Compositional Semantics

The general theory in compositional semantics: The meaning of a phrase is determined by combining the meanings of its subphrases, using rules which are driven by the syntactic structure.

Nothing close to a complete compositional semantics for English is known; not least because nothing close to a complete meaning representation is known. (That is to say, we don't know what the output is supposed to be.)

Simple Example: Event sentence

Consider the following sentence and plausible representations of meaning.

Sentence: "John ate a ripe apple."
Syntax tree :

S ---> NP ---> Name ---> John
   |
   |-> VP ---> Verb ---> ate
           |
           |-> NP ---> Det ---> a
                   |
                   |-> Adj ---> ripe
                   |
                   |-> Noun ---> apple

Representation

      Person(p1).
      Name(p1,"John").
      Ripe(o1).
      Apple(o1).
      Event(e1,Eat).
      Actor(e1,p1).
      Object(e1,o1).

Lexicon

"apple" ---> Content: Apple.
"ate". --> Content: Eat.
"John" --> Create symbol S. Assert Person(S) and Name(S,"John"). 
          Denotation = S.

Compositional rules

Rule 1:

Given: NP ---> Name ---> W. 
   Denotation(NP) = Denotation(W).

Rule 2:

Given: NP ---> Det
           |
           |-> Adj
           |
          ...
           |-> Adj
           |
           |-> Noun.

Create a new symbol S. For each Adj/Noun P, assert P.Content(S).
    Denotation(NP) = S.

Rule 3:

Given: S ---> NP1
          |
          |-> VP ---> Verb
                  |
                  |-> NP2

Create a new symbol E. Assert Event(E,Verb.Content). 
    Assert Actor(E,Denotation(NP1))
    Assert Object(E,Denotation(NP2))