Parts and Boundaries 1 - the technology of conceptual semantics

The following two sentences are synonymous:

  Bill went into the house.
  Bill entered the house.

This means that they encode the same underlying conceptual structure:

  go(e,bill,t)
  to(t,i)
  in(i,h)
  house(h)

This is equivalent to Jackendoff's notation, where the referential indices are left implicit:

  [GO([BILL],[TO([IN([HOUSE])])])]

The mapping between sentences and concepts is ensured by the following CCG lexicon:

  went :- S1\NP2/PP3 : go(1,2,3)
  entered :- S1\NP2/NP3 : go(1,2,4), to(4,5), in(5,3)
  Bill :- NPbill
  into :- PP1/NP2 : to(1,3), in(3,2)
  the house :- NP1 : house(1)

The conceptual predicates are organised into an ontology:

           entity
         /   / \  \
       /    /   \   \
     /     /     \    \
 thing  place  path  event
   |      |      |     |
   |      |      |     |
 house    in    to     go

This is to be understood as follows:

• Every entity belongs to exactly one of the following four categories: thing, place, path or event.
• Every 'house' is also a 'thing'.
• Every 'in' is also a 'place'.
• Every 'to' is also a 'path'.
• Every 'go' is also an 'event'.

More formally:

• ∀x. thing(x) xor place(x) xor path(x) xor event(x)
• ∀x. house(x) -> thing(x)
• ∀x,y. in(x,y) -> place(x) and thing(y)
• ∀x,y. to(x,y) -> path(x) and place(y)
• ∀x,y,z. go(x,y,z) -> event(x) and thing(y) and path(z)

Note that we do NOT NEED to decompose lexical concepts like 'into' or 'enter':

• ∀x,y. into(x,y) -> ∃z. to(x,z) and in(z,y)
• ∀x,y,z. to(x,y) and in(y,z) -> into(x,z)
• ∀x,y,z. enter(x,y,z) -> ∃w. go(x,y,w) and into(w,z)
• ∀x,y,z,w. go(x,y,z) and into(z,w) -> enter(x,y,w)

In other words, 'into' is a subtype of 'in', and 'enter' is a subtype of 'go'.

The semantic interpretation process takes place as follows:

1. The input sentence S is parsed using the lexicon/grammar, yielding a lexico-syntactic conceptual structure C (or a set of these if S is ambiguous).
2. C is tested for 'consistency' with the ontology.