Parts and Boundaries 2 - The puzzle and a preliminary solution

Consider the following sentence:

  The light flashed until dawn.

This sentence expresses repetition, despite the fact that neither of its component parts does - 'the light flashed' and 'until dawn'. Where does the sense of repetition come from, and why is it necessary here?

Here is a rough form of the explanation:

1. The sentence 'the light flashed' denotes a BOUNDED event.
2. The PP 'until dawn' combines with an UNBOUNDED event to form a BOUNDED event.
3. The lexico-syntactic conceptual structure of 'the light flashed until dawn' is thus INCONSISTENT with the ontology.
4. The inconsistent conceptual structure can be made consistent by COERCING the bounded event E denoted by 'the light flashed' into an UNBOUNDED event consisting of a plurality of events of the same type as E.

Here is the corresponding lexicon:

  the light flashed :- S1 : lightflash(1)
  until dawn :- S1\S2 : untildawn(1,2)

This lexicon is used to derive the following lexico-syntactic conceptual structure for the sentence 'the light flashed until dawn':

 untildawn(e,f), lightflash(f)

And here is the corresponding ontology:

               event
              /     \
            /         \
         bounded     plural
         /     \   
        /       \  
  lightflash  untildawn 

More formally:

• ∀x. lightflash(x) -> bounded(x)
• ∀x,y. untildawn(x,y) -> bounded(x) and ~bounded(y)
• ∀x,y. plural(x,y) -> ~bounded(x) and bounded(y)

It is clear that using the lexico-syntactic coceptual structure of 'the light flashed until dawn' and this ontology, we can derive the following contradiction:

  bounded(f) and ~bounded(f)

The interpretation is rescued by applying the following COERCION RULE to the interpretation of sentence 'the light flashed':

  Sx => Sy : plural(y,x)

This yields the following COERCED conceptual structure for the whole sentence, which is consistent with the ontology:

  untildawn(e,f)
  plural(f,g)
  lightflash(g)

This is not a million miles away from Jackendoff's own notation:

 [UNTIL([PLURAL([LIGHT FLASHED])],[DAWN])]

Note that there are two alternatives that do not require such post-derivational coercion:

1. Treat 'the light flashed' as lexico-syntactically ambiguous, i.e.
   1. S₁ : lightflash(1)
   2. S₁ : plural(1,2), lightflash(2)
2. Treat 'until dawn' as lexico-syntactically ambiguous, i.e.
   1. S₁/S₂ : untildawn(1,2)
   2. S₁/S₂ : untildawn(1,3), plural(3,2)

In both these cases, the lexico-syntactic conceptual structure will be consistent with the ontology.