What is the proper term for a scope-resolved MRS without unbound variables?

In section 4.1 of the MRS paper it says:

Definition 4 (Scope-resolved MRS structure) A scope-resolved MRS structure is an MRS structure that satisfies the following conditions:

  1. The MRS structure forms a tree of EP conjunctions, where dominance is determined by the outscopes ordering on EP conjunctions (i.e., a connected graph, with a single root that dominates every other node, and no nodes having more than one parent).
  2. The top handle and all handle arguments (holes) are identified with an EP label.
  3. All constraints are satisfied. With respect to outscopes constraints, for instance, if there is a constraint in C which specifies that E outscopes E′ then the outscopes order between the EP conjunctions in R must be such that E outscopes E′.7

So, scope-resolved means all the holes are filled and no qeq’s are violated. But you can still have logical variables that are unbound as I learned here.

Definition 5 tantalizingly talks about the issue without giving a term for it that I can find:

Definition 5 (Well-formed MRS structure) A well-formed MRS structure is an MRS structure that link-subsumes one or more scope-resolved MRSs.
…Thus a scope-resolved MRS without unbound variables will correspond to a closed sentence (a statement) in predicate calculus.

So, what is the proper term for a scope-resolved MRS without unbound variables?

It is more than “well-formed” because it is “scope-resolved”
It is more than “scope-resolved” because it has all the scopes set up such that there are no unbound variables.
Therefore it is…what?

I can’t recall a discussion specifically for MRS, but I think the standard terms in logic are “closed” (no free variables) and “open” (at least one free variable):

That’s the term the paper used too for the “bound vs. unbound” part. So I guess I could call this a “Scope-Resolved Closed” tree? Kind of a mouthful. An “SRC”? Since it appears that this isn’t a form that is really used in the ERG context, I might just call it a “solved” tree.

Just trying to use the proper terms as I write up what I’m working on. Thanks @guyemerson

As far as I understood. An MRS is not well-formed if it contains a free variable (x, e, i…), not initialized by a quantifier. In a sense, all scope-resolved MRSs could be potentially transformed into a logical ‘sentence’ (or closed formula, following the terminology from the link that @guyemerson shared above) in some logical language… The only possible free variables before the scoped-resolved construction are the h (holes) variables.

@arademaker it turns out you can have:

  • a well-formed MRS
  • that you have scope-resolved into a tree properly following the HCONS constraints

but the well-formed, scope-resolved tree still has free variables because the quantifiers aren’t being initialized in the right place.

I was surprised that the HCONS didn’t enforce this but I found that out the hard way. It is one more thing you have to check to build a [trying out my new term] “solved” tree.

This is why I’m trying to find a term for this form…Hard to discuss otherwise.

HCONS are just one kind of constraint. Definition 4 says “all constraints are satisfied”, and this would include the “variable binding conditions” discussed at the bottom of page 9. If that’s what you’re getting at, I would just use the term “scope-resolved”.

I think it would only be necessary to distinguish “open scope-resolved” and “closed scope-resolved” MRSs if you want to resolve scope for partial MRSs, such as where a quantifier is missing. For example, considering a ditransitive verb phrase, the subject is missing but maybe you still want to resolve the scope of the two objects.

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