Hello,
> (...) I am a bit surprised by the fact that the rule S -> VP is correct.
> Could you provide some intuition as to why that is the case?
This type of rule is typically useful to cover sentences with verbs in imperative mode such as: "Come!" or "Take your coat!", where the conjugated verb does not require any explicit subject.
> (...) Why is the statement "Dependency grammars describe
> functional dependencies between words in a sequence" correct?
> In particular, in the slides we saw that Dependency Grammars
> "focus on words and their relations (not necessarily in sequence)"
While constituency grammars typically focus on word order (as described by sequences of constituents), dependency grammars focus on syntactic relations between words.
For example, a context-free rule such as:
NP --> Det N
expresses the fact that a nominal phrase can consist of a noun preceded by a determiner (without explicitly saying anything about the nature of syntactic relation between the determiner and the noun), a dependency structure such as:
cat --> sleeps
in the sentence "the cat sleeps on the chair"
expresses the fact that there is a syntactic relation (a subject-verb relation in this specific case) between the word "cat" and the word "sleeps" (without explictly saying anything about the order in which the words should occur).
Best,
Martin.