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Are there connections/translation or common tools usage/adaptation between combinatory (concrete) categorial grammars (incl. Lambek calculus) and abstract categorial grammars? Can tools for one of them be used as tools for the other? Is the analysis for the same sentence available in both of these grammars for comparison?

The answer to this question can lead to understanding how (and if) Grammatical Framwork and CCG parsers be used together or in place of one another, see question https://cs.stackexchange.com/questions/85623/semantic-parsing-with-grammatical-framework-is-this-possible and answer https://groups.google.com/forum/#!topic/gf-dev/otGvS6dIAdM

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    You can’t compare them directly. Of course the common ground is categorical grammar but it comes in many flavors which makes a comparison pointless.
    – Atamiri
    Commented Jan 17, 2018 at 14:02

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