Abstract
A variation of the standard non-associative Lambek calculus with the slightly non-standard yet very traditional semantic interpretation turns out to straightforwardly and uniformly express the instances of non-canonical coordination while maintaining phrase structure constituents. Non-canonical coordination looks just as canonical on our analyses. Gapping, typically problematic in Categorial Grammar–based approaches, is analyzed like the ordinary object coordination. Furthermore, the calculus uniformly treats quantification in any position, quantification ambiguity and islands. It lets us give what seems to be the simplest account for both narrow- and wide-scope quantification into coordinated phrases and of narrow- and wide-scope modal auxiliaries in gapping.
The calculus lets us express standard covert movements and anaphoric-like references (analogues of overt movements) in types – as well as describe how the context can block these movements.
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- 1.
A notable exception is quantification, see Sect. 4.
- 2.
We call this rule essentially admissible because it cannot transform \((\mathord \bullet ,\mathord \bullet ) \vdash A\) to \(\mathord \bullet \vdash A\). Therefore, we will have many derivations and sequents that differ only in \((\mathord \bullet ,\mathord \bullet )\) vs. \(\mathord \bullet \). Since they are morally the same, it saves a lot of tedium to treat them as identical, assuming that \((\mathord \bullet ,\mathord \bullet )\) can always be replaced by \(\mathord \bullet \). We will use this assumption throughout.
- 3.
Incidentally, such a mark restricts the use of the structure constants such as \({and}_L\) and especially \({and}_D\) below – in effect restricting gapping to coordination.
References
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Acknowledgments
I am very grateful to Yusuke Kubota for very helpful conversations and many suggestions.
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Kiselyov, O. (2015). Canonical Constituents and Non-canonical Coordination. In: Murata, T., Mineshima, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2014. Lecture Notes in Computer Science(), vol 9067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48119-6_8
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DOI: https://doi.org/10.1007/978-3-662-48119-6_8
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