SynSem_Problems_ScopalNonScopal

Distinguishing Scopal from Non-Scopal Semantic Arguments

Background

We take it as given (for now) that certain predicates have scopal argument positions, i.e. contribute to the articulation of the scope tree. Examples are the sole argument of seem and not and the second argument of deny in the examples below:

• It seems that Kim left.

• The dog did not bark.

• Kim denies that the dog barked.

In calling these argument positions scopal, we believe we are making at least the following claims:

1. Quantifiers may scope in between the predicate and its scopal argument.

   • The dog did not chase every cat.

   • Kim denied that every dog barked.

2. A proposition embedded as a scopal argument is not necessarily (for the purposes of e.g. presupposition calculation) in the same context as the embedding predicate.
   • Kim believes that every dog barked.

Currently, in the English Resource Grammar (and DELPH-IN grammars more generally), we distinguish two types of elements which are adverbial modifiers syntactically and predicates (operators/scopal predicates or non-scopal predicates) semantically, which we call scopal and non-scopal modifiers. The former take the syntactic head they combine with as a scopal argument:

• Kim never left.

While the latter instead are predicated of the event variable of the head they combine with:

• Kim left quickly.

While what we construct in the ERG are meaning representations (and not logical forms), for the subset of expressions which can be handled in some suitable object language, there is meant to be a mapping from each meaning representation produced by the ERG to one or more expressions in that object language. Assuming something like higher-order predicate logic, we imagine that our non-scopal modifiers correspond to ordinary predicates while our scopal modifiers correspond to operators.

Problem Statement

While we feel that some items are fairly clearly in one category (scopal modifiers) or the other, we find it difficult to categorize many other times. Accordingly, we have the following questions:

1. Is this distinction in fact well-defined?
2. If so, what tests can we use to classify particular predicates?
3. If not, what representation should we use? (Underspecification, assimilate all modifiers to one type, other?)

Key Examples

The modifiers for a long time and deliberately seem like good candidates for non-scopal modifiers, but then it is not clear to us what it means for them to modify negated clauses:

• Kim didn't speak for a long time.

• Kim deliberately didn't speak.

Note also close semantic similarity between negation and fail, where we are more comfortable having non-scopal modification of failing events:

• Kim failed to speak for a long time.

• Kim deliberately failed to speak.

We can also pair likely non-scopal modifiers with verbs that seem to be close paraphrases, and which (as verbs) we expect to take verbal projections as clausal arguments:

• Kim successfully barked. / Kim succeeded in barking. [Nominalization might make this one moot.]

• We were happy to discuss scope. / We happily discussed scope.

What about when a (putative) scopal modifier appears to modify only a (putative) non-scopal modifier but not the head?

• Kim probably baked a cake for Sandy. / Kim baked a cake probably for Sandy.

Possible Semantic Tests

• Entailment

Possible Syntactic Correlates

• Syntactic position