-Order Modal Logic, North-Holland, Amsterdam.
T. Janssen, 1983, Foundations and Applications of Montague Grammar, dissertation, Mathematical Center, Amsterdam.
E. Keenan and Y. Stavi, 1981, ‘A Characterization of Natural Language Determiners’, to appear in Linguistics and Philosophy.
E. Keenan and L. Faltz, 1985, Boolean Semantics for Natural Language, Reidel, Dordrecht.
J. Lambek, 1958, ‘The Mathematics of Sentence Structure’, American Mathematical Monthly 65, 154–170.
J. Lambek, 1980, ‘From λ-Calculus to Cartesian-Closed Categories’, in J. Seldin and J. Hindley, eds, 1980, To H.B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, Academic Press, New York, 375–402.
W.V.O. Quine, 1971, ‘Predicate-Functor Logic’, in J. Fenstad (ed), 309–315.
M. Steedman, 1985, ‘Combinators, Categorial Grammars and Parasitic Gaps’, School of Epistemics, Edinburgh.
F. Zwarts, 1986, Categoriale Grammatica en Algebraïsche Semantiek, proefschrift, Nederlands Instituut, Rijksuniversiteit, Groningen.
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© 1987 Plenum Press, New York
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van Benthem, J. (1987). Categorial Grammar and Lambda Calculus. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0897-3_4
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DOI: https://doi.org/10.1007/978-1-4613-0897-3_4
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