Abstract
We ask to what extent a satisfactory categorial analysis of non-local scope construal can already be realized while restricting to a non-commutative, non-associative setting, and without relaxing compositionality to a relation. In response, we show a variety of data on the topic can be dealt with through an adaptation of classical non-associative Lambek calculus (CNL, [3]) that incorporates Girard’s concept of polarity ([5]). The latter notion originated in the constructivization of classical logic, recognizable by computer scientists as the definition of continuation-passing style (CPS) translations.
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References
Bastenhof, A.: Polarized Classical Non-associative Lambek Calculus and Formal Semantics. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS, vol. 6736, pp. 33–48. Springer, Heidelberg (2011)
Belnap, N.D.: Display logic. Journal of Philosophical Logic 11(4), 375–417 (1982)
De Groote, P., Lamarche, F.: Classical non associative Lambek calculus. Studia Logica 71, 355–388 (2002)
Gamut, L.T.F.: Logic, Language and Meaning. Intensional Logic and Logical Grammar, vol. 2. University of Chicago Press (1991)
Girard, J.-Y.: A new constructive logic: classical logic. Mathematical Structures in Computer Science 1(3), 255–296 (1991)
Hendriks, H.: Studied flexibility. Categories and types in syntax and semantics. PhD thesis, ILLC Amsterdam (1993)
Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65, 154–169 (1958)
Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Proceedings of the Twelfth Symposium in Applied Mathematics, Structure of Language and its Mathematical Aspects (1961)
Montague, R.: Universal grammar. Theoria 36(3), 373–398 (1970)
Moortgat, M.: Categorial type logics. In: Handbook of Logic and Language, pp. 93–177. Elsevier (1997)
Moortgat, M.: Symmetric categorial grammar: residuation and Galois connections. CoRR, abs/1008.0170 (2010)
Partee, B., Rooth, M.: Generalized conjunction and type ambiguity. In: Bäuerle, R., Schwarze, C., von Stechow, A. (eds.) Meaning, Use, and Interpretation of Language, pp. 361–383. Gruyter, Berlin (1983)
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Bastenhof, A. (2012). Polarities in Logic and Semantics. In: Aloni, M., Kimmelman, V., Roelofsen, F., Sassoon, G.W., Schulz, K., Westera, M. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science, vol 7218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31482-7_24
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DOI: https://doi.org/10.1007/978-3-642-31482-7_24
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