I think I will
I think I shall
going to
gonna
Structure
- Verb[( よ ) う ] + と・思う
- 食べ ようと思う
- 飲 もうと思う
- 行 こうと思う
[Verb[(よ)う]と思う - used to declare a decision that has just been. Since it is a direct declaration it is only used for the speaker’s/writer’s intentions]
[Verb[(よ)う]と思っている - describes an intention that has been already held for some time, or to speak about the intentions of others]
冷蔵庫に入っているチーズを誰も食べないから、食べようともう。
No one is eating the cheese in the the refrigerator, so I think I will eat it.
Why isn’t 食べない in the progressive form? 「食べていない」, as the English translation would indicate?
@deltacat3 This sentence can be interpreted as “no one will eat the cheese” or “no one is eating the cheese (because it is just sitting there, not being eaten).” That being said, I think that the translation could use some work to prevent any further confusion. Cheers!
Is this structure used informally only (like the volitional form alone), or can it be used in a formal context as well?
Hey and welcome to the community forums! 
ようと思う can be used in formal and casual circumstances. So you can use it when talking to your superior at work, or to someone you don’t know.
Remember about polite ます though 
Also, when you want to talk about plans of 3rd person, you should use ようと思っている(ようと思っています) rather than ようと思う.
I hope it helps,
Cheers!
