Wednesday, June 13, 2018

grammar - How to dissect and parse 'to whose extent'?



Source: p 182, WordNet: An Electronic Lexical Database,
by Christiane Fellbaum PhD Linguistics (Princeton)



Graphically, mathematical lattices can be depicted as line diagrams that represent a formal concept by a small circle. [See p 181 of the link for a picture.] For each formal g,
the smallest formal concept   to whose extent g belongs   is denoted by γg, ...



Please correct me if I err, but 'to the extent of which' can be called a 'relative phrase', based on p 186, A Student's Introduction to English Grammar (2005), by Huddleston & Pullum.
My tribulations with it inspired me to Google examples 'to whose extent' for practice.


I know that as a relative determiner, whose  =  of whom  or  [of] which.
The quote concerns only objects (and not persons); so whose  =  of which. Then:

to whose extent  =  to the extent of which.


Then how do you dissect and parse this relative phrase?



Answer




For each formal g, the smallest formal concept    to whose extent g belongs
is denoted by γg



Much more often, I hear/read "X belongs to Y", but in this sentence, to appears before belongs. Also, whose is kind of functioning here as a "possessive that" for lack of a better term.


So this sentence can be rewritten like this:




For each formal g, the smallest formal concept    that its extent g belongs to
is denoted by yg.



So:




  • Each "formal g" is associated with an "extent g" (implied).




  • Extents belong to one or more "formal concepts."





  • The smallest of these "formal concepts" is called yg.




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