"subject to" vs. "subject of" - which expression should be used and when? [closed]

I am not an English native speaker so please excuse me if the following is a dumb question.

If you want to express that something belongs to something it is commonly a good way to use the word subject, but do you say (for instance):

• This procedure is subject to the syntactical analysis
  or

• This procedure is subject of the syntactical analysis.

• She is the subject to someone else's lust.
  or

• She is the subject of someone else's lust.
  

So which expression should I use and when should I use it? Are there some rules or some specific properties that determine this?

"Subject" here means two different things, and comes into English by two different paths. "Subject to" comes from the general sense of subjection, that is to say the overlordship of one over another. Much as people who were under the rulership of a king were called his subjects. This usage is attested very early in the English language.

"Subject" in the sense of the underlying meaning of a thing (the subject or an email or conversation for example) is really a shortened form of "subject matter" and is related to the grammatical term "subject" meaning, roughly speaking, the doer of the (active) verb.

So they came into English in by slightly different routes, even though they have largely the same derivation. In both cases they convey the sense of something that lies underneath. In the first case "subject to" it is underneath in the sense of domination, in the later "subject of" it is underneath in the sense of underlying meaning, or underlying subject matter.

So whether to use "of" or "to" depends entirely on if you are intending domination or subject matter.

In the particular examples you have:

This procedure is subject to syntactic analysis.

Here the procedure is ruled by syntactic analysis, which is to say, if syntactic analysis is applied, there is an obligation to accept it.

This procedure is subject of syntactic analysis.

This sentence is actually syntactically incorrect. "Subject" needs a determiner to be correct here. "this procedure is a subject of syntactic analysis" for example. This indicates that one of the underlying meanings, or one of the subject matters of syntactic analysis is this particular procedure.

See Etymology Online for more on this matter.

The idiom subject to describes subjugation of the original idea. For example,

The document is subject to changes made within the writer's mindset.

Here, the document is "subject to" or "has no way of avoiding" the changes made.

Subject of is not an idiom, as it does not have any special meaning. It is just an example of how the word "of" is often used. For example,

Geometry is a subject of our curriculum.

Here, subject is only being modified by the prepositional phrase "of our curriculum", which shows how "subject of" functions as not one unit, but rather two separate words.

So saying "this procedure is subject to the syntactical analysis" implies that the procedure must abide by the rules laid out by syntactical analysis, while saying "this procedure is [a] subject of the syntactical analysis" is just saying that the procedure is a subset of syntactical analysis.