Abstract
The formulation of Combinatory Categorial Grammar (CCG) [7], especially the choice of combinatory rules and their nominatum, strongly imply connection with a typed-version of Combinatory Logic (CL). Since typed CL is a term calculus for an implication fragment of a Hilbert-style proof system, in the sense of the Curry-Howard isomorphism, it seems plausible to regard CCG as a grammar that corresponds to a Hilbert-style proof system, in that the associative Lambek calculus [3] corresponds to a Gentzen-style proof system.
We are grateful to Nicholas Asher, Frank Veltman, Alastair Butler, Shunsuke Yatabe and other audience of LENLS8 for their valuable comments and suggestions for the earlier version of this paper. We are also grateful to Kei Yura in Joint Research Symposium 2011.
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Ozaki, H., Bekki, D. (2012). Extractability as the Deduction Theorem in Subdirectional Combinatory Logic. In: Béchet, D., Dikovsky, A. (eds) Logical Aspects of Computational Linguistics. LACL 2012. Lecture Notes in Computer Science, vol 7351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31262-5_13
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DOI: https://doi.org/10.1007/978-3-642-31262-5_13
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