My understanding is that the LTOP, or local top, is a pointer to the top handle of a local subgraph as an MRS is be assembled during the analysis of an input (e.g., sentence). The GTOP, or global top, points to the top handle of a completely analyzed input. In many grammars, the GTOP is not precisely the top label, but rather a handle QEQ to the top label (in other words, the GTOP is QEQ to the highest LTOP).
The MRS introduction paper says as much in section 4.3:
In order to state the rules of combination involving handles, we will
assume that MRSs have an extra attribute, the local top, or ltop, which will
be the topmost label in an MRS which is not the label of a floating ep (i.e.,
not the label of a quantifier). For instance, in (25), the ltop is the label
corresponding to the ep for probably, h5. In an MRS corresponding to a
complete utterance, the top handle will be qeq to the local top. We will
assume that when an MRS is composed, the top handle for each phrase in
the composition is the same: that is, the top handle we introduced in §4.1
is a ‘global’ top handle gtop, in contrast to the local top for the phrase,
which is the label of the topmost ep in that phrase which is not a floating
ep. For phrases that only contain floating eps, the ltop is not bound to any
label. So the revised MRS structure is a tuple 〈GT , LT , R, C〉, where LT is
the local top. As before, GT is the global top handle and R and C are the
ep bag and handle constraints. For convenience, in the representations in
this section, we will consistently use h0 for the global top.
So as you are building an MRS, you working with the LTOP. When you are done, you cap it off with a new handle QEQ to that LTOP. In the past we may have been imprecise with our use of the terminology, such as calling everything LTOP.
In the SimpleMRS format, the top handle was called
LTOP, so we decided to start calling it
TOP and PyDelphin implemented that change, as
TOP can be seen as ambiguous between
LTOP (for partial MRSs being assembled) and
GTOP (for complete representations). You should be able to tell the difference by seeing if the value of
TOP is the value of any scopal argument or
RSTR. If not, this handle (conventionally
h0) is the global top. I don’t think all processors made a similar change to
TOP, so you’ll still see
LTOP coming up. You can see some discussion we had about it in this thread from the old developers list. I couldn’t turn up much more than this, so those discussions may have happened in-person or over email.