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In the sentence:

A man loves Mary

The lambda notation of the determiner 'a' is:

λY.λX.∃z.Y(z)∧X(z)

What about the general determiner 'a'? Is the lambda notation the same? or it should be:

λX.∃z.X(z)

and why?

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Perhaps "a" is an ambiguous reduced form derived from either (any) or (some). Thus "A man loves Mary" could be from either "Any man loves Mary" or "Some man loves Mary". Note the ambiguity of "Mary doesn't love a man".

I don't see lambda notation as being germane to the relationship between (some) and (any). If there are two senses, we'd obviously need two lambda representations.

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