grammatical and semantic difference of "嘘と思う" and "嘘だと思う"


Before I move on to the topic, here is my analysis based on my grammar book:

> これを **嬉しい** と思う。
>
> これを **親切だ** と思う。

The bolded part are quotation (引用), and the と behaves as a 格助詞 (quotation
particle).

> これを **嬉しく** 思う。
>
> これを **親切に** 思う。

The bolded part are adverbial phrases.

Following this logic, I conclude that

> これを **嘘だ** と思う。 →quotation (引用)
>
> これを **嘘と** 思う。 →adverbial phrases

Hopefully someone could comment on my analysis, and more importantly, the
difference of their usage. I mean, the situation when the two sentences are
not interchangeable. One Japanese told me that the two sentences have little
difference and can be used interchangeably, but I wonder if there is any
exception.

Feel free to add more/change words to make the sentence sound more natural,
違和感がない. For instance, 「 **それをうそと思う** かはあなた次第だ」

"当然のことと思う"/"当然のことだと思う" is another pair where I have the same question.




This depends on the verb you're using. For many verbs, `AをBとV` and `AをBだとV`
are completely interchangeable. (I may be wrong, but maybe だ tends to be
dropped more often if it's in either highly-casual speech or a highly-stiff
written document.)

  * それを嘘と思う = それを嘘だと思う
  * それを嘘と見なす = それを嘘だと見なす
  * それを嘘と考える = それを嘘だと考える
  * それを嘘と仮定する = それを嘘だと仮定する

But you cannot add だ at least for these verbs:

  * 娘を花子と名付ける (×娘を花子だと名付ける)
  * これをゼータ関数と定義する (×これをゼータ関数だと定義する)
  * 人はそれを愛と呼ぶ (×人はそれを愛だと呼ぶ)

I can't explain well why. Recently @DariusJahandarie introduced me an article
exactly regarding this topic, so I hope it helps you too:

[Tsuyoshi Sawada, _Da_ -Deletion: Classification of Clause-Final Elements in
Japanese](http://www.ic.nanzan-u.ac.jp/LINGUISTICS/publication/pdf/NLSI3_2-8-sawada.pdf),
Nanzan Linguistics: Special Issue 3, Vol. 2, 139-163 (PDF)

Section 8, On The Ambiguity of _To_ , seems to be particularly related. But I
haven't read them all, and note that some examples marked with `*` (incorrect)
actually look okay to me. Particularly, the author says `AをBと思った` is wrong
(see (66)), but I don't think so.

